Research ArticleMultihop Capability Analysis in Wireless Information andPower Transfer Multirelay Cooperative Networks
Qilin Wu 12 Xianzhong Zhou1 Qian Cao 2 and Huan Fang 3
1School of Management and Engineering Nanjing University Nanjing 210093 China2Institute of Networks and Distributed System Chaohu University Hefei 238000 China3School of Mathematics and Big Data Anhui University of Science and Technology Huainan 232001 China
Correspondence should be addressed to Qian Cao caoqianchueducn
Received 4 October 2017 Accepted 11 December 2017 Published 17 January 2018
Academic Editor Nathalie Mitton
Copyright copy 2018 QilinWu et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
We study simultaneous wireless information and power transfer (SWIPT) in multihop wireless cooperative networks where themultihop capability that denotes the largest number of transmission hops is investigated By utilizing the broadcast nature ofmultihop wireless networks we first propose a cooperative forwarding power (CFP) scheme In CFP scheme the multiple relaysand receiver have distinctly different tasks Specifically multiple relays close to the transmitter harvest power from the transmitterfirst and then cooperatively forward the power (not the information) towards the receiver The receiver receives the information(not the power) from the transmitter first and then it harvests the power from the relays and is taken as the transmitter of the nexthop Furthermore for performance comparison we suggest two schemes cooperative forwarding information and power (CFIP)and direct receiving information and power (DFIP) Also we construct an analysis model to investigate the multihop capabilitiesof CFP CFIP and DFIP schemes under the given targeted throughput requirement Finally simulation results validate the analysismodel and show that the multihop capability of CFP is better than CFIP and DFIP and for improving the multihop capabilities itis best effective to increase the average number of relay nodes in cooperative set
1 Introduction
Among several wireless energy harvesting techniques simul-taneous wireless information and power transfer (SWIPT)has drawn great attention [1ndash3] SWIPT was first proposed in[1 2] where the transmitter sends one wireless signal and thereceiver harvests energy and decodes information from thesignal at the same timeOwing to practical constraint SWIPTcannot be performed on one circuit Therefore two practicalarchitectures called time switching and power splitting havebeen proposed by permitting the receiver to have two circuitsto carry out energy harvesting and information decodingseparately [3]
On the other hand cooperative communication has beenshown to be a promising method to mitigate the wire-less channel impairments by applying either amplify-and-forward (AF) or decode-and-forward (DF) relaying protocol[4] in relay nodes However a relay node needs to expend
its energy for accomplishing the information forwardingwhich can make the relay node reluctant to participate in thecooperation Fortunately by using energy harvesting node asrelay the cooperative excitement of relay node can be ignitedand the network performance can be significantly improved
The performance of SWIPT in cooperative relay networkshas been analyzed in various studies (see Section 2) butthese studies assume that they have at most two hops fromsource to destination with the signal forwarding by relaysFor multihop (more than two hops) networks because theenergy harvesting efficiency cannot reach 100 (the rangeof 10ndash80 is normal) [5] the difficulty is how to trans-mit energy and information simultaneously from source todestination that is solving the SWIPT issue in the multihopcase To solve this problem we consider using cooperativemultiple relays by fully utilizing the broadcast nature ofmultihop wireless networks Unlike previous studies Chenet al [6] considered multihop scenarios and identified the
HindawiWireless Communications and Mobile ComputingVolume 2018 Article ID 1857015 12 pageshttpsdoiorg10115520181857015
2 Wireless Communications and Mobile Computing
largest number of transmission hops However the work in[6] did not consider multiple cooperative relays and failedto provide insights into the impact factors that affected thelargest number of transmission hops
Although the use of cooperative relays can reduce theloss of energy it is not guaranteed that the information istransmitted to the destination with enough power Thenwhat is the largest number of transmission hops underthe given targeted throughput requirement This problemis closely related to the initial energy of source node thenumber of relay nodes communication distance and otherparameters which sparks our research motivation In thispaper we first propose a cooperative forwarding power (CFP)scheme and then for performance comparison we suggesttwo schemes cooperative forwarding information and power(CFIP) and direct receiving information and power (DFIP)Furthermore we construct analysis model to investigate themultihop capabilities of CFP CFIP and DFIP schemes underthe given targeted throughput requirement from applicationlayer Finally simulation results validate the analysis modeland show that the multihop capability of CFP is better thanCFIP and DFIP and for improving the multihop capabilitiesit is best effective to increase the average number of relaynodes in a cooperative set Therefore through our study inthis paper the appropriate values of related parameters canbe set to achieve the given transmission hops from source todestination
The remainder of this paper is organized as follows Firstthe related works are described in Section 2 Next systemmodels and network scenario are given in Section 3 and inSection 4 we present CFP CFIP and DFIP schemes After-wards Section 5 presents analytical models for evaluatingthe performance of the three schemes and simulation resultsare given to validate the analytical model and obtain someimportant insights in Section 6 Finally conclusions are givenin Section 7
2 Related Works
According to the difference in information transmissionways communication systems adopted by existing literaturecan be categorized into point-to-point SWIPT systems andcooperative relay SWIPT systems In the following wepresent an overview of existing literature in the above twoSWIPT systems
(A) Point-to-Point SWIPT Systems After the pioneeringworks of Varshney [1] and Grover and Sahai [2] the perfor-mance of practical SWIPT systems is investigated in severalstudies Zhang and Ho [3] considered two scenarios wherethe information receiver and energy receiver are separated orcolocatedMore importantly thework in [3] used rate-energyregion to characterize the tradeoff between information rateand energy transfer and proposed two practical receiverdesigns namely time switching and power splitting forcolocated receivers Later in [7ndash9] sophisticated architecturesfor improving the rate-energy region were further proposedMoreover multiuser scheduling in SWIPT system was stud-ied for achieving the maximum sum throughput in [10]
and tradeoff between the average per user harvested energyand ergodic achievable rate in [11] Unlike the above worksZhong et al [12] considered a novel network architecturewhere the source is powered by a dedicated power beacon(PB) and gave the average throughput analysis for two dif-ferent transmission modes namely delay tolerant and delayintolerant Recently for reutilizing interferences to avoid agreat waste of energy Zhao et al [13 14] proposed a novelSWIPT scheme based on opportunistic communicationsin interference alignment (IA) networks and analyzed theperformance of SWIPT in IA networks respectively
(B) Cooperative Relay SWIPT Systems Considering thatthere is no direct point-to-point link between the sourceand destination it is necessary to make use of relay forforwarding information to destination where the relay nodeis energy-constrained and needs to harvest energy fromthe source Nasir et al [15] proposed time switching-basedrelaying (TSR) and power splitting-based relaying (PSR)protocols and derived the throughput for both TSR and PSRunder delay-limited and delay-tolerant transmission modesAfterwards Do [16] considered that both relay and destina-tion are mobile node and analyzed the optimal throughputperformance for the proposed time power switching-basedrelaying (TPSR) protocol Unlike the previous studies Zhangand Chen [17] considered that the relay can harvest energyfrom source destination or joint source and destinationand investigated the maximal throughputs of three wirelesspower transfer (WPT) schemes respectively Furthermoreto overcome the loss of spectral efficiency induced by one-way relaying and half-duplex relaying two-way relaying [18ndash20] and full-duplex relaying [21ndash23] were introduced intoSWIPT system respectively Instead of considering one relay-assisted SWIPT cooperative system in the aforementionedworks the works of [24ndash26] investigated multirelay-assistedcase and analyzed the outage probability and end-to-endrate respectively Unlike the existing prominent works weinvestigate SWIPT in a multihop scenario and analyzethe multihop capability of SWIPT system with multirelay-assisted cooperative transmission
3 System Model
We consider a network scenario shown in Figure 1 wherethe source node (119878) wants to transmit data packets to thedestination node (119863) We assume that a path 119877119878 1199011 1199012 119901119894 119901119896 119863 has been selected by virtue of a routingalgorithm and all nodes are equipped with a single omni-directional antenna and work in half-duplex mode Forcooperative transmission we also assume that each node ina routing path 119877 is surrounded by a number of relays Inaddition for facilitating the analysis we suggest the relay andchannel models as follows
(A) Relay Model We assume that 119878 is considered as anenergy-unconstrained nodewith amaximum transmit power119875119904 while other relay nodes are energy-constrained andhave not energy to complete the forwarding operation butthey can harvest energy from the received signal by power
Wireless Communications and Mobile Computing 3
RoutingRelay node
S p1 pi pi+1 pk D
Figure 1 Network scenario
splitting More specifically each relay 119894 splits a portion of thereceived signal energy 120572119894 for information decoding and theremaining part 1 minus 120572119894 for energy harvesting Since the pro-cessing power consumed by the receive circuitry at the relaynodes is assumed to be negligible as compared to the powerused for signal forwarding [15] we assume that all nodes havethe energy to receive signal In this paper all relays form acooperative set and simultaneously forward the signals to thereceiver by using distributed space-time codes (DSTC) [27]
(B) Channel Model We assume that the additive white Gaus-sian noises (AWGN) at all nodes are independent circularsymmetric complex Gaussian random variables with zeromean and unit variance The channel fading is modeled bylarge-scale path loss and statistically independent small-scaleRayleigh fading It is also assumed that the fading channelgains are assumed to be constant during one block time 119879119905Vin which the information is transmitted from the transmitterto receiver and independent and identical distribution (iid)is used from one transmission to the next Also we assumethat perfect channel state information (CSI) is available at thereceiver side through channel estimation and ℎ119894119895 denotes thechannel gain between node 119894 and node 119895 which are circularsymmetric complex Gaussian random variables with zeromean and unit variance [5 15 18]
4 Proposed Scheme
To investigate the multihop capability in SWIPT multihopcooperative networks we give the following three transmis-sion schemes We first propose cooperative forwarding power(CFP) scheme In CFP scheme the relays and receiver havedistinctly different tasks Specifically multiple relays close tothe transmitter harvest power from the transmitter first andthen cooperatively forward the power (not the information)towards the receiver The receiver receives the information(not the power) from the transmitter first and then it harveststhe power from the relays and is taken as the transmitter ofthe next hop Furthermore we use the following two schemesas comparison
(A) Cooperative Forwarding Information and Power (CFIP)Scheme In this scheme it is assumed that there is no directlink between the transmitter and receiver of a path (thisassumption is adopted by most of the previous studies [5 15ndash26]) such as 119901119894 and 119901119894+1 in Figure 1 Multiple relays harvest
power and decode the information from the transmitter firstand then cooperatively forward the information and powerto the receiver Then the receiver harvests the power anddecodes the information from the relays and is taken as thetransmitter of the next hop to transmit the information andpower Note that at present CFIP is often used in at mosttwo-hop scenarios by most of the previous works to analyzesystem performance So we extend this scheme to multihopscenario for comparing and analyzing themultihop capabilityin SWIPT cooperative networks
(B) Direct Receiving Information and Power (DFIP) SchemeThis scheme does not consider cooperative transmissionwhich means that the receiver harvests power and decodesthe information from the transmitter directly (this assump-tion is adopted by most of the previous studies [3 7ndash14])Then the receiver is taken as the transmitter of the nexthop to transmit the information and power The purpose ofproposing this scheme is to investigate whether cooperativetransmission can bringmore performance improvement thandirect transmission in SWIPT networks
It should be pointed out that our schemes are indepen-dent of the specific routing protocol and only require anexisting path from source to destination In fact the analysisresults of multihop capability can be used to design a newrouting protocol in SWIPT networks Also our schemes areindifferent to the specific method of relay selection becausethe analysis results of multihop capability are related to thenumber of relays instead of which node becomes a relay
5 Analytical Model
51 For CFP Scheme In CFP scheme one transmission isdivided into two phases In the first phase the transmitter(source or 119901119894) transmits the signal to the receiver (119901119894 ordestination) and thus the relays overhear the signal andharvest the power from the signal and at the same timethe receiver decodes the information from the signal In thesecond phase the relays form a cooperative set according tothe DSTC to forward the harvested power by transmittingthe special signal to the receiver cooperatively and then thereceiver harvests the power from the special signal and istaken as the transmitter in the next hop with the harvestedpower Note here that the special signal is different fromthe signal from the transmitter to receiver and does notinclude the useful information that needs to be decoded by
4 Wireless Communications and Mobile Computing
the receiver Therefore for the special signal we let the relaystransmit a PTS (power ready to send) frame cooperativelyin which the frame format is extended to the RTS and CTScontrol frames in IEEE 80211 protocol [28]
First of all let us consider that the signal is transmittedfrom the source to receiver node1199011 in Figure 1 Let 119910119903119894 denotethe received signal at relay 119894 around the source node in the firstphase we can derive
where ℎ119904119894 is the source to relay 119894 channel gain 119889119904119894 is thedistance from 119878 to relay 119894 119898 is the path loss exponent 119899119903119894is the additive white Gaussian noise at relay 119894 with zero meanand 1205902119899119903 variance and 119909119904 is the normalized information signalfrom the source Because the relays do not decode the signalfrom the transmitter to receiver we can let 120572119894 = 0 Accordingto (1) the harvested energy 119864119903119894 at relay 119894 during energyharvesting time 119879119905V is given by
where 120578 is the energy harvesting efficiency coefficient and119879119905Vis the transmission time for the signal Note that we do notconsider multirate network scenarios which means that 119879119905Vis equal for any one hop in the routing path In (2) we ignorethe impact of noise since the noise power is normally verysmall and below the sensitivity of the energy receiver [29]
In the second phase each relay 119894 uses the transmissionpower 119875119903119894 = 119864119903119894119879119888V and forms a cooperative set with otherrelays to transmit the PTS frame towards the receiver 1199011simultaneously Consequently 1199011 does not decode the PTSframe but only harvests the energy that can be expressed by1198641199011 as
where ℎ1198941199011 is channel gain from the relay 119894 to receiver 1199011 119879119888Vis the transmission time for the PTS119873119903 is the average numberof relay nodes in cooperative set and 1198891198941199011 is the distance fromthe relay 119894 to receiver 1199011 So we can derive the transmissionpower 1198751199011 from 1199011 to receiver node 1199012 in the second hop asfollows
According to the abovementioned analysis let 119875119901119895minus1denote 119895th (119895 ge 2) hop transmission power where the signalis transmitted from 119901119895minus1 to 119901119895 node (1199010 is the source node)we can obtain
where |ℎ119901119896minus2119894| |ℎ119894119901119896minus1 | denote the channel gains from 119901119896minus2to its relay 119894 and from its relay 119894 to 119901119896minus1 respectively and119889119898119901119896minus2 119894 119889119898119894119901119896minus1 denote the distance from 119901119896minus2 to its relay 119894 andfrom its relay 119894 to 119901119896minus1 respectively So we can obtain thesignal-to-noise ratio (SNR) 120574119895 at the receiver node 119901119895 asfollows 120574119895 = 119875119901119895minus1|ℎ119901119895minus1 119901119895 |2(1205902119901119895minus1 119901119895119889119898119901119895minus1119901119895) where 1205902119901119895minus1119901119895denotes the variance of additive white Gaussian noise atreceiver 119901119895 Given a targeted throughput 1198770 if we find themaximum value of 119897 for that log2(1 + 120574119897) ge 1198770 holds wecan derive that the value of 119897 is the largest number of hopssupported by the CFP scheme Therefore we can derive
In formula (6) for calculability we replace the exponentialrandom variables |ℎ119901119896minus2119894|2 |ℎ119894119901119896minus1 |2 and |ℎ119901119897minus1119901119897 |2with theirmean values 120582119903 120582119891 and 120582119889 respectively Since we haveassumed that the channel gain is circular symmetric complexGaussian randomvariables with zeromean and unit variancewe get 120582119903 = 120582119891 = 120582119889 = 1 Furthermore we assume that119889119901119896minus2 119894119889119894119901119896minus1 is constant and equal to 119889119888 Also 119889119901119897minus1119901119897 whichis the distance from 119901119897minus1 to 119901119897 is set to be constant value 119889119889Consequently we can obtain
(119897 minus 1) log2 (1205782119873119903119889119898119888 ) ge log2 (21198770 minus 1119875119904 119889119898119889 1205902) (7)
where we let 1205902119901119897minus1119901119897 be equal to constant value 1205902 In formula(7) if (21198770minus1)119889119898119889 1205902 gt 119875119904 that is log2(119875119904(119889119898119889 1205902)+1) lt 1198770 thesignal cannot be transmitted from the source node to the nexthop for satisfying the targeted throughput 1198770 Therefore formultihop transmission it is required that (21198770 minus1)119889119898119889 1205902 lt 119875119904Furthermore we consider that in a routing path (such asin Figure 1) the transmission power of node 119901119894+1 is lowerthan that of node 119901119894 because the transmission power of node119901119894+1 is charged from the node 119901119894 So it is also required that1205782(119873119903119889119898119888 ) lt 1 Note that we do not consider the caseof 1205782(119873119903119889119898119888 ) ge 1 because in this case the transmissionpower of node 119901119894+1 is greater than that of node 119901119894 so that theinformation can be transmitted all the time Accordingly wecan derive the largest number of hops 119871cfpmax supported by theCFP scheme as follows
where lfloorrfloor denotes the round down function From formula(8) we can find that the largest number of hops is affected bythe parameters 119875119904 120578 120572119873119903 and 119889119888 In simulation we will givethe detailed analysis for these parameters
Wireless Communications and Mobile Computing 5
52 For CFIP Scheme Unlike CFP scheme in CFIP schemea relay 119894 not only harvests the power but also decodes theinformation from the transmitter So we have 120572119894 = 0 Ifwe consider that the transmitter is the source node a relay119894 harvests the power 1198641015840119903119894 as follows
1198641015840119903119894 = 120578 (1 minus 120572) 119875119904 1003816100381610038161003816ℎ11990411989410038161003816100381610038162 119879119905V119889119898119904119894 (9)
Note here that for ease of analysis we let 120572119894 be constant andequal to 120572 Let 1198751015840119901119895minus1 denote jth (119895 ge 2) hop transmissionpower where the signal is transmitted from 119901119895minus1 to 119901119895through multiple relays we can obtain
1198751015840119901119895minus1 = (120578 (1 minus 120572))2(119895minus1) 119875119904times 119895prod119896=2
where1198731015840119903 is the average number of relay nodes in cooperativeset Note that because only the relay which can decodethe information successfully becomes one member of thecooperative set in CFIP scheme we have 1198731015840119903 le 119873119903 Let 1205741015840119895denote SNR at the receiver node 119901119895 we can derive
1205741015840119895 = 120578 (1 minus 120572) 1198731015840119903sum119894=1
where 1205902119894119901119895 is the variance of additive white Gaussian noiseat receiver 119901119895 Similarly to the above analysis for CFP whilerequiring log2(1 + 1205741015840119897 ) ge 1198770 we can obtain
(119897 minus 1) log2 ((120578 (1 minus 120572))2 1198731015840119903119889119898119888 )ge log2((21198770 minus 1) 119889119898119888 1205902120578 (1 minus 120572)1198731015840119903119875119904 )
(12)
where we let 1205902119894119901119895 be equal to constant value 1205902 In formula(12) we have (120578(1minus120572))2(1198731015840119903119889119898119888 ) lt 1 because the transmissionpower of node119901119894+1 is lower than that of node119901119894 Furthermorefor multihop transmission we have (21198770 minus 1)119889119898119888 1205902120578(1 minus120572)1198731015840119903119875119904 lt 1 that is log2(120578(1 minus 120572)1198751199041198731015840119903119889119898119888 1205902 + 1) gt 1198770Otherwise the information cannot be transmitted from thesource to 1199011 Consequently the largest number of hops 119871cfipmaxsupported by the CFIP scheme can be given as follows
119871cfipmax = 1 + lfloor log2 ((21198770 minus 1) 119889119898119888 1205902120578 (1 minus 120572)1198731015840119903119875119904)log2 (1205782 (1 minus 120572)2 (1198731015840119903119889119898119888 )) rfloor (13)
53 For DFIP Scheme Unlike CFP and CFIP schemes inDFIP scheme the receiver harvests the power and decodesthe information from the transmitter directly without relaycooperation Therefore if we consider that the transmitter is
the source node the receiver 1199011 harvests the power 1198641198891 asfollows
1198641198891 = 120578 (1 minus 120572) 119875119904 1003816100381610038161003816ℎ119904110038161003816100381610038162 119879119905V1198891198981199041 (14)
where ℎ1199041 is channel gain from the source node to receiver1199011 and 1198891199041 is the distance from the source to 1199011 Then thenode 1199011 transmits the information to the next hop node 1199012using the power 1198751198891 = 1198641198891119879119905V Let 119875119889119895minus1 denote 119895th (119895 ge 2)hop transmission power where the signal is transmitted from119901119895minus1 to 119901119895 we can obtain
119875119889119895minus1 = (120578 (1 minus 120572))(119895minus1) 119875119904 119895prod119896=2
So we can obtain SNR 120574119889119895 at receiver 119901119895 as 120574119889119895 =119875119889119895minus1|ℎ119901119895minus1 119901119895 |2(1205902119901119895minus1 119901119895119889119898119901119895minus1 119901119895) Similarly to the above analy-sis for CFP and CFIP while requiring log2(1 + 120574119889119897 ) ge 1198770 wecan obtain
(119897 minus 1) log2 (120578 (1 minus 120572)119889119898119889
) ge log2 (21198770 minus 1119875119904 119889119898119889 1205902) (16)
Accordingly we can derive the largest number of hops 119871dfipmaxsupported by the DFIP scheme as follows
119871dfipmax = 1 + lfloor log2 (((21198770 minus 1) 119875119904) 119889119898119889 1205902)log2 (120578 (1 minus 120572) 119889119898119889 ) rfloor (17)
In formula (17) we have 120578(1 minus 120572)119889119898119889 lt 1 because thetransmission power of node 119901119894+1 is lower than that of node 119901119894Formultihop transmission it is required that (21198770 minus1)119889119898119889 1205902 lt119875119904 Otherwise the information cannot be transmitted fromthe source to 11990116 Numerical Results and Analysis
In this section we perform computer simulations to validateour theory analysis and gain insights into the multihopcapabilities of the proposed CFP CFIP and DFIP schemesAlso we need to observe whether the values of 119871cfpmax schemeare larger than the values of 119871cfipmax and 119871dfipmax with the giventargeted throughput 1198770 under the effect of different networkparameters In the following simulations we set 1205902 = minus70 dB1198770 = 2 bitssecHz and 119898 = 27 (which corresponds to anurban cellular network environment [5]) and give the numer-ical results considering the effect of parameters 119875119904 120578 120572 119873119903and 119889119888 For simplicity we assume that 119889119889 = 119889119888 and1198731015840119903 = 119873119903
First we observe the numerical results about the valuesof 119871cfpmax 119871cfipmax and 119871dfipmax affected by the values of cooperativetransmission distance (CTD) 119889119888 that denotes the productof two distances from sender to relay and from relay toreceiver which are shown in Figure 2 From Figure 2 wecan find that the analytical results are practically consistentwith the simulation results which verifies the effectiveness ofour theory analytical model Note that for CFIP scheme the
6 Wireless Communications and Mobile Computing
3 4 5 6 7 8 9 102dc (m)
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
2468
1012141618202224262830323436
The l
arge
st nu
mbe
r of h
ops
Figure 2 Analytical versus simulation results with different CTDwhere 119875119904 = 2W 120578 = 06 120572 = 05 and119873119903 = 10simulation results are not in full agreement with the analysisresults because1198731015840119903 is smaller than119873119903 in practice Besides wecan also observe the following
(1) The CTD has an important impact on the largestnumber of transmission hops it is because withthe increase of 119889119888 both the harvested energy andreceived signal strength at sender node of the next hopdecrease due to the larger path loss Consequently theachievable number of transmission hops is reducedwith no sufficient energy especially for the largervalues of 119889119888
(2) The multihop capability of CFP is better than CFIPand DFIP it is because in CFP scheme multiplerelays forward only the power (not the information)towards the receiver cooperatively so that the sendernode of the next hop can obtain more energy tosupport the larger transmission hops especially forthe smaller values of 119889119888
(3) The multihop capability of CFP and CFIP is betterthan DFIP since they use multiple relays to harvestenergy It can be observed in (8) and (13) that thevalues of 119871cfpmax and 119871cfipmax increase with the increase of119873119903 and 1198731015840119903 Furthermore if we consider the fact thatthe value of119873119903 is larger than1198731015840119903 this can further themultihop capability of CFP compared to CFIP
As the analytical results agree well with the simulationresults for the purpose of conciseness in the following wewill plot the simulation results for different parameters 120578 120572
119873119903 and119875119904 when119889119888 = 3mBut for119889119888 = 8mand119889119888 = 15mweonly give analytical results Next we investigate the impacts oftwo parameters 120578 and120572 on the largest number of transmissionhops respectively with considering the effect of CTD 119889119888From Figures 3 and 4 we can obtain the following
(1) For the small values of 119889119888 by increasing the value of120578 or reducing the value of 120572 the largest number oftransmission hops can be improved But if increasingthe value of 119889119888 the largest number of transmissionhops cannot obtain obvious improvement throughchanging the values of 120578 or 120572 In (8) (13) and (17)because 120578 and 120572 have a limited range of values (isin[0 1]) while 119889119888 has a larger value the values of119871cfpmax 119871cfipmax and 119871dfipmax cannot be affected obviously bychanging the values of 120578 or 120572
(2) The multihop capability of CFP is better than CFIPand DFIP especially for the smaller values of 119889119888which is because multiple relays forward only thepower cooperatively For example from Figure 3 wecan observe the impact of parameter 120578 on resultsand obtain that when 119889119888 = 3m the average largestnumber of hops of CFP CFIP and DFIP is 18 8 and49 respectively when 119889119888 = 8m the average valuesare 45 38 and 29 respectively when 119889119888 = 15m theaverage values are 31 28 and 2 respectively
Finally let us study the impacts of two parameters 119873119903and 119875119904 on the multihop capability respectively In Figure 5we give the simulation results for the effect of parameter 119873119903with considering the effect of 119889119888 Considering that 119883 lt 1of fractional denominator log2119883 in (8) and (13) we considera larger range of values of 119873119903 and vary the values of 119873119903 fordifferent values of 119889119888 (ie let the maximum value of 119873119903 beequal to lfloor11988927119888 rfloor) In order to facilitate drawing a numericalvalue 119909 on the 119909-axis of Figure 5 only denotes an exponentialquantity and in fact the corresponding value of 119873119903 is equalto lfloor119889119909119888 rfloor From Figure 5 we can see the following
(1) With the increase of 119873119903 the multihop capabilities ofthree schemes are improved correspondingly and themultihop capability of CFP is better than CFIP andDFIP Specifically when 119889119888 = 3m the average largestnumber of hops of CFP CFIP and DFIP is 103 63and 5 respectively when 119889119888 = 8m the average valuesare 75 51 and 3 respectively when 119889119888 = 15m theaverage values are 6 46 and 2 respectively
(2) Although with the increase of 119889119888 the multihopcapabilities of three schemes are weakened corre-spondingly the degree of weakening is depressedcompared with the case of considering the effect ofparameters 120578 or 120572 For example considering that thevalue of 119889119888 changes from 3m to 15m in CFP schemethe degree of weakening is (103 minus 6)103 times 100 =2718 when considering the effect of parameter119873119903but the value is (18 minus 31)18 times 100 = 8278when considering the effect of parameter 120578Thereforeincreasing the number119873119903 of relay nodes can improvethemultihop capabilities effectively when the CTD 119889119888
Wireless Communications and Mobile Computing 7
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
02 03 04 05 06 07 08010
5
10
15
20
25
30
35
40
45
50Th
e lar
gest
num
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f hop
s
(a)
CFPCIFPDIFP
02 03 04 05 06 07 08011
2
3
4
5
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7
The l
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(b)
CFPCIFPDIFP
1
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The l
arge
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02 03 04 05 06 07 0801
(c)
Figure 3 Numerical results for the impact of parameter 120578 on themultihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8mand (c) 119889119888 = 15m where 119875119904 = 2W 120572 = 05 and119873119903 = 20
increases it is because119873119903 has a larger range value andcan affect the values of 119871cfpmax 119871cfipmax and 119871dfipmax in (8)(13) and (17) obviously
In Figure 6 we investigate the impact of parameter 119875119904on the numerical results with considering the effect of 119889119888 Inorder to compare the results with parameter 119873119903 in a larger
range of values we also let a numerical value 119909 on the 119909-axisof Figure 6 only denote an exponential quantity where thecorresponding value of 119875119904 is equal to lfloor119889119909119888 rfloor From Figure 6 wecan observe the following
(1) With the increase of 119875119904 the multihop capabilitiesof the three schemes are improved correspondingly
8 Wireless Communications and Mobile Computing
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
02 03 04 05 06 07 08 09012
4
6
8
10
12
14
16
18
20
22Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
02 03 04 05 06 07 08 09011
2
3
4
5
6
7
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
02 03 04 05 06 07 08 0901 1
2
3
4
5
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 4 Numerical results for the impact of parameter 120572 on the multihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8m(c) and 119889119888 = 15m where 119875119904 = 2W 120578 = 06 and119873119903 = 20
and the multihop capability of CFP is better thanCFIP and DFIP However with the increase of 119889119888the multihop capabilities of the three schemes areweakened correspondingly Specifically when 119889119888 =3m the average largest number of hops of CFP CFIPand DFIP is 214 99 and 55 respectively when
119889119888 = 8m the average values are 59 48 and 34respectively when 119889119888 = 15m the average values are41 36 and 28 respectively
(2) Compared with the case of considering the effectof parameter 119873119903 the degree of weakening is much
Wireless Communications and Mobile Computing 9
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
18
20Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
18
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 5 Numerical results for the impact of parameter 119873119903 on the multihop capability with different values of CTD (a) 119889119888 = 3m (b)119889119888 = 8m and (c) 119889119888 = 15m where 119875119904 = 2W 120578 = 06 and 120572 = 05
worse For example considering that the value of 119889119888changes from 3m to 15m in CFP scheme the degreeofweakening is (214minus41)214times100 = 808whenconsidering the effect of parameter119875119904 but the value ofthe degree of weakening is (103 minus 6)103 times 100 =2718 when considering the effect of parameter119873119903
Therefore for improving the multihop capabilitiesincreasing the value of parameter119873119903 is more effective
According to the abovementioned results and analysiswe can obtain the important conclusions as follows (1) themultihop capability of CFP is better than CFIP and DFIP
10 Wireless Communications and Mobile Computing
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Ps
4
6
8
10
12
14
16
18
20
22
24
26Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
7
8
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 6 Numerical results for the impact of parameter119875119904 on themultihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8mand (c) 119889119888 = 15m where 120578 = 06 120572 = 05 and119873119903 = 20
(2) all of the parameters 119875119904 120578 120572 119873119903 and 119889119888 can affectthe multihop capability of the three schemes where theparameter 119889119888 can produce an important effect and (3) forimproving the multihop capability it is best effective toincrease the value of parameter119873119903 Of course we can furtherimprove the multihop capability by simultaneously adjustingthe values of parameters 119875119904 120578 and 120572
7 Conclusions
In this paper we study SWIPT in multihop wireless coop-erative networks where the multihop capabilities of CFPCFIP and DFIP schemes are analyzed For this purposewe construct analysis model to investigate the multihopcapabilities of CFP CFIP and DFIP schemes respectively
Wireless Communications and Mobile Computing 11
Finally numerical results show that the multihop capabilityof CFP is better than CFIP and DFIP and for improvingthe multihop capabilities it is best effective to increase theaverage number of relay nodes in cooperative set
Through the analysis model proposed in this paper theappropriate values of related parameters that is initial energyof source node the number of relay nodes the energyharvesting efficiency coefficient and power splitting coeffi-cient can be set to achieve the given transmission hops fromsource to destination
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work is funded by the China Postdoctoral Science Foun-dation (Grant no 2014M561627) the Natural Science Foun-dation ofAnhui Province (Grant no 1308085MF101) theNat-ural Science Foundation of Anhui Higher Education Insti-tutions (Grant no KJ2014A172) and the Science ResearchProject of Chaohu University (Grant no XLZ-201703)
References
[1] L R Varshney ldquoTransporting information and energy simul-taneouslyrdquo in Proceedings of the IEEE International Symposiumon Information Theory (ISIT rsquo08) pp 1612ndash1616 IEEE TorontoCanada July 2008
[2] P Grover and A Sahai ldquoShannonmeets tesla wireless informa-tion andpower transferrdquo inProceedings of the IEEE InternationalSymposium on Information Theory (ISIT rsquo10) pp 2363ndash2367Austin Tex USA June 2010
[3] R Zhang and C K Ho ldquoMIMO broadcasting for simultaneouswireless information and power transferrdquo IEEE Transactions onWireless Communications vol 12 no 5 pp 1989ndash2001 2013
[4] J N LanemanDN Tse andGWornell ldquoCooperative diversityin wireless networks efficient protocols and outage behaviorrdquoInstitute of Electrical and Electronics Engineers Transactions onInformation Theory vol 50 no 12 pp 3062ndash3080 2004
[5] A A Nasir X Zhou S Durrani and R A Kennedy ldquoWireless-powered relays in cooperative communications time-switchingrelaying protocols and throughput analysisrdquo IEEE Transactionson Communications vol 63 no 5 pp 1607ndash1622 2015
[6] E Chen M Xia D B da Costa and S Aissa ldquoMulti-Hopcooperative relaying with energy harvesting from cochannelinterferencesrdquo IEEE Communications Letters vol 21 no 5 pp1199ndash1202 2017
[7] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4761 2013
[8] L Liu R Zhang and K-C Chua ldquoWireless information trans-fer with opportunistic energy harvestingrdquo IEEE Transactions onWireless Communications vol 12 no 1 pp 288ndash300 2013
[9] L Liu R Zhang and K C Chua ldquoWireless information andpower transfer a dynamic power splitting approachrdquo IEEETransactions on Communications vol 61 no 9 pp 3990ndash40012013
[10] H Ju and R Zhang ldquoThroughput maximization in wire-less powered communication networksrdquo IEEE Transactions onWireless Communications vol 13 no 1 pp 418ndash428 2014
[11] R Morsi D S Michalopoulos and R Schober ldquoMultiuserscheduling schemes for simultaneous wireless information andpower transfer over fading channelsrdquo IEEE Transactions onWireless Communications vol 14 no 4 pp 1967ndash1982 2015
[12] C Zhong X Chen Z Zhang and G K Karagiannidis ldquoWire-less-powered communications performance analysis and opti-mizationrdquo IEEE Transactions on Communications vol 63 no12 pp 5178ndash5190 2015
[13] N Zhao F R Yu and V C M Leung ldquoOpportunistic com-munications in interference alignment networks with wirelesspower transferrdquo IEEE Wireless Communications Magazine vol22 no 1 pp 88ndash95 2015
[14] N Zhao ldquoJoint optimization of power splitting and allocationfor SWIPT in interference alignment networksrdquo in v preprintpp 1701ndash01952 httpsarxivorgabs170101952 2017
[15] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[16] D-T Do ldquoTime power switching based relaying protocol inenergy harvesting mobile node optimal throughput analysisrdquoMobile Information Systems vol 2015 Article ID 769286 8pages 2015
[17] C Zhang and Y Chen ldquoWireless power transfer strategies forcooperative relay system tomaximize information throughputrdquoIEEE Access vol 5 pp 2573ndash2582 2017
[18] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[19] Y Liu LWangM Elkashlan T Q Duong andANallanathanldquoTwo-way relay networks with wireless power transfer designand performance analysisrdquo IET Communications vol 10 no 14pp 1810ndash1819 2016
[20] T P Do I Song and Y H Kim ldquoSimultaneous wireless transferof power and information in a decode-and-forward two-wayrelaying networkrdquo IEEE Transactions on Wireless Communica-tions vol 16 no 3 pp 1579ndash1592 2017
[21] C Zhong H A Suraweera G Zheng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[22] Y Zeng and R Zhang ldquoFull-duplex wireless-powered relay withself-energy recyclingrdquo IEEE Wireless Communications Lettersvol 4 no 2 pp 201ndash204 2015
[23] D Wang R Zhang X Cheng and L Yang ldquoCapacity-enhancing full-duplex relay networks based on power-splitting(PS-)SWIPTrdquo IEEE Transactions on Vehicular Technology vol66 no 6 pp 5445ndash5450 2017
[24] ZDing I Krikidis B Sharif andHV Poor ldquoWireless informa-tion and power transfer in cooperative networks with spatiallyrandom relaysrdquo IEEETransactions onWireless Communicationsvol 13 no 8 pp 4440ndash4453 2014
[25] M Haghifam B Makki M Nasiri-Kenari and T SvenssonOn wireless energy and information transfer in relay networkshttpsarxivorgabs160707087 2016
12 Wireless Communications and Mobile Computing
[26] Y Liu ldquoWireless information and power transfer formultirelay-assisted cooperative communicationrdquo IEEE CommunicationsLetters vol 20 no 4 pp 784ndash787 2016
[27] J N Laneman and G W Wornell ldquoDistributed space-timecoded protocols for exploiting cooperative diversity in wirelessnetworksrdquo Institute of Electrical and Electronics Engineers Trans-actions on Information Theory vol 49 no 10 pp 2415ndash24252003
[28] IEEE Std IEEE Standard for Wireless LAN Medium AccessControl (MAC) and Physical Layer (PHY) Specifications(1999)
[29] N T Do V N Q Bao and B An ldquoOutage performance analysisof relay selection schemes in wireless energy harvesting coop-erative networks over non-identical rayleigh fading channelsrdquoSensors vol 16 no 3 article no 295 2016
Chemical EngineeringInternational Journal of Antennas and
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Submit your manuscripts atwwwhindawicom
2 Wireless Communications and Mobile Computing
largest number of transmission hops However the work in[6] did not consider multiple cooperative relays and failedto provide insights into the impact factors that affected thelargest number of transmission hops
Although the use of cooperative relays can reduce theloss of energy it is not guaranteed that the information istransmitted to the destination with enough power Thenwhat is the largest number of transmission hops underthe given targeted throughput requirement This problemis closely related to the initial energy of source node thenumber of relay nodes communication distance and otherparameters which sparks our research motivation In thispaper we first propose a cooperative forwarding power (CFP)scheme and then for performance comparison we suggesttwo schemes cooperative forwarding information and power(CFIP) and direct receiving information and power (DFIP)Furthermore we construct analysis model to investigate themultihop capabilities of CFP CFIP and DFIP schemes underthe given targeted throughput requirement from applicationlayer Finally simulation results validate the analysis modeland show that the multihop capability of CFP is better thanCFIP and DFIP and for improving the multihop capabilitiesit is best effective to increase the average number of relaynodes in a cooperative set Therefore through our study inthis paper the appropriate values of related parameters canbe set to achieve the given transmission hops from source todestination
The remainder of this paper is organized as follows Firstthe related works are described in Section 2 Next systemmodels and network scenario are given in Section 3 and inSection 4 we present CFP CFIP and DFIP schemes After-wards Section 5 presents analytical models for evaluatingthe performance of the three schemes and simulation resultsare given to validate the analytical model and obtain someimportant insights in Section 6 Finally conclusions are givenin Section 7
2 Related Works
According to the difference in information transmissionways communication systems adopted by existing literaturecan be categorized into point-to-point SWIPT systems andcooperative relay SWIPT systems In the following wepresent an overview of existing literature in the above twoSWIPT systems
(A) Point-to-Point SWIPT Systems After the pioneeringworks of Varshney [1] and Grover and Sahai [2] the perfor-mance of practical SWIPT systems is investigated in severalstudies Zhang and Ho [3] considered two scenarios wherethe information receiver and energy receiver are separated orcolocatedMore importantly thework in [3] used rate-energyregion to characterize the tradeoff between information rateand energy transfer and proposed two practical receiverdesigns namely time switching and power splitting forcolocated receivers Later in [7ndash9] sophisticated architecturesfor improving the rate-energy region were further proposedMoreover multiuser scheduling in SWIPT system was stud-ied for achieving the maximum sum throughput in [10]
and tradeoff between the average per user harvested energyand ergodic achievable rate in [11] Unlike the above worksZhong et al [12] considered a novel network architecturewhere the source is powered by a dedicated power beacon(PB) and gave the average throughput analysis for two dif-ferent transmission modes namely delay tolerant and delayintolerant Recently for reutilizing interferences to avoid agreat waste of energy Zhao et al [13 14] proposed a novelSWIPT scheme based on opportunistic communicationsin interference alignment (IA) networks and analyzed theperformance of SWIPT in IA networks respectively
(B) Cooperative Relay SWIPT Systems Considering thatthere is no direct point-to-point link between the sourceand destination it is necessary to make use of relay forforwarding information to destination where the relay nodeis energy-constrained and needs to harvest energy fromthe source Nasir et al [15] proposed time switching-basedrelaying (TSR) and power splitting-based relaying (PSR)protocols and derived the throughput for both TSR and PSRunder delay-limited and delay-tolerant transmission modesAfterwards Do [16] considered that both relay and destina-tion are mobile node and analyzed the optimal throughputperformance for the proposed time power switching-basedrelaying (TPSR) protocol Unlike the previous studies Zhangand Chen [17] considered that the relay can harvest energyfrom source destination or joint source and destinationand investigated the maximal throughputs of three wirelesspower transfer (WPT) schemes respectively Furthermoreto overcome the loss of spectral efficiency induced by one-way relaying and half-duplex relaying two-way relaying [18ndash20] and full-duplex relaying [21ndash23] were introduced intoSWIPT system respectively Instead of considering one relay-assisted SWIPT cooperative system in the aforementionedworks the works of [24ndash26] investigated multirelay-assistedcase and analyzed the outage probability and end-to-endrate respectively Unlike the existing prominent works weinvestigate SWIPT in a multihop scenario and analyzethe multihop capability of SWIPT system with multirelay-assisted cooperative transmission
3 System Model
We consider a network scenario shown in Figure 1 wherethe source node (119878) wants to transmit data packets to thedestination node (119863) We assume that a path 119877119878 1199011 1199012 119901119894 119901119896 119863 has been selected by virtue of a routingalgorithm and all nodes are equipped with a single omni-directional antenna and work in half-duplex mode Forcooperative transmission we also assume that each node ina routing path 119877 is surrounded by a number of relays Inaddition for facilitating the analysis we suggest the relay andchannel models as follows
(A) Relay Model We assume that 119878 is considered as anenergy-unconstrained nodewith amaximum transmit power119875119904 while other relay nodes are energy-constrained andhave not energy to complete the forwarding operation butthey can harvest energy from the received signal by power
Wireless Communications and Mobile Computing 3
RoutingRelay node
S p1 pi pi+1 pk D
Figure 1 Network scenario
splitting More specifically each relay 119894 splits a portion of thereceived signal energy 120572119894 for information decoding and theremaining part 1 minus 120572119894 for energy harvesting Since the pro-cessing power consumed by the receive circuitry at the relaynodes is assumed to be negligible as compared to the powerused for signal forwarding [15] we assume that all nodes havethe energy to receive signal In this paper all relays form acooperative set and simultaneously forward the signals to thereceiver by using distributed space-time codes (DSTC) [27]
(B) Channel Model We assume that the additive white Gaus-sian noises (AWGN) at all nodes are independent circularsymmetric complex Gaussian random variables with zeromean and unit variance The channel fading is modeled bylarge-scale path loss and statistically independent small-scaleRayleigh fading It is also assumed that the fading channelgains are assumed to be constant during one block time 119879119905Vin which the information is transmitted from the transmitterto receiver and independent and identical distribution (iid)is used from one transmission to the next Also we assumethat perfect channel state information (CSI) is available at thereceiver side through channel estimation and ℎ119894119895 denotes thechannel gain between node 119894 and node 119895 which are circularsymmetric complex Gaussian random variables with zeromean and unit variance [5 15 18]
4 Proposed Scheme
To investigate the multihop capability in SWIPT multihopcooperative networks we give the following three transmis-sion schemes We first propose cooperative forwarding power(CFP) scheme In CFP scheme the relays and receiver havedistinctly different tasks Specifically multiple relays close tothe transmitter harvest power from the transmitter first andthen cooperatively forward the power (not the information)towards the receiver The receiver receives the information(not the power) from the transmitter first and then it harveststhe power from the relays and is taken as the transmitter ofthe next hop Furthermore we use the following two schemesas comparison
(A) Cooperative Forwarding Information and Power (CFIP)Scheme In this scheme it is assumed that there is no directlink between the transmitter and receiver of a path (thisassumption is adopted by most of the previous studies [5 15ndash26]) such as 119901119894 and 119901119894+1 in Figure 1 Multiple relays harvest
power and decode the information from the transmitter firstand then cooperatively forward the information and powerto the receiver Then the receiver harvests the power anddecodes the information from the relays and is taken as thetransmitter of the next hop to transmit the information andpower Note that at present CFIP is often used in at mosttwo-hop scenarios by most of the previous works to analyzesystem performance So we extend this scheme to multihopscenario for comparing and analyzing themultihop capabilityin SWIPT cooperative networks
(B) Direct Receiving Information and Power (DFIP) SchemeThis scheme does not consider cooperative transmissionwhich means that the receiver harvests power and decodesthe information from the transmitter directly (this assump-tion is adopted by most of the previous studies [3 7ndash14])Then the receiver is taken as the transmitter of the nexthop to transmit the information and power The purpose ofproposing this scheme is to investigate whether cooperativetransmission can bringmore performance improvement thandirect transmission in SWIPT networks
It should be pointed out that our schemes are indepen-dent of the specific routing protocol and only require anexisting path from source to destination In fact the analysisresults of multihop capability can be used to design a newrouting protocol in SWIPT networks Also our schemes areindifferent to the specific method of relay selection becausethe analysis results of multihop capability are related to thenumber of relays instead of which node becomes a relay
5 Analytical Model
51 For CFP Scheme In CFP scheme one transmission isdivided into two phases In the first phase the transmitter(source or 119901119894) transmits the signal to the receiver (119901119894 ordestination) and thus the relays overhear the signal andharvest the power from the signal and at the same timethe receiver decodes the information from the signal In thesecond phase the relays form a cooperative set according tothe DSTC to forward the harvested power by transmittingthe special signal to the receiver cooperatively and then thereceiver harvests the power from the special signal and istaken as the transmitter in the next hop with the harvestedpower Note here that the special signal is different fromthe signal from the transmitter to receiver and does notinclude the useful information that needs to be decoded by
4 Wireless Communications and Mobile Computing
the receiver Therefore for the special signal we let the relaystransmit a PTS (power ready to send) frame cooperativelyin which the frame format is extended to the RTS and CTScontrol frames in IEEE 80211 protocol [28]
First of all let us consider that the signal is transmittedfrom the source to receiver node1199011 in Figure 1 Let 119910119903119894 denotethe received signal at relay 119894 around the source node in the firstphase we can derive
where ℎ119904119894 is the source to relay 119894 channel gain 119889119904119894 is thedistance from 119878 to relay 119894 119898 is the path loss exponent 119899119903119894is the additive white Gaussian noise at relay 119894 with zero meanand 1205902119899119903 variance and 119909119904 is the normalized information signalfrom the source Because the relays do not decode the signalfrom the transmitter to receiver we can let 120572119894 = 0 Accordingto (1) the harvested energy 119864119903119894 at relay 119894 during energyharvesting time 119879119905V is given by
where 120578 is the energy harvesting efficiency coefficient and119879119905Vis the transmission time for the signal Note that we do notconsider multirate network scenarios which means that 119879119905Vis equal for any one hop in the routing path In (2) we ignorethe impact of noise since the noise power is normally verysmall and below the sensitivity of the energy receiver [29]
In the second phase each relay 119894 uses the transmissionpower 119875119903119894 = 119864119903119894119879119888V and forms a cooperative set with otherrelays to transmit the PTS frame towards the receiver 1199011simultaneously Consequently 1199011 does not decode the PTSframe but only harvests the energy that can be expressed by1198641199011 as
where ℎ1198941199011 is channel gain from the relay 119894 to receiver 1199011 119879119888Vis the transmission time for the PTS119873119903 is the average numberof relay nodes in cooperative set and 1198891198941199011 is the distance fromthe relay 119894 to receiver 1199011 So we can derive the transmissionpower 1198751199011 from 1199011 to receiver node 1199012 in the second hop asfollows
According to the abovementioned analysis let 119875119901119895minus1denote 119895th (119895 ge 2) hop transmission power where the signalis transmitted from 119901119895minus1 to 119901119895 node (1199010 is the source node)we can obtain
where |ℎ119901119896minus2119894| |ℎ119894119901119896minus1 | denote the channel gains from 119901119896minus2to its relay 119894 and from its relay 119894 to 119901119896minus1 respectively and119889119898119901119896minus2 119894 119889119898119894119901119896minus1 denote the distance from 119901119896minus2 to its relay 119894 andfrom its relay 119894 to 119901119896minus1 respectively So we can obtain thesignal-to-noise ratio (SNR) 120574119895 at the receiver node 119901119895 asfollows 120574119895 = 119875119901119895minus1|ℎ119901119895minus1 119901119895 |2(1205902119901119895minus1 119901119895119889119898119901119895minus1119901119895) where 1205902119901119895minus1119901119895denotes the variance of additive white Gaussian noise atreceiver 119901119895 Given a targeted throughput 1198770 if we find themaximum value of 119897 for that log2(1 + 120574119897) ge 1198770 holds wecan derive that the value of 119897 is the largest number of hopssupported by the CFP scheme Therefore we can derive
In formula (6) for calculability we replace the exponentialrandom variables |ℎ119901119896minus2119894|2 |ℎ119894119901119896minus1 |2 and |ℎ119901119897minus1119901119897 |2with theirmean values 120582119903 120582119891 and 120582119889 respectively Since we haveassumed that the channel gain is circular symmetric complexGaussian randomvariables with zeromean and unit variancewe get 120582119903 = 120582119891 = 120582119889 = 1 Furthermore we assume that119889119901119896minus2 119894119889119894119901119896minus1 is constant and equal to 119889119888 Also 119889119901119897minus1119901119897 whichis the distance from 119901119897minus1 to 119901119897 is set to be constant value 119889119889Consequently we can obtain
(119897 minus 1) log2 (1205782119873119903119889119898119888 ) ge log2 (21198770 minus 1119875119904 119889119898119889 1205902) (7)
where we let 1205902119901119897minus1119901119897 be equal to constant value 1205902 In formula(7) if (21198770minus1)119889119898119889 1205902 gt 119875119904 that is log2(119875119904(119889119898119889 1205902)+1) lt 1198770 thesignal cannot be transmitted from the source node to the nexthop for satisfying the targeted throughput 1198770 Therefore formultihop transmission it is required that (21198770 minus1)119889119898119889 1205902 lt 119875119904Furthermore we consider that in a routing path (such asin Figure 1) the transmission power of node 119901119894+1 is lowerthan that of node 119901119894 because the transmission power of node119901119894+1 is charged from the node 119901119894 So it is also required that1205782(119873119903119889119898119888 ) lt 1 Note that we do not consider the caseof 1205782(119873119903119889119898119888 ) ge 1 because in this case the transmissionpower of node 119901119894+1 is greater than that of node 119901119894 so that theinformation can be transmitted all the time Accordingly wecan derive the largest number of hops 119871cfpmax supported by theCFP scheme as follows
where lfloorrfloor denotes the round down function From formula(8) we can find that the largest number of hops is affected bythe parameters 119875119904 120578 120572119873119903 and 119889119888 In simulation we will givethe detailed analysis for these parameters
Wireless Communications and Mobile Computing 5
52 For CFIP Scheme Unlike CFP scheme in CFIP schemea relay 119894 not only harvests the power but also decodes theinformation from the transmitter So we have 120572119894 = 0 Ifwe consider that the transmitter is the source node a relay119894 harvests the power 1198641015840119903119894 as follows
1198641015840119903119894 = 120578 (1 minus 120572) 119875119904 1003816100381610038161003816ℎ11990411989410038161003816100381610038162 119879119905V119889119898119904119894 (9)
Note here that for ease of analysis we let 120572119894 be constant andequal to 120572 Let 1198751015840119901119895minus1 denote jth (119895 ge 2) hop transmissionpower where the signal is transmitted from 119901119895minus1 to 119901119895through multiple relays we can obtain
1198751015840119901119895minus1 = (120578 (1 minus 120572))2(119895minus1) 119875119904times 119895prod119896=2
where1198731015840119903 is the average number of relay nodes in cooperativeset Note that because only the relay which can decodethe information successfully becomes one member of thecooperative set in CFIP scheme we have 1198731015840119903 le 119873119903 Let 1205741015840119895denote SNR at the receiver node 119901119895 we can derive
1205741015840119895 = 120578 (1 minus 120572) 1198731015840119903sum119894=1
where 1205902119894119901119895 is the variance of additive white Gaussian noiseat receiver 119901119895 Similarly to the above analysis for CFP whilerequiring log2(1 + 1205741015840119897 ) ge 1198770 we can obtain
(119897 minus 1) log2 ((120578 (1 minus 120572))2 1198731015840119903119889119898119888 )ge log2((21198770 minus 1) 119889119898119888 1205902120578 (1 minus 120572)1198731015840119903119875119904 )
(12)
where we let 1205902119894119901119895 be equal to constant value 1205902 In formula(12) we have (120578(1minus120572))2(1198731015840119903119889119898119888 ) lt 1 because the transmissionpower of node119901119894+1 is lower than that of node119901119894 Furthermorefor multihop transmission we have (21198770 minus 1)119889119898119888 1205902120578(1 minus120572)1198731015840119903119875119904 lt 1 that is log2(120578(1 minus 120572)1198751199041198731015840119903119889119898119888 1205902 + 1) gt 1198770Otherwise the information cannot be transmitted from thesource to 1199011 Consequently the largest number of hops 119871cfipmaxsupported by the CFIP scheme can be given as follows
119871cfipmax = 1 + lfloor log2 ((21198770 minus 1) 119889119898119888 1205902120578 (1 minus 120572)1198731015840119903119875119904)log2 (1205782 (1 minus 120572)2 (1198731015840119903119889119898119888 )) rfloor (13)
53 For DFIP Scheme Unlike CFP and CFIP schemes inDFIP scheme the receiver harvests the power and decodesthe information from the transmitter directly without relaycooperation Therefore if we consider that the transmitter is
the source node the receiver 1199011 harvests the power 1198641198891 asfollows
1198641198891 = 120578 (1 minus 120572) 119875119904 1003816100381610038161003816ℎ119904110038161003816100381610038162 119879119905V1198891198981199041 (14)
where ℎ1199041 is channel gain from the source node to receiver1199011 and 1198891199041 is the distance from the source to 1199011 Then thenode 1199011 transmits the information to the next hop node 1199012using the power 1198751198891 = 1198641198891119879119905V Let 119875119889119895minus1 denote 119895th (119895 ge 2)hop transmission power where the signal is transmitted from119901119895minus1 to 119901119895 we can obtain
119875119889119895minus1 = (120578 (1 minus 120572))(119895minus1) 119875119904 119895prod119896=2
So we can obtain SNR 120574119889119895 at receiver 119901119895 as 120574119889119895 =119875119889119895minus1|ℎ119901119895minus1 119901119895 |2(1205902119901119895minus1 119901119895119889119898119901119895minus1 119901119895) Similarly to the above analy-sis for CFP and CFIP while requiring log2(1 + 120574119889119897 ) ge 1198770 wecan obtain
(119897 minus 1) log2 (120578 (1 minus 120572)119889119898119889
) ge log2 (21198770 minus 1119875119904 119889119898119889 1205902) (16)
Accordingly we can derive the largest number of hops 119871dfipmaxsupported by the DFIP scheme as follows
119871dfipmax = 1 + lfloor log2 (((21198770 minus 1) 119875119904) 119889119898119889 1205902)log2 (120578 (1 minus 120572) 119889119898119889 ) rfloor (17)
In formula (17) we have 120578(1 minus 120572)119889119898119889 lt 1 because thetransmission power of node 119901119894+1 is lower than that of node 119901119894Formultihop transmission it is required that (21198770 minus1)119889119898119889 1205902 lt119875119904 Otherwise the information cannot be transmitted fromthe source to 11990116 Numerical Results and Analysis
In this section we perform computer simulations to validateour theory analysis and gain insights into the multihopcapabilities of the proposed CFP CFIP and DFIP schemesAlso we need to observe whether the values of 119871cfpmax schemeare larger than the values of 119871cfipmax and 119871dfipmax with the giventargeted throughput 1198770 under the effect of different networkparameters In the following simulations we set 1205902 = minus70 dB1198770 = 2 bitssecHz and 119898 = 27 (which corresponds to anurban cellular network environment [5]) and give the numer-ical results considering the effect of parameters 119875119904 120578 120572 119873119903and 119889119888 For simplicity we assume that 119889119889 = 119889119888 and1198731015840119903 = 119873119903
First we observe the numerical results about the valuesof 119871cfpmax 119871cfipmax and 119871dfipmax affected by the values of cooperativetransmission distance (CTD) 119889119888 that denotes the productof two distances from sender to relay and from relay toreceiver which are shown in Figure 2 From Figure 2 wecan find that the analytical results are practically consistentwith the simulation results which verifies the effectiveness ofour theory analytical model Note that for CFIP scheme the
6 Wireless Communications and Mobile Computing
3 4 5 6 7 8 9 102dc (m)
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
2468
1012141618202224262830323436
The l
arge
st nu
mbe
r of h
ops
Figure 2 Analytical versus simulation results with different CTDwhere 119875119904 = 2W 120578 = 06 120572 = 05 and119873119903 = 10simulation results are not in full agreement with the analysisresults because1198731015840119903 is smaller than119873119903 in practice Besides wecan also observe the following
(1) The CTD has an important impact on the largestnumber of transmission hops it is because withthe increase of 119889119888 both the harvested energy andreceived signal strength at sender node of the next hopdecrease due to the larger path loss Consequently theachievable number of transmission hops is reducedwith no sufficient energy especially for the largervalues of 119889119888
(2) The multihop capability of CFP is better than CFIPand DFIP it is because in CFP scheme multiplerelays forward only the power (not the information)towards the receiver cooperatively so that the sendernode of the next hop can obtain more energy tosupport the larger transmission hops especially forthe smaller values of 119889119888
(3) The multihop capability of CFP and CFIP is betterthan DFIP since they use multiple relays to harvestenergy It can be observed in (8) and (13) that thevalues of 119871cfpmax and 119871cfipmax increase with the increase of119873119903 and 1198731015840119903 Furthermore if we consider the fact thatthe value of119873119903 is larger than1198731015840119903 this can further themultihop capability of CFP compared to CFIP
As the analytical results agree well with the simulationresults for the purpose of conciseness in the following wewill plot the simulation results for different parameters 120578 120572
119873119903 and119875119904 when119889119888 = 3mBut for119889119888 = 8mand119889119888 = 15mweonly give analytical results Next we investigate the impacts oftwo parameters 120578 and120572 on the largest number of transmissionhops respectively with considering the effect of CTD 119889119888From Figures 3 and 4 we can obtain the following
(1) For the small values of 119889119888 by increasing the value of120578 or reducing the value of 120572 the largest number oftransmission hops can be improved But if increasingthe value of 119889119888 the largest number of transmissionhops cannot obtain obvious improvement throughchanging the values of 120578 or 120572 In (8) (13) and (17)because 120578 and 120572 have a limited range of values (isin[0 1]) while 119889119888 has a larger value the values of119871cfpmax 119871cfipmax and 119871dfipmax cannot be affected obviously bychanging the values of 120578 or 120572
(2) The multihop capability of CFP is better than CFIPand DFIP especially for the smaller values of 119889119888which is because multiple relays forward only thepower cooperatively For example from Figure 3 wecan observe the impact of parameter 120578 on resultsand obtain that when 119889119888 = 3m the average largestnumber of hops of CFP CFIP and DFIP is 18 8 and49 respectively when 119889119888 = 8m the average valuesare 45 38 and 29 respectively when 119889119888 = 15m theaverage values are 31 28 and 2 respectively
Finally let us study the impacts of two parameters 119873119903and 119875119904 on the multihop capability respectively In Figure 5we give the simulation results for the effect of parameter 119873119903with considering the effect of 119889119888 Considering that 119883 lt 1of fractional denominator log2119883 in (8) and (13) we considera larger range of values of 119873119903 and vary the values of 119873119903 fordifferent values of 119889119888 (ie let the maximum value of 119873119903 beequal to lfloor11988927119888 rfloor) In order to facilitate drawing a numericalvalue 119909 on the 119909-axis of Figure 5 only denotes an exponentialquantity and in fact the corresponding value of 119873119903 is equalto lfloor119889119909119888 rfloor From Figure 5 we can see the following
(1) With the increase of 119873119903 the multihop capabilities ofthree schemes are improved correspondingly and themultihop capability of CFP is better than CFIP andDFIP Specifically when 119889119888 = 3m the average largestnumber of hops of CFP CFIP and DFIP is 103 63and 5 respectively when 119889119888 = 8m the average valuesare 75 51 and 3 respectively when 119889119888 = 15m theaverage values are 6 46 and 2 respectively
(2) Although with the increase of 119889119888 the multihopcapabilities of three schemes are weakened corre-spondingly the degree of weakening is depressedcompared with the case of considering the effect ofparameters 120578 or 120572 For example considering that thevalue of 119889119888 changes from 3m to 15m in CFP schemethe degree of weakening is (103 minus 6)103 times 100 =2718 when considering the effect of parameter119873119903but the value is (18 minus 31)18 times 100 = 8278when considering the effect of parameter 120578Thereforeincreasing the number119873119903 of relay nodes can improvethemultihop capabilities effectively when the CTD 119889119888
Wireless Communications and Mobile Computing 7
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
02 03 04 05 06 07 08010
5
10
15
20
25
30
35
40
45
50Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
02 03 04 05 06 07 08011
2
3
4
5
6
7
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
1
2
3
4
5
The l
arge
st nu
mbe
r of h
ops
02 03 04 05 06 07 0801
(c)
Figure 3 Numerical results for the impact of parameter 120578 on themultihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8mand (c) 119889119888 = 15m where 119875119904 = 2W 120572 = 05 and119873119903 = 20
increases it is because119873119903 has a larger range value andcan affect the values of 119871cfpmax 119871cfipmax and 119871dfipmax in (8)(13) and (17) obviously
In Figure 6 we investigate the impact of parameter 119875119904on the numerical results with considering the effect of 119889119888 Inorder to compare the results with parameter 119873119903 in a larger
range of values we also let a numerical value 119909 on the 119909-axisof Figure 6 only denote an exponential quantity where thecorresponding value of 119875119904 is equal to lfloor119889119909119888 rfloor From Figure 6 wecan observe the following
(1) With the increase of 119875119904 the multihop capabilitiesof the three schemes are improved correspondingly
8 Wireless Communications and Mobile Computing
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
02 03 04 05 06 07 08 09012
4
6
8
10
12
14
16
18
20
22Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
02 03 04 05 06 07 08 09011
2
3
4
5
6
7
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
02 03 04 05 06 07 08 0901 1
2
3
4
5
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 4 Numerical results for the impact of parameter 120572 on the multihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8m(c) and 119889119888 = 15m where 119875119904 = 2W 120578 = 06 and119873119903 = 20
and the multihop capability of CFP is better thanCFIP and DFIP However with the increase of 119889119888the multihop capabilities of the three schemes areweakened correspondingly Specifically when 119889119888 =3m the average largest number of hops of CFP CFIPand DFIP is 214 99 and 55 respectively when
119889119888 = 8m the average values are 59 48 and 34respectively when 119889119888 = 15m the average values are41 36 and 28 respectively
(2) Compared with the case of considering the effectof parameter 119873119903 the degree of weakening is much
Wireless Communications and Mobile Computing 9
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
18
20Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
18
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 5 Numerical results for the impact of parameter 119873119903 on the multihop capability with different values of CTD (a) 119889119888 = 3m (b)119889119888 = 8m and (c) 119889119888 = 15m where 119875119904 = 2W 120578 = 06 and 120572 = 05
worse For example considering that the value of 119889119888changes from 3m to 15m in CFP scheme the degreeofweakening is (214minus41)214times100 = 808whenconsidering the effect of parameter119875119904 but the value ofthe degree of weakening is (103 minus 6)103 times 100 =2718 when considering the effect of parameter119873119903
Therefore for improving the multihop capabilitiesincreasing the value of parameter119873119903 is more effective
According to the abovementioned results and analysiswe can obtain the important conclusions as follows (1) themultihop capability of CFP is better than CFIP and DFIP
10 Wireless Communications and Mobile Computing
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Ps
4
6
8
10
12
14
16
18
20
22
24
26Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
7
8
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 6 Numerical results for the impact of parameter119875119904 on themultihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8mand (c) 119889119888 = 15m where 120578 = 06 120572 = 05 and119873119903 = 20
(2) all of the parameters 119875119904 120578 120572 119873119903 and 119889119888 can affectthe multihop capability of the three schemes where theparameter 119889119888 can produce an important effect and (3) forimproving the multihop capability it is best effective toincrease the value of parameter119873119903 Of course we can furtherimprove the multihop capability by simultaneously adjustingthe values of parameters 119875119904 120578 and 120572
7 Conclusions
In this paper we study SWIPT in multihop wireless coop-erative networks where the multihop capabilities of CFPCFIP and DFIP schemes are analyzed For this purposewe construct analysis model to investigate the multihopcapabilities of CFP CFIP and DFIP schemes respectively
Wireless Communications and Mobile Computing 11
Finally numerical results show that the multihop capabilityof CFP is better than CFIP and DFIP and for improvingthe multihop capabilities it is best effective to increase theaverage number of relay nodes in cooperative set
Through the analysis model proposed in this paper theappropriate values of related parameters that is initial energyof source node the number of relay nodes the energyharvesting efficiency coefficient and power splitting coeffi-cient can be set to achieve the given transmission hops fromsource to destination
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work is funded by the China Postdoctoral Science Foun-dation (Grant no 2014M561627) the Natural Science Foun-dation ofAnhui Province (Grant no 1308085MF101) theNat-ural Science Foundation of Anhui Higher Education Insti-tutions (Grant no KJ2014A172) and the Science ResearchProject of Chaohu University (Grant no XLZ-201703)
References
[1] L R Varshney ldquoTransporting information and energy simul-taneouslyrdquo in Proceedings of the IEEE International Symposiumon Information Theory (ISIT rsquo08) pp 1612ndash1616 IEEE TorontoCanada July 2008
[2] P Grover and A Sahai ldquoShannonmeets tesla wireless informa-tion andpower transferrdquo inProceedings of the IEEE InternationalSymposium on Information Theory (ISIT rsquo10) pp 2363ndash2367Austin Tex USA June 2010
[3] R Zhang and C K Ho ldquoMIMO broadcasting for simultaneouswireless information and power transferrdquo IEEE Transactions onWireless Communications vol 12 no 5 pp 1989ndash2001 2013
[4] J N LanemanDN Tse andGWornell ldquoCooperative diversityin wireless networks efficient protocols and outage behaviorrdquoInstitute of Electrical and Electronics Engineers Transactions onInformation Theory vol 50 no 12 pp 3062ndash3080 2004
[5] A A Nasir X Zhou S Durrani and R A Kennedy ldquoWireless-powered relays in cooperative communications time-switchingrelaying protocols and throughput analysisrdquo IEEE Transactionson Communications vol 63 no 5 pp 1607ndash1622 2015
[6] E Chen M Xia D B da Costa and S Aissa ldquoMulti-Hopcooperative relaying with energy harvesting from cochannelinterferencesrdquo IEEE Communications Letters vol 21 no 5 pp1199ndash1202 2017
[7] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4761 2013
[8] L Liu R Zhang and K-C Chua ldquoWireless information trans-fer with opportunistic energy harvestingrdquo IEEE Transactions onWireless Communications vol 12 no 1 pp 288ndash300 2013
[9] L Liu R Zhang and K C Chua ldquoWireless information andpower transfer a dynamic power splitting approachrdquo IEEETransactions on Communications vol 61 no 9 pp 3990ndash40012013
[10] H Ju and R Zhang ldquoThroughput maximization in wire-less powered communication networksrdquo IEEE Transactions onWireless Communications vol 13 no 1 pp 418ndash428 2014
[11] R Morsi D S Michalopoulos and R Schober ldquoMultiuserscheduling schemes for simultaneous wireless information andpower transfer over fading channelsrdquo IEEE Transactions onWireless Communications vol 14 no 4 pp 1967ndash1982 2015
[12] C Zhong X Chen Z Zhang and G K Karagiannidis ldquoWire-less-powered communications performance analysis and opti-mizationrdquo IEEE Transactions on Communications vol 63 no12 pp 5178ndash5190 2015
[13] N Zhao F R Yu and V C M Leung ldquoOpportunistic com-munications in interference alignment networks with wirelesspower transferrdquo IEEE Wireless Communications Magazine vol22 no 1 pp 88ndash95 2015
[14] N Zhao ldquoJoint optimization of power splitting and allocationfor SWIPT in interference alignment networksrdquo in v preprintpp 1701ndash01952 httpsarxivorgabs170101952 2017
[15] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[16] D-T Do ldquoTime power switching based relaying protocol inenergy harvesting mobile node optimal throughput analysisrdquoMobile Information Systems vol 2015 Article ID 769286 8pages 2015
[17] C Zhang and Y Chen ldquoWireless power transfer strategies forcooperative relay system tomaximize information throughputrdquoIEEE Access vol 5 pp 2573ndash2582 2017
[18] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[19] Y Liu LWangM Elkashlan T Q Duong andANallanathanldquoTwo-way relay networks with wireless power transfer designand performance analysisrdquo IET Communications vol 10 no 14pp 1810ndash1819 2016
[20] T P Do I Song and Y H Kim ldquoSimultaneous wireless transferof power and information in a decode-and-forward two-wayrelaying networkrdquo IEEE Transactions on Wireless Communica-tions vol 16 no 3 pp 1579ndash1592 2017
[21] C Zhong H A Suraweera G Zheng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[22] Y Zeng and R Zhang ldquoFull-duplex wireless-powered relay withself-energy recyclingrdquo IEEE Wireless Communications Lettersvol 4 no 2 pp 201ndash204 2015
[23] D Wang R Zhang X Cheng and L Yang ldquoCapacity-enhancing full-duplex relay networks based on power-splitting(PS-)SWIPTrdquo IEEE Transactions on Vehicular Technology vol66 no 6 pp 5445ndash5450 2017
[24] ZDing I Krikidis B Sharif andHV Poor ldquoWireless informa-tion and power transfer in cooperative networks with spatiallyrandom relaysrdquo IEEETransactions onWireless Communicationsvol 13 no 8 pp 4440ndash4453 2014
[25] M Haghifam B Makki M Nasiri-Kenari and T SvenssonOn wireless energy and information transfer in relay networkshttpsarxivorgabs160707087 2016
12 Wireless Communications and Mobile Computing
[26] Y Liu ldquoWireless information and power transfer formultirelay-assisted cooperative communicationrdquo IEEE CommunicationsLetters vol 20 no 4 pp 784ndash787 2016
[27] J N Laneman and G W Wornell ldquoDistributed space-timecoded protocols for exploiting cooperative diversity in wirelessnetworksrdquo Institute of Electrical and Electronics Engineers Trans-actions on Information Theory vol 49 no 10 pp 2415ndash24252003
[28] IEEE Std IEEE Standard for Wireless LAN Medium AccessControl (MAC) and Physical Layer (PHY) Specifications(1999)
[29] N T Do V N Q Bao and B An ldquoOutage performance analysisof relay selection schemes in wireless energy harvesting coop-erative networks over non-identical rayleigh fading channelsrdquoSensors vol 16 no 3 article no 295 2016
Chemical EngineeringInternational Journal of Antennas and
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Advances in
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Submit your manuscripts atwwwhindawicom
Wireless Communications and Mobile Computing 3
RoutingRelay node
S p1 pi pi+1 pk D
Figure 1 Network scenario
splitting More specifically each relay 119894 splits a portion of thereceived signal energy 120572119894 for information decoding and theremaining part 1 minus 120572119894 for energy harvesting Since the pro-cessing power consumed by the receive circuitry at the relaynodes is assumed to be negligible as compared to the powerused for signal forwarding [15] we assume that all nodes havethe energy to receive signal In this paper all relays form acooperative set and simultaneously forward the signals to thereceiver by using distributed space-time codes (DSTC) [27]
(B) Channel Model We assume that the additive white Gaus-sian noises (AWGN) at all nodes are independent circularsymmetric complex Gaussian random variables with zeromean and unit variance The channel fading is modeled bylarge-scale path loss and statistically independent small-scaleRayleigh fading It is also assumed that the fading channelgains are assumed to be constant during one block time 119879119905Vin which the information is transmitted from the transmitterto receiver and independent and identical distribution (iid)is used from one transmission to the next Also we assumethat perfect channel state information (CSI) is available at thereceiver side through channel estimation and ℎ119894119895 denotes thechannel gain between node 119894 and node 119895 which are circularsymmetric complex Gaussian random variables with zeromean and unit variance [5 15 18]
4 Proposed Scheme
To investigate the multihop capability in SWIPT multihopcooperative networks we give the following three transmis-sion schemes We first propose cooperative forwarding power(CFP) scheme In CFP scheme the relays and receiver havedistinctly different tasks Specifically multiple relays close tothe transmitter harvest power from the transmitter first andthen cooperatively forward the power (not the information)towards the receiver The receiver receives the information(not the power) from the transmitter first and then it harveststhe power from the relays and is taken as the transmitter ofthe next hop Furthermore we use the following two schemesas comparison
(A) Cooperative Forwarding Information and Power (CFIP)Scheme In this scheme it is assumed that there is no directlink between the transmitter and receiver of a path (thisassumption is adopted by most of the previous studies [5 15ndash26]) such as 119901119894 and 119901119894+1 in Figure 1 Multiple relays harvest
power and decode the information from the transmitter firstand then cooperatively forward the information and powerto the receiver Then the receiver harvests the power anddecodes the information from the relays and is taken as thetransmitter of the next hop to transmit the information andpower Note that at present CFIP is often used in at mosttwo-hop scenarios by most of the previous works to analyzesystem performance So we extend this scheme to multihopscenario for comparing and analyzing themultihop capabilityin SWIPT cooperative networks
(B) Direct Receiving Information and Power (DFIP) SchemeThis scheme does not consider cooperative transmissionwhich means that the receiver harvests power and decodesthe information from the transmitter directly (this assump-tion is adopted by most of the previous studies [3 7ndash14])Then the receiver is taken as the transmitter of the nexthop to transmit the information and power The purpose ofproposing this scheme is to investigate whether cooperativetransmission can bringmore performance improvement thandirect transmission in SWIPT networks
It should be pointed out that our schemes are indepen-dent of the specific routing protocol and only require anexisting path from source to destination In fact the analysisresults of multihop capability can be used to design a newrouting protocol in SWIPT networks Also our schemes areindifferent to the specific method of relay selection becausethe analysis results of multihop capability are related to thenumber of relays instead of which node becomes a relay
5 Analytical Model
51 For CFP Scheme In CFP scheme one transmission isdivided into two phases In the first phase the transmitter(source or 119901119894) transmits the signal to the receiver (119901119894 ordestination) and thus the relays overhear the signal andharvest the power from the signal and at the same timethe receiver decodes the information from the signal In thesecond phase the relays form a cooperative set according tothe DSTC to forward the harvested power by transmittingthe special signal to the receiver cooperatively and then thereceiver harvests the power from the special signal and istaken as the transmitter in the next hop with the harvestedpower Note here that the special signal is different fromthe signal from the transmitter to receiver and does notinclude the useful information that needs to be decoded by
4 Wireless Communications and Mobile Computing
the receiver Therefore for the special signal we let the relaystransmit a PTS (power ready to send) frame cooperativelyin which the frame format is extended to the RTS and CTScontrol frames in IEEE 80211 protocol [28]
First of all let us consider that the signal is transmittedfrom the source to receiver node1199011 in Figure 1 Let 119910119903119894 denotethe received signal at relay 119894 around the source node in the firstphase we can derive
where ℎ119904119894 is the source to relay 119894 channel gain 119889119904119894 is thedistance from 119878 to relay 119894 119898 is the path loss exponent 119899119903119894is the additive white Gaussian noise at relay 119894 with zero meanand 1205902119899119903 variance and 119909119904 is the normalized information signalfrom the source Because the relays do not decode the signalfrom the transmitter to receiver we can let 120572119894 = 0 Accordingto (1) the harvested energy 119864119903119894 at relay 119894 during energyharvesting time 119879119905V is given by
where 120578 is the energy harvesting efficiency coefficient and119879119905Vis the transmission time for the signal Note that we do notconsider multirate network scenarios which means that 119879119905Vis equal for any one hop in the routing path In (2) we ignorethe impact of noise since the noise power is normally verysmall and below the sensitivity of the energy receiver [29]
In the second phase each relay 119894 uses the transmissionpower 119875119903119894 = 119864119903119894119879119888V and forms a cooperative set with otherrelays to transmit the PTS frame towards the receiver 1199011simultaneously Consequently 1199011 does not decode the PTSframe but only harvests the energy that can be expressed by1198641199011 as
where ℎ1198941199011 is channel gain from the relay 119894 to receiver 1199011 119879119888Vis the transmission time for the PTS119873119903 is the average numberof relay nodes in cooperative set and 1198891198941199011 is the distance fromthe relay 119894 to receiver 1199011 So we can derive the transmissionpower 1198751199011 from 1199011 to receiver node 1199012 in the second hop asfollows
According to the abovementioned analysis let 119875119901119895minus1denote 119895th (119895 ge 2) hop transmission power where the signalis transmitted from 119901119895minus1 to 119901119895 node (1199010 is the source node)we can obtain
where |ℎ119901119896minus2119894| |ℎ119894119901119896minus1 | denote the channel gains from 119901119896minus2to its relay 119894 and from its relay 119894 to 119901119896minus1 respectively and119889119898119901119896minus2 119894 119889119898119894119901119896minus1 denote the distance from 119901119896minus2 to its relay 119894 andfrom its relay 119894 to 119901119896minus1 respectively So we can obtain thesignal-to-noise ratio (SNR) 120574119895 at the receiver node 119901119895 asfollows 120574119895 = 119875119901119895minus1|ℎ119901119895minus1 119901119895 |2(1205902119901119895minus1 119901119895119889119898119901119895minus1119901119895) where 1205902119901119895minus1119901119895denotes the variance of additive white Gaussian noise atreceiver 119901119895 Given a targeted throughput 1198770 if we find themaximum value of 119897 for that log2(1 + 120574119897) ge 1198770 holds wecan derive that the value of 119897 is the largest number of hopssupported by the CFP scheme Therefore we can derive
In formula (6) for calculability we replace the exponentialrandom variables |ℎ119901119896minus2119894|2 |ℎ119894119901119896minus1 |2 and |ℎ119901119897minus1119901119897 |2with theirmean values 120582119903 120582119891 and 120582119889 respectively Since we haveassumed that the channel gain is circular symmetric complexGaussian randomvariables with zeromean and unit variancewe get 120582119903 = 120582119891 = 120582119889 = 1 Furthermore we assume that119889119901119896minus2 119894119889119894119901119896minus1 is constant and equal to 119889119888 Also 119889119901119897minus1119901119897 whichis the distance from 119901119897minus1 to 119901119897 is set to be constant value 119889119889Consequently we can obtain
(119897 minus 1) log2 (1205782119873119903119889119898119888 ) ge log2 (21198770 minus 1119875119904 119889119898119889 1205902) (7)
where we let 1205902119901119897minus1119901119897 be equal to constant value 1205902 In formula(7) if (21198770minus1)119889119898119889 1205902 gt 119875119904 that is log2(119875119904(119889119898119889 1205902)+1) lt 1198770 thesignal cannot be transmitted from the source node to the nexthop for satisfying the targeted throughput 1198770 Therefore formultihop transmission it is required that (21198770 minus1)119889119898119889 1205902 lt 119875119904Furthermore we consider that in a routing path (such asin Figure 1) the transmission power of node 119901119894+1 is lowerthan that of node 119901119894 because the transmission power of node119901119894+1 is charged from the node 119901119894 So it is also required that1205782(119873119903119889119898119888 ) lt 1 Note that we do not consider the caseof 1205782(119873119903119889119898119888 ) ge 1 because in this case the transmissionpower of node 119901119894+1 is greater than that of node 119901119894 so that theinformation can be transmitted all the time Accordingly wecan derive the largest number of hops 119871cfpmax supported by theCFP scheme as follows
where lfloorrfloor denotes the round down function From formula(8) we can find that the largest number of hops is affected bythe parameters 119875119904 120578 120572119873119903 and 119889119888 In simulation we will givethe detailed analysis for these parameters
Wireless Communications and Mobile Computing 5
52 For CFIP Scheme Unlike CFP scheme in CFIP schemea relay 119894 not only harvests the power but also decodes theinformation from the transmitter So we have 120572119894 = 0 Ifwe consider that the transmitter is the source node a relay119894 harvests the power 1198641015840119903119894 as follows
1198641015840119903119894 = 120578 (1 minus 120572) 119875119904 1003816100381610038161003816ℎ11990411989410038161003816100381610038162 119879119905V119889119898119904119894 (9)
Note here that for ease of analysis we let 120572119894 be constant andequal to 120572 Let 1198751015840119901119895minus1 denote jth (119895 ge 2) hop transmissionpower where the signal is transmitted from 119901119895minus1 to 119901119895through multiple relays we can obtain
1198751015840119901119895minus1 = (120578 (1 minus 120572))2(119895minus1) 119875119904times 119895prod119896=2
where1198731015840119903 is the average number of relay nodes in cooperativeset Note that because only the relay which can decodethe information successfully becomes one member of thecooperative set in CFIP scheme we have 1198731015840119903 le 119873119903 Let 1205741015840119895denote SNR at the receiver node 119901119895 we can derive
1205741015840119895 = 120578 (1 minus 120572) 1198731015840119903sum119894=1
where 1205902119894119901119895 is the variance of additive white Gaussian noiseat receiver 119901119895 Similarly to the above analysis for CFP whilerequiring log2(1 + 1205741015840119897 ) ge 1198770 we can obtain
(119897 minus 1) log2 ((120578 (1 minus 120572))2 1198731015840119903119889119898119888 )ge log2((21198770 minus 1) 119889119898119888 1205902120578 (1 minus 120572)1198731015840119903119875119904 )
(12)
where we let 1205902119894119901119895 be equal to constant value 1205902 In formula(12) we have (120578(1minus120572))2(1198731015840119903119889119898119888 ) lt 1 because the transmissionpower of node119901119894+1 is lower than that of node119901119894 Furthermorefor multihop transmission we have (21198770 minus 1)119889119898119888 1205902120578(1 minus120572)1198731015840119903119875119904 lt 1 that is log2(120578(1 minus 120572)1198751199041198731015840119903119889119898119888 1205902 + 1) gt 1198770Otherwise the information cannot be transmitted from thesource to 1199011 Consequently the largest number of hops 119871cfipmaxsupported by the CFIP scheme can be given as follows
119871cfipmax = 1 + lfloor log2 ((21198770 minus 1) 119889119898119888 1205902120578 (1 minus 120572)1198731015840119903119875119904)log2 (1205782 (1 minus 120572)2 (1198731015840119903119889119898119888 )) rfloor (13)
53 For DFIP Scheme Unlike CFP and CFIP schemes inDFIP scheme the receiver harvests the power and decodesthe information from the transmitter directly without relaycooperation Therefore if we consider that the transmitter is
the source node the receiver 1199011 harvests the power 1198641198891 asfollows
1198641198891 = 120578 (1 minus 120572) 119875119904 1003816100381610038161003816ℎ119904110038161003816100381610038162 119879119905V1198891198981199041 (14)
where ℎ1199041 is channel gain from the source node to receiver1199011 and 1198891199041 is the distance from the source to 1199011 Then thenode 1199011 transmits the information to the next hop node 1199012using the power 1198751198891 = 1198641198891119879119905V Let 119875119889119895minus1 denote 119895th (119895 ge 2)hop transmission power where the signal is transmitted from119901119895minus1 to 119901119895 we can obtain
119875119889119895minus1 = (120578 (1 minus 120572))(119895minus1) 119875119904 119895prod119896=2
So we can obtain SNR 120574119889119895 at receiver 119901119895 as 120574119889119895 =119875119889119895minus1|ℎ119901119895minus1 119901119895 |2(1205902119901119895minus1 119901119895119889119898119901119895minus1 119901119895) Similarly to the above analy-sis for CFP and CFIP while requiring log2(1 + 120574119889119897 ) ge 1198770 wecan obtain
(119897 minus 1) log2 (120578 (1 minus 120572)119889119898119889
) ge log2 (21198770 minus 1119875119904 119889119898119889 1205902) (16)
Accordingly we can derive the largest number of hops 119871dfipmaxsupported by the DFIP scheme as follows
119871dfipmax = 1 + lfloor log2 (((21198770 minus 1) 119875119904) 119889119898119889 1205902)log2 (120578 (1 minus 120572) 119889119898119889 ) rfloor (17)
In formula (17) we have 120578(1 minus 120572)119889119898119889 lt 1 because thetransmission power of node 119901119894+1 is lower than that of node 119901119894Formultihop transmission it is required that (21198770 minus1)119889119898119889 1205902 lt119875119904 Otherwise the information cannot be transmitted fromthe source to 11990116 Numerical Results and Analysis
In this section we perform computer simulations to validateour theory analysis and gain insights into the multihopcapabilities of the proposed CFP CFIP and DFIP schemesAlso we need to observe whether the values of 119871cfpmax schemeare larger than the values of 119871cfipmax and 119871dfipmax with the giventargeted throughput 1198770 under the effect of different networkparameters In the following simulations we set 1205902 = minus70 dB1198770 = 2 bitssecHz and 119898 = 27 (which corresponds to anurban cellular network environment [5]) and give the numer-ical results considering the effect of parameters 119875119904 120578 120572 119873119903and 119889119888 For simplicity we assume that 119889119889 = 119889119888 and1198731015840119903 = 119873119903
First we observe the numerical results about the valuesof 119871cfpmax 119871cfipmax and 119871dfipmax affected by the values of cooperativetransmission distance (CTD) 119889119888 that denotes the productof two distances from sender to relay and from relay toreceiver which are shown in Figure 2 From Figure 2 wecan find that the analytical results are practically consistentwith the simulation results which verifies the effectiveness ofour theory analytical model Note that for CFIP scheme the
6 Wireless Communications and Mobile Computing
3 4 5 6 7 8 9 102dc (m)
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
2468
1012141618202224262830323436
The l
arge
st nu
mbe
r of h
ops
Figure 2 Analytical versus simulation results with different CTDwhere 119875119904 = 2W 120578 = 06 120572 = 05 and119873119903 = 10simulation results are not in full agreement with the analysisresults because1198731015840119903 is smaller than119873119903 in practice Besides wecan also observe the following
(1) The CTD has an important impact on the largestnumber of transmission hops it is because withthe increase of 119889119888 both the harvested energy andreceived signal strength at sender node of the next hopdecrease due to the larger path loss Consequently theachievable number of transmission hops is reducedwith no sufficient energy especially for the largervalues of 119889119888
(2) The multihop capability of CFP is better than CFIPand DFIP it is because in CFP scheme multiplerelays forward only the power (not the information)towards the receiver cooperatively so that the sendernode of the next hop can obtain more energy tosupport the larger transmission hops especially forthe smaller values of 119889119888
(3) The multihop capability of CFP and CFIP is betterthan DFIP since they use multiple relays to harvestenergy It can be observed in (8) and (13) that thevalues of 119871cfpmax and 119871cfipmax increase with the increase of119873119903 and 1198731015840119903 Furthermore if we consider the fact thatthe value of119873119903 is larger than1198731015840119903 this can further themultihop capability of CFP compared to CFIP
As the analytical results agree well with the simulationresults for the purpose of conciseness in the following wewill plot the simulation results for different parameters 120578 120572
119873119903 and119875119904 when119889119888 = 3mBut for119889119888 = 8mand119889119888 = 15mweonly give analytical results Next we investigate the impacts oftwo parameters 120578 and120572 on the largest number of transmissionhops respectively with considering the effect of CTD 119889119888From Figures 3 and 4 we can obtain the following
(1) For the small values of 119889119888 by increasing the value of120578 or reducing the value of 120572 the largest number oftransmission hops can be improved But if increasingthe value of 119889119888 the largest number of transmissionhops cannot obtain obvious improvement throughchanging the values of 120578 or 120572 In (8) (13) and (17)because 120578 and 120572 have a limited range of values (isin[0 1]) while 119889119888 has a larger value the values of119871cfpmax 119871cfipmax and 119871dfipmax cannot be affected obviously bychanging the values of 120578 or 120572
(2) The multihop capability of CFP is better than CFIPand DFIP especially for the smaller values of 119889119888which is because multiple relays forward only thepower cooperatively For example from Figure 3 wecan observe the impact of parameter 120578 on resultsand obtain that when 119889119888 = 3m the average largestnumber of hops of CFP CFIP and DFIP is 18 8 and49 respectively when 119889119888 = 8m the average valuesare 45 38 and 29 respectively when 119889119888 = 15m theaverage values are 31 28 and 2 respectively
Finally let us study the impacts of two parameters 119873119903and 119875119904 on the multihop capability respectively In Figure 5we give the simulation results for the effect of parameter 119873119903with considering the effect of 119889119888 Considering that 119883 lt 1of fractional denominator log2119883 in (8) and (13) we considera larger range of values of 119873119903 and vary the values of 119873119903 fordifferent values of 119889119888 (ie let the maximum value of 119873119903 beequal to lfloor11988927119888 rfloor) In order to facilitate drawing a numericalvalue 119909 on the 119909-axis of Figure 5 only denotes an exponentialquantity and in fact the corresponding value of 119873119903 is equalto lfloor119889119909119888 rfloor From Figure 5 we can see the following
(1) With the increase of 119873119903 the multihop capabilities ofthree schemes are improved correspondingly and themultihop capability of CFP is better than CFIP andDFIP Specifically when 119889119888 = 3m the average largestnumber of hops of CFP CFIP and DFIP is 103 63and 5 respectively when 119889119888 = 8m the average valuesare 75 51 and 3 respectively when 119889119888 = 15m theaverage values are 6 46 and 2 respectively
(2) Although with the increase of 119889119888 the multihopcapabilities of three schemes are weakened corre-spondingly the degree of weakening is depressedcompared with the case of considering the effect ofparameters 120578 or 120572 For example considering that thevalue of 119889119888 changes from 3m to 15m in CFP schemethe degree of weakening is (103 minus 6)103 times 100 =2718 when considering the effect of parameter119873119903but the value is (18 minus 31)18 times 100 = 8278when considering the effect of parameter 120578Thereforeincreasing the number119873119903 of relay nodes can improvethemultihop capabilities effectively when the CTD 119889119888
Wireless Communications and Mobile Computing 7
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
02 03 04 05 06 07 08010
5
10
15
20
25
30
35
40
45
50Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
02 03 04 05 06 07 08011
2
3
4
5
6
7
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
1
2
3
4
5
The l
arge
st nu
mbe
r of h
ops
02 03 04 05 06 07 0801
(c)
Figure 3 Numerical results for the impact of parameter 120578 on themultihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8mand (c) 119889119888 = 15m where 119875119904 = 2W 120572 = 05 and119873119903 = 20
increases it is because119873119903 has a larger range value andcan affect the values of 119871cfpmax 119871cfipmax and 119871dfipmax in (8)(13) and (17) obviously
In Figure 6 we investigate the impact of parameter 119875119904on the numerical results with considering the effect of 119889119888 Inorder to compare the results with parameter 119873119903 in a larger
range of values we also let a numerical value 119909 on the 119909-axisof Figure 6 only denote an exponential quantity where thecorresponding value of 119875119904 is equal to lfloor119889119909119888 rfloor From Figure 6 wecan observe the following
(1) With the increase of 119875119904 the multihop capabilitiesof the three schemes are improved correspondingly
8 Wireless Communications and Mobile Computing
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
02 03 04 05 06 07 08 09012
4
6
8
10
12
14
16
18
20
22Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
02 03 04 05 06 07 08 09011
2
3
4
5
6
7
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
02 03 04 05 06 07 08 0901 1
2
3
4
5
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 4 Numerical results for the impact of parameter 120572 on the multihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8m(c) and 119889119888 = 15m where 119875119904 = 2W 120578 = 06 and119873119903 = 20
and the multihop capability of CFP is better thanCFIP and DFIP However with the increase of 119889119888the multihop capabilities of the three schemes areweakened correspondingly Specifically when 119889119888 =3m the average largest number of hops of CFP CFIPand DFIP is 214 99 and 55 respectively when
119889119888 = 8m the average values are 59 48 and 34respectively when 119889119888 = 15m the average values are41 36 and 28 respectively
(2) Compared with the case of considering the effectof parameter 119873119903 the degree of weakening is much
Wireless Communications and Mobile Computing 9
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
18
20Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
18
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 5 Numerical results for the impact of parameter 119873119903 on the multihop capability with different values of CTD (a) 119889119888 = 3m (b)119889119888 = 8m and (c) 119889119888 = 15m where 119875119904 = 2W 120578 = 06 and 120572 = 05
worse For example considering that the value of 119889119888changes from 3m to 15m in CFP scheme the degreeofweakening is (214minus41)214times100 = 808whenconsidering the effect of parameter119875119904 but the value ofthe degree of weakening is (103 minus 6)103 times 100 =2718 when considering the effect of parameter119873119903
Therefore for improving the multihop capabilitiesincreasing the value of parameter119873119903 is more effective
According to the abovementioned results and analysiswe can obtain the important conclusions as follows (1) themultihop capability of CFP is better than CFIP and DFIP
10 Wireless Communications and Mobile Computing
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Ps
4
6
8
10
12
14
16
18
20
22
24
26Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
7
8
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 6 Numerical results for the impact of parameter119875119904 on themultihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8mand (c) 119889119888 = 15m where 120578 = 06 120572 = 05 and119873119903 = 20
(2) all of the parameters 119875119904 120578 120572 119873119903 and 119889119888 can affectthe multihop capability of the three schemes where theparameter 119889119888 can produce an important effect and (3) forimproving the multihop capability it is best effective toincrease the value of parameter119873119903 Of course we can furtherimprove the multihop capability by simultaneously adjustingthe values of parameters 119875119904 120578 and 120572
7 Conclusions
In this paper we study SWIPT in multihop wireless coop-erative networks where the multihop capabilities of CFPCFIP and DFIP schemes are analyzed For this purposewe construct analysis model to investigate the multihopcapabilities of CFP CFIP and DFIP schemes respectively
Wireless Communications and Mobile Computing 11
Finally numerical results show that the multihop capabilityof CFP is better than CFIP and DFIP and for improvingthe multihop capabilities it is best effective to increase theaverage number of relay nodes in cooperative set
Through the analysis model proposed in this paper theappropriate values of related parameters that is initial energyof source node the number of relay nodes the energyharvesting efficiency coefficient and power splitting coeffi-cient can be set to achieve the given transmission hops fromsource to destination
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work is funded by the China Postdoctoral Science Foun-dation (Grant no 2014M561627) the Natural Science Foun-dation ofAnhui Province (Grant no 1308085MF101) theNat-ural Science Foundation of Anhui Higher Education Insti-tutions (Grant no KJ2014A172) and the Science ResearchProject of Chaohu University (Grant no XLZ-201703)
References
[1] L R Varshney ldquoTransporting information and energy simul-taneouslyrdquo in Proceedings of the IEEE International Symposiumon Information Theory (ISIT rsquo08) pp 1612ndash1616 IEEE TorontoCanada July 2008
[2] P Grover and A Sahai ldquoShannonmeets tesla wireless informa-tion andpower transferrdquo inProceedings of the IEEE InternationalSymposium on Information Theory (ISIT rsquo10) pp 2363ndash2367Austin Tex USA June 2010
[3] R Zhang and C K Ho ldquoMIMO broadcasting for simultaneouswireless information and power transferrdquo IEEE Transactions onWireless Communications vol 12 no 5 pp 1989ndash2001 2013
[4] J N LanemanDN Tse andGWornell ldquoCooperative diversityin wireless networks efficient protocols and outage behaviorrdquoInstitute of Electrical and Electronics Engineers Transactions onInformation Theory vol 50 no 12 pp 3062ndash3080 2004
[5] A A Nasir X Zhou S Durrani and R A Kennedy ldquoWireless-powered relays in cooperative communications time-switchingrelaying protocols and throughput analysisrdquo IEEE Transactionson Communications vol 63 no 5 pp 1607ndash1622 2015
[6] E Chen M Xia D B da Costa and S Aissa ldquoMulti-Hopcooperative relaying with energy harvesting from cochannelinterferencesrdquo IEEE Communications Letters vol 21 no 5 pp1199ndash1202 2017
[7] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4761 2013
[8] L Liu R Zhang and K-C Chua ldquoWireless information trans-fer with opportunistic energy harvestingrdquo IEEE Transactions onWireless Communications vol 12 no 1 pp 288ndash300 2013
[9] L Liu R Zhang and K C Chua ldquoWireless information andpower transfer a dynamic power splitting approachrdquo IEEETransactions on Communications vol 61 no 9 pp 3990ndash40012013
[10] H Ju and R Zhang ldquoThroughput maximization in wire-less powered communication networksrdquo IEEE Transactions onWireless Communications vol 13 no 1 pp 418ndash428 2014
[11] R Morsi D S Michalopoulos and R Schober ldquoMultiuserscheduling schemes for simultaneous wireless information andpower transfer over fading channelsrdquo IEEE Transactions onWireless Communications vol 14 no 4 pp 1967ndash1982 2015
[12] C Zhong X Chen Z Zhang and G K Karagiannidis ldquoWire-less-powered communications performance analysis and opti-mizationrdquo IEEE Transactions on Communications vol 63 no12 pp 5178ndash5190 2015
[13] N Zhao F R Yu and V C M Leung ldquoOpportunistic com-munications in interference alignment networks with wirelesspower transferrdquo IEEE Wireless Communications Magazine vol22 no 1 pp 88ndash95 2015
[14] N Zhao ldquoJoint optimization of power splitting and allocationfor SWIPT in interference alignment networksrdquo in v preprintpp 1701ndash01952 httpsarxivorgabs170101952 2017
[15] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[16] D-T Do ldquoTime power switching based relaying protocol inenergy harvesting mobile node optimal throughput analysisrdquoMobile Information Systems vol 2015 Article ID 769286 8pages 2015
[17] C Zhang and Y Chen ldquoWireless power transfer strategies forcooperative relay system tomaximize information throughputrdquoIEEE Access vol 5 pp 2573ndash2582 2017
[18] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[19] Y Liu LWangM Elkashlan T Q Duong andANallanathanldquoTwo-way relay networks with wireless power transfer designand performance analysisrdquo IET Communications vol 10 no 14pp 1810ndash1819 2016
[20] T P Do I Song and Y H Kim ldquoSimultaneous wireless transferof power and information in a decode-and-forward two-wayrelaying networkrdquo IEEE Transactions on Wireless Communica-tions vol 16 no 3 pp 1579ndash1592 2017
[21] C Zhong H A Suraweera G Zheng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[22] Y Zeng and R Zhang ldquoFull-duplex wireless-powered relay withself-energy recyclingrdquo IEEE Wireless Communications Lettersvol 4 no 2 pp 201ndash204 2015
[23] D Wang R Zhang X Cheng and L Yang ldquoCapacity-enhancing full-duplex relay networks based on power-splitting(PS-)SWIPTrdquo IEEE Transactions on Vehicular Technology vol66 no 6 pp 5445ndash5450 2017
[24] ZDing I Krikidis B Sharif andHV Poor ldquoWireless informa-tion and power transfer in cooperative networks with spatiallyrandom relaysrdquo IEEETransactions onWireless Communicationsvol 13 no 8 pp 4440ndash4453 2014
[25] M Haghifam B Makki M Nasiri-Kenari and T SvenssonOn wireless energy and information transfer in relay networkshttpsarxivorgabs160707087 2016
12 Wireless Communications and Mobile Computing
[26] Y Liu ldquoWireless information and power transfer formultirelay-assisted cooperative communicationrdquo IEEE CommunicationsLetters vol 20 no 4 pp 784ndash787 2016
[27] J N Laneman and G W Wornell ldquoDistributed space-timecoded protocols for exploiting cooperative diversity in wirelessnetworksrdquo Institute of Electrical and Electronics Engineers Trans-actions on Information Theory vol 49 no 10 pp 2415ndash24252003
[28] IEEE Std IEEE Standard for Wireless LAN Medium AccessControl (MAC) and Physical Layer (PHY) Specifications(1999)
[29] N T Do V N Q Bao and B An ldquoOutage performance analysisof relay selection schemes in wireless energy harvesting coop-erative networks over non-identical rayleigh fading channelsrdquoSensors vol 16 no 3 article no 295 2016
Chemical EngineeringInternational Journal of Antennas and
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Navigation and Observation
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Hindawi
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Advances in
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Submit your manuscripts atwwwhindawicom
4 Wireless Communications and Mobile Computing
the receiver Therefore for the special signal we let the relaystransmit a PTS (power ready to send) frame cooperativelyin which the frame format is extended to the RTS and CTScontrol frames in IEEE 80211 protocol [28]
First of all let us consider that the signal is transmittedfrom the source to receiver node1199011 in Figure 1 Let 119910119903119894 denotethe received signal at relay 119894 around the source node in the firstphase we can derive
where ℎ119904119894 is the source to relay 119894 channel gain 119889119904119894 is thedistance from 119878 to relay 119894 119898 is the path loss exponent 119899119903119894is the additive white Gaussian noise at relay 119894 with zero meanand 1205902119899119903 variance and 119909119904 is the normalized information signalfrom the source Because the relays do not decode the signalfrom the transmitter to receiver we can let 120572119894 = 0 Accordingto (1) the harvested energy 119864119903119894 at relay 119894 during energyharvesting time 119879119905V is given by
where 120578 is the energy harvesting efficiency coefficient and119879119905Vis the transmission time for the signal Note that we do notconsider multirate network scenarios which means that 119879119905Vis equal for any one hop in the routing path In (2) we ignorethe impact of noise since the noise power is normally verysmall and below the sensitivity of the energy receiver [29]
In the second phase each relay 119894 uses the transmissionpower 119875119903119894 = 119864119903119894119879119888V and forms a cooperative set with otherrelays to transmit the PTS frame towards the receiver 1199011simultaneously Consequently 1199011 does not decode the PTSframe but only harvests the energy that can be expressed by1198641199011 as
where ℎ1198941199011 is channel gain from the relay 119894 to receiver 1199011 119879119888Vis the transmission time for the PTS119873119903 is the average numberof relay nodes in cooperative set and 1198891198941199011 is the distance fromthe relay 119894 to receiver 1199011 So we can derive the transmissionpower 1198751199011 from 1199011 to receiver node 1199012 in the second hop asfollows
According to the abovementioned analysis let 119875119901119895minus1denote 119895th (119895 ge 2) hop transmission power where the signalis transmitted from 119901119895minus1 to 119901119895 node (1199010 is the source node)we can obtain
where |ℎ119901119896minus2119894| |ℎ119894119901119896minus1 | denote the channel gains from 119901119896minus2to its relay 119894 and from its relay 119894 to 119901119896minus1 respectively and119889119898119901119896minus2 119894 119889119898119894119901119896minus1 denote the distance from 119901119896minus2 to its relay 119894 andfrom its relay 119894 to 119901119896minus1 respectively So we can obtain thesignal-to-noise ratio (SNR) 120574119895 at the receiver node 119901119895 asfollows 120574119895 = 119875119901119895minus1|ℎ119901119895minus1 119901119895 |2(1205902119901119895minus1 119901119895119889119898119901119895minus1119901119895) where 1205902119901119895minus1119901119895denotes the variance of additive white Gaussian noise atreceiver 119901119895 Given a targeted throughput 1198770 if we find themaximum value of 119897 for that log2(1 + 120574119897) ge 1198770 holds wecan derive that the value of 119897 is the largest number of hopssupported by the CFP scheme Therefore we can derive
In formula (6) for calculability we replace the exponentialrandom variables |ℎ119901119896minus2119894|2 |ℎ119894119901119896minus1 |2 and |ℎ119901119897minus1119901119897 |2with theirmean values 120582119903 120582119891 and 120582119889 respectively Since we haveassumed that the channel gain is circular symmetric complexGaussian randomvariables with zeromean and unit variancewe get 120582119903 = 120582119891 = 120582119889 = 1 Furthermore we assume that119889119901119896minus2 119894119889119894119901119896minus1 is constant and equal to 119889119888 Also 119889119901119897minus1119901119897 whichis the distance from 119901119897minus1 to 119901119897 is set to be constant value 119889119889Consequently we can obtain
(119897 minus 1) log2 (1205782119873119903119889119898119888 ) ge log2 (21198770 minus 1119875119904 119889119898119889 1205902) (7)
where we let 1205902119901119897minus1119901119897 be equal to constant value 1205902 In formula(7) if (21198770minus1)119889119898119889 1205902 gt 119875119904 that is log2(119875119904(119889119898119889 1205902)+1) lt 1198770 thesignal cannot be transmitted from the source node to the nexthop for satisfying the targeted throughput 1198770 Therefore formultihop transmission it is required that (21198770 minus1)119889119898119889 1205902 lt 119875119904Furthermore we consider that in a routing path (such asin Figure 1) the transmission power of node 119901119894+1 is lowerthan that of node 119901119894 because the transmission power of node119901119894+1 is charged from the node 119901119894 So it is also required that1205782(119873119903119889119898119888 ) lt 1 Note that we do not consider the caseof 1205782(119873119903119889119898119888 ) ge 1 because in this case the transmissionpower of node 119901119894+1 is greater than that of node 119901119894 so that theinformation can be transmitted all the time Accordingly wecan derive the largest number of hops 119871cfpmax supported by theCFP scheme as follows
where lfloorrfloor denotes the round down function From formula(8) we can find that the largest number of hops is affected bythe parameters 119875119904 120578 120572119873119903 and 119889119888 In simulation we will givethe detailed analysis for these parameters
Wireless Communications and Mobile Computing 5
52 For CFIP Scheme Unlike CFP scheme in CFIP schemea relay 119894 not only harvests the power but also decodes theinformation from the transmitter So we have 120572119894 = 0 Ifwe consider that the transmitter is the source node a relay119894 harvests the power 1198641015840119903119894 as follows
1198641015840119903119894 = 120578 (1 minus 120572) 119875119904 1003816100381610038161003816ℎ11990411989410038161003816100381610038162 119879119905V119889119898119904119894 (9)
Note here that for ease of analysis we let 120572119894 be constant andequal to 120572 Let 1198751015840119901119895minus1 denote jth (119895 ge 2) hop transmissionpower where the signal is transmitted from 119901119895minus1 to 119901119895through multiple relays we can obtain
1198751015840119901119895minus1 = (120578 (1 minus 120572))2(119895minus1) 119875119904times 119895prod119896=2
where1198731015840119903 is the average number of relay nodes in cooperativeset Note that because only the relay which can decodethe information successfully becomes one member of thecooperative set in CFIP scheme we have 1198731015840119903 le 119873119903 Let 1205741015840119895denote SNR at the receiver node 119901119895 we can derive
1205741015840119895 = 120578 (1 minus 120572) 1198731015840119903sum119894=1
where 1205902119894119901119895 is the variance of additive white Gaussian noiseat receiver 119901119895 Similarly to the above analysis for CFP whilerequiring log2(1 + 1205741015840119897 ) ge 1198770 we can obtain
(119897 minus 1) log2 ((120578 (1 minus 120572))2 1198731015840119903119889119898119888 )ge log2((21198770 minus 1) 119889119898119888 1205902120578 (1 minus 120572)1198731015840119903119875119904 )
(12)
where we let 1205902119894119901119895 be equal to constant value 1205902 In formula(12) we have (120578(1minus120572))2(1198731015840119903119889119898119888 ) lt 1 because the transmissionpower of node119901119894+1 is lower than that of node119901119894 Furthermorefor multihop transmission we have (21198770 minus 1)119889119898119888 1205902120578(1 minus120572)1198731015840119903119875119904 lt 1 that is log2(120578(1 minus 120572)1198751199041198731015840119903119889119898119888 1205902 + 1) gt 1198770Otherwise the information cannot be transmitted from thesource to 1199011 Consequently the largest number of hops 119871cfipmaxsupported by the CFIP scheme can be given as follows
119871cfipmax = 1 + lfloor log2 ((21198770 minus 1) 119889119898119888 1205902120578 (1 minus 120572)1198731015840119903119875119904)log2 (1205782 (1 minus 120572)2 (1198731015840119903119889119898119888 )) rfloor (13)
53 For DFIP Scheme Unlike CFP and CFIP schemes inDFIP scheme the receiver harvests the power and decodesthe information from the transmitter directly without relaycooperation Therefore if we consider that the transmitter is
the source node the receiver 1199011 harvests the power 1198641198891 asfollows
1198641198891 = 120578 (1 minus 120572) 119875119904 1003816100381610038161003816ℎ119904110038161003816100381610038162 119879119905V1198891198981199041 (14)
where ℎ1199041 is channel gain from the source node to receiver1199011 and 1198891199041 is the distance from the source to 1199011 Then thenode 1199011 transmits the information to the next hop node 1199012using the power 1198751198891 = 1198641198891119879119905V Let 119875119889119895minus1 denote 119895th (119895 ge 2)hop transmission power where the signal is transmitted from119901119895minus1 to 119901119895 we can obtain
119875119889119895minus1 = (120578 (1 minus 120572))(119895minus1) 119875119904 119895prod119896=2
So we can obtain SNR 120574119889119895 at receiver 119901119895 as 120574119889119895 =119875119889119895minus1|ℎ119901119895minus1 119901119895 |2(1205902119901119895minus1 119901119895119889119898119901119895minus1 119901119895) Similarly to the above analy-sis for CFP and CFIP while requiring log2(1 + 120574119889119897 ) ge 1198770 wecan obtain
(119897 minus 1) log2 (120578 (1 minus 120572)119889119898119889
) ge log2 (21198770 minus 1119875119904 119889119898119889 1205902) (16)
Accordingly we can derive the largest number of hops 119871dfipmaxsupported by the DFIP scheme as follows
119871dfipmax = 1 + lfloor log2 (((21198770 minus 1) 119875119904) 119889119898119889 1205902)log2 (120578 (1 minus 120572) 119889119898119889 ) rfloor (17)
In formula (17) we have 120578(1 minus 120572)119889119898119889 lt 1 because thetransmission power of node 119901119894+1 is lower than that of node 119901119894Formultihop transmission it is required that (21198770 minus1)119889119898119889 1205902 lt119875119904 Otherwise the information cannot be transmitted fromthe source to 11990116 Numerical Results and Analysis
In this section we perform computer simulations to validateour theory analysis and gain insights into the multihopcapabilities of the proposed CFP CFIP and DFIP schemesAlso we need to observe whether the values of 119871cfpmax schemeare larger than the values of 119871cfipmax and 119871dfipmax with the giventargeted throughput 1198770 under the effect of different networkparameters In the following simulations we set 1205902 = minus70 dB1198770 = 2 bitssecHz and 119898 = 27 (which corresponds to anurban cellular network environment [5]) and give the numer-ical results considering the effect of parameters 119875119904 120578 120572 119873119903and 119889119888 For simplicity we assume that 119889119889 = 119889119888 and1198731015840119903 = 119873119903
First we observe the numerical results about the valuesof 119871cfpmax 119871cfipmax and 119871dfipmax affected by the values of cooperativetransmission distance (CTD) 119889119888 that denotes the productof two distances from sender to relay and from relay toreceiver which are shown in Figure 2 From Figure 2 wecan find that the analytical results are practically consistentwith the simulation results which verifies the effectiveness ofour theory analytical model Note that for CFIP scheme the
6 Wireless Communications and Mobile Computing
3 4 5 6 7 8 9 102dc (m)
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
2468
1012141618202224262830323436
The l
arge
st nu
mbe
r of h
ops
Figure 2 Analytical versus simulation results with different CTDwhere 119875119904 = 2W 120578 = 06 120572 = 05 and119873119903 = 10simulation results are not in full agreement with the analysisresults because1198731015840119903 is smaller than119873119903 in practice Besides wecan also observe the following
(1) The CTD has an important impact on the largestnumber of transmission hops it is because withthe increase of 119889119888 both the harvested energy andreceived signal strength at sender node of the next hopdecrease due to the larger path loss Consequently theachievable number of transmission hops is reducedwith no sufficient energy especially for the largervalues of 119889119888
(2) The multihop capability of CFP is better than CFIPand DFIP it is because in CFP scheme multiplerelays forward only the power (not the information)towards the receiver cooperatively so that the sendernode of the next hop can obtain more energy tosupport the larger transmission hops especially forthe smaller values of 119889119888
(3) The multihop capability of CFP and CFIP is betterthan DFIP since they use multiple relays to harvestenergy It can be observed in (8) and (13) that thevalues of 119871cfpmax and 119871cfipmax increase with the increase of119873119903 and 1198731015840119903 Furthermore if we consider the fact thatthe value of119873119903 is larger than1198731015840119903 this can further themultihop capability of CFP compared to CFIP
As the analytical results agree well with the simulationresults for the purpose of conciseness in the following wewill plot the simulation results for different parameters 120578 120572
119873119903 and119875119904 when119889119888 = 3mBut for119889119888 = 8mand119889119888 = 15mweonly give analytical results Next we investigate the impacts oftwo parameters 120578 and120572 on the largest number of transmissionhops respectively with considering the effect of CTD 119889119888From Figures 3 and 4 we can obtain the following
(1) For the small values of 119889119888 by increasing the value of120578 or reducing the value of 120572 the largest number oftransmission hops can be improved But if increasingthe value of 119889119888 the largest number of transmissionhops cannot obtain obvious improvement throughchanging the values of 120578 or 120572 In (8) (13) and (17)because 120578 and 120572 have a limited range of values (isin[0 1]) while 119889119888 has a larger value the values of119871cfpmax 119871cfipmax and 119871dfipmax cannot be affected obviously bychanging the values of 120578 or 120572
(2) The multihop capability of CFP is better than CFIPand DFIP especially for the smaller values of 119889119888which is because multiple relays forward only thepower cooperatively For example from Figure 3 wecan observe the impact of parameter 120578 on resultsand obtain that when 119889119888 = 3m the average largestnumber of hops of CFP CFIP and DFIP is 18 8 and49 respectively when 119889119888 = 8m the average valuesare 45 38 and 29 respectively when 119889119888 = 15m theaverage values are 31 28 and 2 respectively
Finally let us study the impacts of two parameters 119873119903and 119875119904 on the multihop capability respectively In Figure 5we give the simulation results for the effect of parameter 119873119903with considering the effect of 119889119888 Considering that 119883 lt 1of fractional denominator log2119883 in (8) and (13) we considera larger range of values of 119873119903 and vary the values of 119873119903 fordifferent values of 119889119888 (ie let the maximum value of 119873119903 beequal to lfloor11988927119888 rfloor) In order to facilitate drawing a numericalvalue 119909 on the 119909-axis of Figure 5 only denotes an exponentialquantity and in fact the corresponding value of 119873119903 is equalto lfloor119889119909119888 rfloor From Figure 5 we can see the following
(1) With the increase of 119873119903 the multihop capabilities ofthree schemes are improved correspondingly and themultihop capability of CFP is better than CFIP andDFIP Specifically when 119889119888 = 3m the average largestnumber of hops of CFP CFIP and DFIP is 103 63and 5 respectively when 119889119888 = 8m the average valuesare 75 51 and 3 respectively when 119889119888 = 15m theaverage values are 6 46 and 2 respectively
(2) Although with the increase of 119889119888 the multihopcapabilities of three schemes are weakened corre-spondingly the degree of weakening is depressedcompared with the case of considering the effect ofparameters 120578 or 120572 For example considering that thevalue of 119889119888 changes from 3m to 15m in CFP schemethe degree of weakening is (103 minus 6)103 times 100 =2718 when considering the effect of parameter119873119903but the value is (18 minus 31)18 times 100 = 8278when considering the effect of parameter 120578Thereforeincreasing the number119873119903 of relay nodes can improvethemultihop capabilities effectively when the CTD 119889119888
Wireless Communications and Mobile Computing 7
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
02 03 04 05 06 07 08010
5
10
15
20
25
30
35
40
45
50Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
02 03 04 05 06 07 08011
2
3
4
5
6
7
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
1
2
3
4
5
The l
arge
st nu
mbe
r of h
ops
02 03 04 05 06 07 0801
(c)
Figure 3 Numerical results for the impact of parameter 120578 on themultihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8mand (c) 119889119888 = 15m where 119875119904 = 2W 120572 = 05 and119873119903 = 20
increases it is because119873119903 has a larger range value andcan affect the values of 119871cfpmax 119871cfipmax and 119871dfipmax in (8)(13) and (17) obviously
In Figure 6 we investigate the impact of parameter 119875119904on the numerical results with considering the effect of 119889119888 Inorder to compare the results with parameter 119873119903 in a larger
range of values we also let a numerical value 119909 on the 119909-axisof Figure 6 only denote an exponential quantity where thecorresponding value of 119875119904 is equal to lfloor119889119909119888 rfloor From Figure 6 wecan observe the following
(1) With the increase of 119875119904 the multihop capabilitiesof the three schemes are improved correspondingly
8 Wireless Communications and Mobile Computing
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
02 03 04 05 06 07 08 09012
4
6
8
10
12
14
16
18
20
22Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
02 03 04 05 06 07 08 09011
2
3
4
5
6
7
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
02 03 04 05 06 07 08 0901 1
2
3
4
5
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 4 Numerical results for the impact of parameter 120572 on the multihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8m(c) and 119889119888 = 15m where 119875119904 = 2W 120578 = 06 and119873119903 = 20
and the multihop capability of CFP is better thanCFIP and DFIP However with the increase of 119889119888the multihop capabilities of the three schemes areweakened correspondingly Specifically when 119889119888 =3m the average largest number of hops of CFP CFIPand DFIP is 214 99 and 55 respectively when
119889119888 = 8m the average values are 59 48 and 34respectively when 119889119888 = 15m the average values are41 36 and 28 respectively
(2) Compared with the case of considering the effectof parameter 119873119903 the degree of weakening is much
Wireless Communications and Mobile Computing 9
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
18
20Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
18
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 5 Numerical results for the impact of parameter 119873119903 on the multihop capability with different values of CTD (a) 119889119888 = 3m (b)119889119888 = 8m and (c) 119889119888 = 15m where 119875119904 = 2W 120578 = 06 and 120572 = 05
worse For example considering that the value of 119889119888changes from 3m to 15m in CFP scheme the degreeofweakening is (214minus41)214times100 = 808whenconsidering the effect of parameter119875119904 but the value ofthe degree of weakening is (103 minus 6)103 times 100 =2718 when considering the effect of parameter119873119903
Therefore for improving the multihop capabilitiesincreasing the value of parameter119873119903 is more effective
According to the abovementioned results and analysiswe can obtain the important conclusions as follows (1) themultihop capability of CFP is better than CFIP and DFIP
10 Wireless Communications and Mobile Computing
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Ps
4
6
8
10
12
14
16
18
20
22
24
26Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
7
8
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 6 Numerical results for the impact of parameter119875119904 on themultihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8mand (c) 119889119888 = 15m where 120578 = 06 120572 = 05 and119873119903 = 20
(2) all of the parameters 119875119904 120578 120572 119873119903 and 119889119888 can affectthe multihop capability of the three schemes where theparameter 119889119888 can produce an important effect and (3) forimproving the multihop capability it is best effective toincrease the value of parameter119873119903 Of course we can furtherimprove the multihop capability by simultaneously adjustingthe values of parameters 119875119904 120578 and 120572
7 Conclusions
In this paper we study SWIPT in multihop wireless coop-erative networks where the multihop capabilities of CFPCFIP and DFIP schemes are analyzed For this purposewe construct analysis model to investigate the multihopcapabilities of CFP CFIP and DFIP schemes respectively
Wireless Communications and Mobile Computing 11
Finally numerical results show that the multihop capabilityof CFP is better than CFIP and DFIP and for improvingthe multihop capabilities it is best effective to increase theaverage number of relay nodes in cooperative set
Through the analysis model proposed in this paper theappropriate values of related parameters that is initial energyof source node the number of relay nodes the energyharvesting efficiency coefficient and power splitting coeffi-cient can be set to achieve the given transmission hops fromsource to destination
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work is funded by the China Postdoctoral Science Foun-dation (Grant no 2014M561627) the Natural Science Foun-dation ofAnhui Province (Grant no 1308085MF101) theNat-ural Science Foundation of Anhui Higher Education Insti-tutions (Grant no KJ2014A172) and the Science ResearchProject of Chaohu University (Grant no XLZ-201703)
References
[1] L R Varshney ldquoTransporting information and energy simul-taneouslyrdquo in Proceedings of the IEEE International Symposiumon Information Theory (ISIT rsquo08) pp 1612ndash1616 IEEE TorontoCanada July 2008
[2] P Grover and A Sahai ldquoShannonmeets tesla wireless informa-tion andpower transferrdquo inProceedings of the IEEE InternationalSymposium on Information Theory (ISIT rsquo10) pp 2363ndash2367Austin Tex USA June 2010
[3] R Zhang and C K Ho ldquoMIMO broadcasting for simultaneouswireless information and power transferrdquo IEEE Transactions onWireless Communications vol 12 no 5 pp 1989ndash2001 2013
[4] J N LanemanDN Tse andGWornell ldquoCooperative diversityin wireless networks efficient protocols and outage behaviorrdquoInstitute of Electrical and Electronics Engineers Transactions onInformation Theory vol 50 no 12 pp 3062ndash3080 2004
[5] A A Nasir X Zhou S Durrani and R A Kennedy ldquoWireless-powered relays in cooperative communications time-switchingrelaying protocols and throughput analysisrdquo IEEE Transactionson Communications vol 63 no 5 pp 1607ndash1622 2015
[6] E Chen M Xia D B da Costa and S Aissa ldquoMulti-Hopcooperative relaying with energy harvesting from cochannelinterferencesrdquo IEEE Communications Letters vol 21 no 5 pp1199ndash1202 2017
[7] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4761 2013
[8] L Liu R Zhang and K-C Chua ldquoWireless information trans-fer with opportunistic energy harvestingrdquo IEEE Transactions onWireless Communications vol 12 no 1 pp 288ndash300 2013
[9] L Liu R Zhang and K C Chua ldquoWireless information andpower transfer a dynamic power splitting approachrdquo IEEETransactions on Communications vol 61 no 9 pp 3990ndash40012013
[10] H Ju and R Zhang ldquoThroughput maximization in wire-less powered communication networksrdquo IEEE Transactions onWireless Communications vol 13 no 1 pp 418ndash428 2014
[11] R Morsi D S Michalopoulos and R Schober ldquoMultiuserscheduling schemes for simultaneous wireless information andpower transfer over fading channelsrdquo IEEE Transactions onWireless Communications vol 14 no 4 pp 1967ndash1982 2015
[12] C Zhong X Chen Z Zhang and G K Karagiannidis ldquoWire-less-powered communications performance analysis and opti-mizationrdquo IEEE Transactions on Communications vol 63 no12 pp 5178ndash5190 2015
[13] N Zhao F R Yu and V C M Leung ldquoOpportunistic com-munications in interference alignment networks with wirelesspower transferrdquo IEEE Wireless Communications Magazine vol22 no 1 pp 88ndash95 2015
[14] N Zhao ldquoJoint optimization of power splitting and allocationfor SWIPT in interference alignment networksrdquo in v preprintpp 1701ndash01952 httpsarxivorgabs170101952 2017
[15] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[16] D-T Do ldquoTime power switching based relaying protocol inenergy harvesting mobile node optimal throughput analysisrdquoMobile Information Systems vol 2015 Article ID 769286 8pages 2015
[17] C Zhang and Y Chen ldquoWireless power transfer strategies forcooperative relay system tomaximize information throughputrdquoIEEE Access vol 5 pp 2573ndash2582 2017
[18] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[19] Y Liu LWangM Elkashlan T Q Duong andANallanathanldquoTwo-way relay networks with wireless power transfer designand performance analysisrdquo IET Communications vol 10 no 14pp 1810ndash1819 2016
[20] T P Do I Song and Y H Kim ldquoSimultaneous wireless transferof power and information in a decode-and-forward two-wayrelaying networkrdquo IEEE Transactions on Wireless Communica-tions vol 16 no 3 pp 1579ndash1592 2017
[21] C Zhong H A Suraweera G Zheng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[22] Y Zeng and R Zhang ldquoFull-duplex wireless-powered relay withself-energy recyclingrdquo IEEE Wireless Communications Lettersvol 4 no 2 pp 201ndash204 2015
[23] D Wang R Zhang X Cheng and L Yang ldquoCapacity-enhancing full-duplex relay networks based on power-splitting(PS-)SWIPTrdquo IEEE Transactions on Vehicular Technology vol66 no 6 pp 5445ndash5450 2017
[24] ZDing I Krikidis B Sharif andHV Poor ldquoWireless informa-tion and power transfer in cooperative networks with spatiallyrandom relaysrdquo IEEETransactions onWireless Communicationsvol 13 no 8 pp 4440ndash4453 2014
[25] M Haghifam B Makki M Nasiri-Kenari and T SvenssonOn wireless energy and information transfer in relay networkshttpsarxivorgabs160707087 2016
12 Wireless Communications and Mobile Computing
[26] Y Liu ldquoWireless information and power transfer formultirelay-assisted cooperative communicationrdquo IEEE CommunicationsLetters vol 20 no 4 pp 784ndash787 2016
[27] J N Laneman and G W Wornell ldquoDistributed space-timecoded protocols for exploiting cooperative diversity in wirelessnetworksrdquo Institute of Electrical and Electronics Engineers Trans-actions on Information Theory vol 49 no 10 pp 2415ndash24252003
[28] IEEE Std IEEE Standard for Wireless LAN Medium AccessControl (MAC) and Physical Layer (PHY) Specifications(1999)
[29] N T Do V N Q Bao and B An ldquoOutage performance analysisof relay selection schemes in wireless energy harvesting coop-erative networks over non-identical rayleigh fading channelsrdquoSensors vol 16 no 3 article no 295 2016
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
Wireless Communications and Mobile Computing 5
52 For CFIP Scheme Unlike CFP scheme in CFIP schemea relay 119894 not only harvests the power but also decodes theinformation from the transmitter So we have 120572119894 = 0 Ifwe consider that the transmitter is the source node a relay119894 harvests the power 1198641015840119903119894 as follows
1198641015840119903119894 = 120578 (1 minus 120572) 119875119904 1003816100381610038161003816ℎ11990411989410038161003816100381610038162 119879119905V119889119898119904119894 (9)
Note here that for ease of analysis we let 120572119894 be constant andequal to 120572 Let 1198751015840119901119895minus1 denote jth (119895 ge 2) hop transmissionpower where the signal is transmitted from 119901119895minus1 to 119901119895through multiple relays we can obtain
1198751015840119901119895minus1 = (120578 (1 minus 120572))2(119895minus1) 119875119904times 119895prod119896=2
where1198731015840119903 is the average number of relay nodes in cooperativeset Note that because only the relay which can decodethe information successfully becomes one member of thecooperative set in CFIP scheme we have 1198731015840119903 le 119873119903 Let 1205741015840119895denote SNR at the receiver node 119901119895 we can derive
1205741015840119895 = 120578 (1 minus 120572) 1198731015840119903sum119894=1
where 1205902119894119901119895 is the variance of additive white Gaussian noiseat receiver 119901119895 Similarly to the above analysis for CFP whilerequiring log2(1 + 1205741015840119897 ) ge 1198770 we can obtain
(119897 minus 1) log2 ((120578 (1 minus 120572))2 1198731015840119903119889119898119888 )ge log2((21198770 minus 1) 119889119898119888 1205902120578 (1 minus 120572)1198731015840119903119875119904 )
(12)
where we let 1205902119894119901119895 be equal to constant value 1205902 In formula(12) we have (120578(1minus120572))2(1198731015840119903119889119898119888 ) lt 1 because the transmissionpower of node119901119894+1 is lower than that of node119901119894 Furthermorefor multihop transmission we have (21198770 minus 1)119889119898119888 1205902120578(1 minus120572)1198731015840119903119875119904 lt 1 that is log2(120578(1 minus 120572)1198751199041198731015840119903119889119898119888 1205902 + 1) gt 1198770Otherwise the information cannot be transmitted from thesource to 1199011 Consequently the largest number of hops 119871cfipmaxsupported by the CFIP scheme can be given as follows
119871cfipmax = 1 + lfloor log2 ((21198770 minus 1) 119889119898119888 1205902120578 (1 minus 120572)1198731015840119903119875119904)log2 (1205782 (1 minus 120572)2 (1198731015840119903119889119898119888 )) rfloor (13)
53 For DFIP Scheme Unlike CFP and CFIP schemes inDFIP scheme the receiver harvests the power and decodesthe information from the transmitter directly without relaycooperation Therefore if we consider that the transmitter is
the source node the receiver 1199011 harvests the power 1198641198891 asfollows
1198641198891 = 120578 (1 minus 120572) 119875119904 1003816100381610038161003816ℎ119904110038161003816100381610038162 119879119905V1198891198981199041 (14)
where ℎ1199041 is channel gain from the source node to receiver1199011 and 1198891199041 is the distance from the source to 1199011 Then thenode 1199011 transmits the information to the next hop node 1199012using the power 1198751198891 = 1198641198891119879119905V Let 119875119889119895minus1 denote 119895th (119895 ge 2)hop transmission power where the signal is transmitted from119901119895minus1 to 119901119895 we can obtain
119875119889119895minus1 = (120578 (1 minus 120572))(119895minus1) 119875119904 119895prod119896=2
So we can obtain SNR 120574119889119895 at receiver 119901119895 as 120574119889119895 =119875119889119895minus1|ℎ119901119895minus1 119901119895 |2(1205902119901119895minus1 119901119895119889119898119901119895minus1 119901119895) Similarly to the above analy-sis for CFP and CFIP while requiring log2(1 + 120574119889119897 ) ge 1198770 wecan obtain
(119897 minus 1) log2 (120578 (1 minus 120572)119889119898119889
) ge log2 (21198770 minus 1119875119904 119889119898119889 1205902) (16)
Accordingly we can derive the largest number of hops 119871dfipmaxsupported by the DFIP scheme as follows
119871dfipmax = 1 + lfloor log2 (((21198770 minus 1) 119875119904) 119889119898119889 1205902)log2 (120578 (1 minus 120572) 119889119898119889 ) rfloor (17)
In formula (17) we have 120578(1 minus 120572)119889119898119889 lt 1 because thetransmission power of node 119901119894+1 is lower than that of node 119901119894Formultihop transmission it is required that (21198770 minus1)119889119898119889 1205902 lt119875119904 Otherwise the information cannot be transmitted fromthe source to 11990116 Numerical Results and Analysis
In this section we perform computer simulations to validateour theory analysis and gain insights into the multihopcapabilities of the proposed CFP CFIP and DFIP schemesAlso we need to observe whether the values of 119871cfpmax schemeare larger than the values of 119871cfipmax and 119871dfipmax with the giventargeted throughput 1198770 under the effect of different networkparameters In the following simulations we set 1205902 = minus70 dB1198770 = 2 bitssecHz and 119898 = 27 (which corresponds to anurban cellular network environment [5]) and give the numer-ical results considering the effect of parameters 119875119904 120578 120572 119873119903and 119889119888 For simplicity we assume that 119889119889 = 119889119888 and1198731015840119903 = 119873119903
First we observe the numerical results about the valuesof 119871cfpmax 119871cfipmax and 119871dfipmax affected by the values of cooperativetransmission distance (CTD) 119889119888 that denotes the productof two distances from sender to relay and from relay toreceiver which are shown in Figure 2 From Figure 2 wecan find that the analytical results are practically consistentwith the simulation results which verifies the effectiveness ofour theory analytical model Note that for CFIP scheme the
6 Wireless Communications and Mobile Computing
3 4 5 6 7 8 9 102dc (m)
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
2468
1012141618202224262830323436
The l
arge
st nu
mbe
r of h
ops
Figure 2 Analytical versus simulation results with different CTDwhere 119875119904 = 2W 120578 = 06 120572 = 05 and119873119903 = 10simulation results are not in full agreement with the analysisresults because1198731015840119903 is smaller than119873119903 in practice Besides wecan also observe the following
(1) The CTD has an important impact on the largestnumber of transmission hops it is because withthe increase of 119889119888 both the harvested energy andreceived signal strength at sender node of the next hopdecrease due to the larger path loss Consequently theachievable number of transmission hops is reducedwith no sufficient energy especially for the largervalues of 119889119888
(2) The multihop capability of CFP is better than CFIPand DFIP it is because in CFP scheme multiplerelays forward only the power (not the information)towards the receiver cooperatively so that the sendernode of the next hop can obtain more energy tosupport the larger transmission hops especially forthe smaller values of 119889119888
(3) The multihop capability of CFP and CFIP is betterthan DFIP since they use multiple relays to harvestenergy It can be observed in (8) and (13) that thevalues of 119871cfpmax and 119871cfipmax increase with the increase of119873119903 and 1198731015840119903 Furthermore if we consider the fact thatthe value of119873119903 is larger than1198731015840119903 this can further themultihop capability of CFP compared to CFIP
As the analytical results agree well with the simulationresults for the purpose of conciseness in the following wewill plot the simulation results for different parameters 120578 120572
119873119903 and119875119904 when119889119888 = 3mBut for119889119888 = 8mand119889119888 = 15mweonly give analytical results Next we investigate the impacts oftwo parameters 120578 and120572 on the largest number of transmissionhops respectively with considering the effect of CTD 119889119888From Figures 3 and 4 we can obtain the following
(1) For the small values of 119889119888 by increasing the value of120578 or reducing the value of 120572 the largest number oftransmission hops can be improved But if increasingthe value of 119889119888 the largest number of transmissionhops cannot obtain obvious improvement throughchanging the values of 120578 or 120572 In (8) (13) and (17)because 120578 and 120572 have a limited range of values (isin[0 1]) while 119889119888 has a larger value the values of119871cfpmax 119871cfipmax and 119871dfipmax cannot be affected obviously bychanging the values of 120578 or 120572
(2) The multihop capability of CFP is better than CFIPand DFIP especially for the smaller values of 119889119888which is because multiple relays forward only thepower cooperatively For example from Figure 3 wecan observe the impact of parameter 120578 on resultsand obtain that when 119889119888 = 3m the average largestnumber of hops of CFP CFIP and DFIP is 18 8 and49 respectively when 119889119888 = 8m the average valuesare 45 38 and 29 respectively when 119889119888 = 15m theaverage values are 31 28 and 2 respectively
Finally let us study the impacts of two parameters 119873119903and 119875119904 on the multihop capability respectively In Figure 5we give the simulation results for the effect of parameter 119873119903with considering the effect of 119889119888 Considering that 119883 lt 1of fractional denominator log2119883 in (8) and (13) we considera larger range of values of 119873119903 and vary the values of 119873119903 fordifferent values of 119889119888 (ie let the maximum value of 119873119903 beequal to lfloor11988927119888 rfloor) In order to facilitate drawing a numericalvalue 119909 on the 119909-axis of Figure 5 only denotes an exponentialquantity and in fact the corresponding value of 119873119903 is equalto lfloor119889119909119888 rfloor From Figure 5 we can see the following
(1) With the increase of 119873119903 the multihop capabilities ofthree schemes are improved correspondingly and themultihop capability of CFP is better than CFIP andDFIP Specifically when 119889119888 = 3m the average largestnumber of hops of CFP CFIP and DFIP is 103 63and 5 respectively when 119889119888 = 8m the average valuesare 75 51 and 3 respectively when 119889119888 = 15m theaverage values are 6 46 and 2 respectively
(2) Although with the increase of 119889119888 the multihopcapabilities of three schemes are weakened corre-spondingly the degree of weakening is depressedcompared with the case of considering the effect ofparameters 120578 or 120572 For example considering that thevalue of 119889119888 changes from 3m to 15m in CFP schemethe degree of weakening is (103 minus 6)103 times 100 =2718 when considering the effect of parameter119873119903but the value is (18 minus 31)18 times 100 = 8278when considering the effect of parameter 120578Thereforeincreasing the number119873119903 of relay nodes can improvethemultihop capabilities effectively when the CTD 119889119888
Wireless Communications and Mobile Computing 7
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
02 03 04 05 06 07 08010
5
10
15
20
25
30
35
40
45
50Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
02 03 04 05 06 07 08011
2
3
4
5
6
7
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
1
2
3
4
5
The l
arge
st nu
mbe
r of h
ops
02 03 04 05 06 07 0801
(c)
Figure 3 Numerical results for the impact of parameter 120578 on themultihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8mand (c) 119889119888 = 15m where 119875119904 = 2W 120572 = 05 and119873119903 = 20
increases it is because119873119903 has a larger range value andcan affect the values of 119871cfpmax 119871cfipmax and 119871dfipmax in (8)(13) and (17) obviously
In Figure 6 we investigate the impact of parameter 119875119904on the numerical results with considering the effect of 119889119888 Inorder to compare the results with parameter 119873119903 in a larger
range of values we also let a numerical value 119909 on the 119909-axisof Figure 6 only denote an exponential quantity where thecorresponding value of 119875119904 is equal to lfloor119889119909119888 rfloor From Figure 6 wecan observe the following
(1) With the increase of 119875119904 the multihop capabilitiesof the three schemes are improved correspondingly
8 Wireless Communications and Mobile Computing
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
02 03 04 05 06 07 08 09012
4
6
8
10
12
14
16
18
20
22Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
02 03 04 05 06 07 08 09011
2
3
4
5
6
7
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
02 03 04 05 06 07 08 0901 1
2
3
4
5
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 4 Numerical results for the impact of parameter 120572 on the multihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8m(c) and 119889119888 = 15m where 119875119904 = 2W 120578 = 06 and119873119903 = 20
and the multihop capability of CFP is better thanCFIP and DFIP However with the increase of 119889119888the multihop capabilities of the three schemes areweakened correspondingly Specifically when 119889119888 =3m the average largest number of hops of CFP CFIPand DFIP is 214 99 and 55 respectively when
119889119888 = 8m the average values are 59 48 and 34respectively when 119889119888 = 15m the average values are41 36 and 28 respectively
(2) Compared with the case of considering the effectof parameter 119873119903 the degree of weakening is much
Wireless Communications and Mobile Computing 9
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
18
20Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
18
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 5 Numerical results for the impact of parameter 119873119903 on the multihop capability with different values of CTD (a) 119889119888 = 3m (b)119889119888 = 8m and (c) 119889119888 = 15m where 119875119904 = 2W 120578 = 06 and 120572 = 05
worse For example considering that the value of 119889119888changes from 3m to 15m in CFP scheme the degreeofweakening is (214minus41)214times100 = 808whenconsidering the effect of parameter119875119904 but the value ofthe degree of weakening is (103 minus 6)103 times 100 =2718 when considering the effect of parameter119873119903
Therefore for improving the multihop capabilitiesincreasing the value of parameter119873119903 is more effective
According to the abovementioned results and analysiswe can obtain the important conclusions as follows (1) themultihop capability of CFP is better than CFIP and DFIP
10 Wireless Communications and Mobile Computing
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Ps
4
6
8
10
12
14
16
18
20
22
24
26Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
7
8
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 6 Numerical results for the impact of parameter119875119904 on themultihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8mand (c) 119889119888 = 15m where 120578 = 06 120572 = 05 and119873119903 = 20
(2) all of the parameters 119875119904 120578 120572 119873119903 and 119889119888 can affectthe multihop capability of the three schemes where theparameter 119889119888 can produce an important effect and (3) forimproving the multihop capability it is best effective toincrease the value of parameter119873119903 Of course we can furtherimprove the multihop capability by simultaneously adjustingthe values of parameters 119875119904 120578 and 120572
7 Conclusions
In this paper we study SWIPT in multihop wireless coop-erative networks where the multihop capabilities of CFPCFIP and DFIP schemes are analyzed For this purposewe construct analysis model to investigate the multihopcapabilities of CFP CFIP and DFIP schemes respectively
Wireless Communications and Mobile Computing 11
Finally numerical results show that the multihop capabilityof CFP is better than CFIP and DFIP and for improvingthe multihop capabilities it is best effective to increase theaverage number of relay nodes in cooperative set
Through the analysis model proposed in this paper theappropriate values of related parameters that is initial energyof source node the number of relay nodes the energyharvesting efficiency coefficient and power splitting coeffi-cient can be set to achieve the given transmission hops fromsource to destination
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work is funded by the China Postdoctoral Science Foun-dation (Grant no 2014M561627) the Natural Science Foun-dation ofAnhui Province (Grant no 1308085MF101) theNat-ural Science Foundation of Anhui Higher Education Insti-tutions (Grant no KJ2014A172) and the Science ResearchProject of Chaohu University (Grant no XLZ-201703)
References
[1] L R Varshney ldquoTransporting information and energy simul-taneouslyrdquo in Proceedings of the IEEE International Symposiumon Information Theory (ISIT rsquo08) pp 1612ndash1616 IEEE TorontoCanada July 2008
[2] P Grover and A Sahai ldquoShannonmeets tesla wireless informa-tion andpower transferrdquo inProceedings of the IEEE InternationalSymposium on Information Theory (ISIT rsquo10) pp 2363ndash2367Austin Tex USA June 2010
[3] R Zhang and C K Ho ldquoMIMO broadcasting for simultaneouswireless information and power transferrdquo IEEE Transactions onWireless Communications vol 12 no 5 pp 1989ndash2001 2013
[4] J N LanemanDN Tse andGWornell ldquoCooperative diversityin wireless networks efficient protocols and outage behaviorrdquoInstitute of Electrical and Electronics Engineers Transactions onInformation Theory vol 50 no 12 pp 3062ndash3080 2004
[5] A A Nasir X Zhou S Durrani and R A Kennedy ldquoWireless-powered relays in cooperative communications time-switchingrelaying protocols and throughput analysisrdquo IEEE Transactionson Communications vol 63 no 5 pp 1607ndash1622 2015
[6] E Chen M Xia D B da Costa and S Aissa ldquoMulti-Hopcooperative relaying with energy harvesting from cochannelinterferencesrdquo IEEE Communications Letters vol 21 no 5 pp1199ndash1202 2017
[7] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4761 2013
[8] L Liu R Zhang and K-C Chua ldquoWireless information trans-fer with opportunistic energy harvestingrdquo IEEE Transactions onWireless Communications vol 12 no 1 pp 288ndash300 2013
[9] L Liu R Zhang and K C Chua ldquoWireless information andpower transfer a dynamic power splitting approachrdquo IEEETransactions on Communications vol 61 no 9 pp 3990ndash40012013
[10] H Ju and R Zhang ldquoThroughput maximization in wire-less powered communication networksrdquo IEEE Transactions onWireless Communications vol 13 no 1 pp 418ndash428 2014
[11] R Morsi D S Michalopoulos and R Schober ldquoMultiuserscheduling schemes for simultaneous wireless information andpower transfer over fading channelsrdquo IEEE Transactions onWireless Communications vol 14 no 4 pp 1967ndash1982 2015
[12] C Zhong X Chen Z Zhang and G K Karagiannidis ldquoWire-less-powered communications performance analysis and opti-mizationrdquo IEEE Transactions on Communications vol 63 no12 pp 5178ndash5190 2015
[13] N Zhao F R Yu and V C M Leung ldquoOpportunistic com-munications in interference alignment networks with wirelesspower transferrdquo IEEE Wireless Communications Magazine vol22 no 1 pp 88ndash95 2015
[14] N Zhao ldquoJoint optimization of power splitting and allocationfor SWIPT in interference alignment networksrdquo in v preprintpp 1701ndash01952 httpsarxivorgabs170101952 2017
[15] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[16] D-T Do ldquoTime power switching based relaying protocol inenergy harvesting mobile node optimal throughput analysisrdquoMobile Information Systems vol 2015 Article ID 769286 8pages 2015
[17] C Zhang and Y Chen ldquoWireless power transfer strategies forcooperative relay system tomaximize information throughputrdquoIEEE Access vol 5 pp 2573ndash2582 2017
[18] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[19] Y Liu LWangM Elkashlan T Q Duong andANallanathanldquoTwo-way relay networks with wireless power transfer designand performance analysisrdquo IET Communications vol 10 no 14pp 1810ndash1819 2016
[20] T P Do I Song and Y H Kim ldquoSimultaneous wireless transferof power and information in a decode-and-forward two-wayrelaying networkrdquo IEEE Transactions on Wireless Communica-tions vol 16 no 3 pp 1579ndash1592 2017
[21] C Zhong H A Suraweera G Zheng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[22] Y Zeng and R Zhang ldquoFull-duplex wireless-powered relay withself-energy recyclingrdquo IEEE Wireless Communications Lettersvol 4 no 2 pp 201ndash204 2015
[23] D Wang R Zhang X Cheng and L Yang ldquoCapacity-enhancing full-duplex relay networks based on power-splitting(PS-)SWIPTrdquo IEEE Transactions on Vehicular Technology vol66 no 6 pp 5445ndash5450 2017
[24] ZDing I Krikidis B Sharif andHV Poor ldquoWireless informa-tion and power transfer in cooperative networks with spatiallyrandom relaysrdquo IEEETransactions onWireless Communicationsvol 13 no 8 pp 4440ndash4453 2014
[25] M Haghifam B Makki M Nasiri-Kenari and T SvenssonOn wireless energy and information transfer in relay networkshttpsarxivorgabs160707087 2016
12 Wireless Communications and Mobile Computing
[26] Y Liu ldquoWireless information and power transfer formultirelay-assisted cooperative communicationrdquo IEEE CommunicationsLetters vol 20 no 4 pp 784ndash787 2016
[27] J N Laneman and G W Wornell ldquoDistributed space-timecoded protocols for exploiting cooperative diversity in wirelessnetworksrdquo Institute of Electrical and Electronics Engineers Trans-actions on Information Theory vol 49 no 10 pp 2415ndash24252003
[28] IEEE Std IEEE Standard for Wireless LAN Medium AccessControl (MAC) and Physical Layer (PHY) Specifications(1999)
[29] N T Do V N Q Bao and B An ldquoOutage performance analysisof relay selection schemes in wireless energy harvesting coop-erative networks over non-identical rayleigh fading channelsrdquoSensors vol 16 no 3 article no 295 2016
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
6 Wireless Communications and Mobile Computing
3 4 5 6 7 8 9 102dc (m)
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
2468
1012141618202224262830323436
The l
arge
st nu
mbe
r of h
ops
Figure 2 Analytical versus simulation results with different CTDwhere 119875119904 = 2W 120578 = 06 120572 = 05 and119873119903 = 10simulation results are not in full agreement with the analysisresults because1198731015840119903 is smaller than119873119903 in practice Besides wecan also observe the following
(1) The CTD has an important impact on the largestnumber of transmission hops it is because withthe increase of 119889119888 both the harvested energy andreceived signal strength at sender node of the next hopdecrease due to the larger path loss Consequently theachievable number of transmission hops is reducedwith no sufficient energy especially for the largervalues of 119889119888
(2) The multihop capability of CFP is better than CFIPand DFIP it is because in CFP scheme multiplerelays forward only the power (not the information)towards the receiver cooperatively so that the sendernode of the next hop can obtain more energy tosupport the larger transmission hops especially forthe smaller values of 119889119888
(3) The multihop capability of CFP and CFIP is betterthan DFIP since they use multiple relays to harvestenergy It can be observed in (8) and (13) that thevalues of 119871cfpmax and 119871cfipmax increase with the increase of119873119903 and 1198731015840119903 Furthermore if we consider the fact thatthe value of119873119903 is larger than1198731015840119903 this can further themultihop capability of CFP compared to CFIP
As the analytical results agree well with the simulationresults for the purpose of conciseness in the following wewill plot the simulation results for different parameters 120578 120572
119873119903 and119875119904 when119889119888 = 3mBut for119889119888 = 8mand119889119888 = 15mweonly give analytical results Next we investigate the impacts oftwo parameters 120578 and120572 on the largest number of transmissionhops respectively with considering the effect of CTD 119889119888From Figures 3 and 4 we can obtain the following
(1) For the small values of 119889119888 by increasing the value of120578 or reducing the value of 120572 the largest number oftransmission hops can be improved But if increasingthe value of 119889119888 the largest number of transmissionhops cannot obtain obvious improvement throughchanging the values of 120578 or 120572 In (8) (13) and (17)because 120578 and 120572 have a limited range of values (isin[0 1]) while 119889119888 has a larger value the values of119871cfpmax 119871cfipmax and 119871dfipmax cannot be affected obviously bychanging the values of 120578 or 120572
(2) The multihop capability of CFP is better than CFIPand DFIP especially for the smaller values of 119889119888which is because multiple relays forward only thepower cooperatively For example from Figure 3 wecan observe the impact of parameter 120578 on resultsand obtain that when 119889119888 = 3m the average largestnumber of hops of CFP CFIP and DFIP is 18 8 and49 respectively when 119889119888 = 8m the average valuesare 45 38 and 29 respectively when 119889119888 = 15m theaverage values are 31 28 and 2 respectively
Finally let us study the impacts of two parameters 119873119903and 119875119904 on the multihop capability respectively In Figure 5we give the simulation results for the effect of parameter 119873119903with considering the effect of 119889119888 Considering that 119883 lt 1of fractional denominator log2119883 in (8) and (13) we considera larger range of values of 119873119903 and vary the values of 119873119903 fordifferent values of 119889119888 (ie let the maximum value of 119873119903 beequal to lfloor11988927119888 rfloor) In order to facilitate drawing a numericalvalue 119909 on the 119909-axis of Figure 5 only denotes an exponentialquantity and in fact the corresponding value of 119873119903 is equalto lfloor119889119909119888 rfloor From Figure 5 we can see the following
(1) With the increase of 119873119903 the multihop capabilities ofthree schemes are improved correspondingly and themultihop capability of CFP is better than CFIP andDFIP Specifically when 119889119888 = 3m the average largestnumber of hops of CFP CFIP and DFIP is 103 63and 5 respectively when 119889119888 = 8m the average valuesare 75 51 and 3 respectively when 119889119888 = 15m theaverage values are 6 46 and 2 respectively
(2) Although with the increase of 119889119888 the multihopcapabilities of three schemes are weakened corre-spondingly the degree of weakening is depressedcompared with the case of considering the effect ofparameters 120578 or 120572 For example considering that thevalue of 119889119888 changes from 3m to 15m in CFP schemethe degree of weakening is (103 minus 6)103 times 100 =2718 when considering the effect of parameter119873119903but the value is (18 minus 31)18 times 100 = 8278when considering the effect of parameter 120578Thereforeincreasing the number119873119903 of relay nodes can improvethemultihop capabilities effectively when the CTD 119889119888
Wireless Communications and Mobile Computing 7
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
02 03 04 05 06 07 08010
5
10
15
20
25
30
35
40
45
50Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
02 03 04 05 06 07 08011
2
3
4
5
6
7
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
1
2
3
4
5
The l
arge
st nu
mbe
r of h
ops
02 03 04 05 06 07 0801
(c)
Figure 3 Numerical results for the impact of parameter 120578 on themultihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8mand (c) 119889119888 = 15m where 119875119904 = 2W 120572 = 05 and119873119903 = 20
increases it is because119873119903 has a larger range value andcan affect the values of 119871cfpmax 119871cfipmax and 119871dfipmax in (8)(13) and (17) obviously
In Figure 6 we investigate the impact of parameter 119875119904on the numerical results with considering the effect of 119889119888 Inorder to compare the results with parameter 119873119903 in a larger
range of values we also let a numerical value 119909 on the 119909-axisof Figure 6 only denote an exponential quantity where thecorresponding value of 119875119904 is equal to lfloor119889119909119888 rfloor From Figure 6 wecan observe the following
(1) With the increase of 119875119904 the multihop capabilitiesof the three schemes are improved correspondingly
8 Wireless Communications and Mobile Computing
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
02 03 04 05 06 07 08 09012
4
6
8
10
12
14
16
18
20
22Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
02 03 04 05 06 07 08 09011
2
3
4
5
6
7
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
02 03 04 05 06 07 08 0901 1
2
3
4
5
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 4 Numerical results for the impact of parameter 120572 on the multihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8m(c) and 119889119888 = 15m where 119875119904 = 2W 120578 = 06 and119873119903 = 20
and the multihop capability of CFP is better thanCFIP and DFIP However with the increase of 119889119888the multihop capabilities of the three schemes areweakened correspondingly Specifically when 119889119888 =3m the average largest number of hops of CFP CFIPand DFIP is 214 99 and 55 respectively when
119889119888 = 8m the average values are 59 48 and 34respectively when 119889119888 = 15m the average values are41 36 and 28 respectively
(2) Compared with the case of considering the effectof parameter 119873119903 the degree of weakening is much
Wireless Communications and Mobile Computing 9
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
18
20Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
18
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 5 Numerical results for the impact of parameter 119873119903 on the multihop capability with different values of CTD (a) 119889119888 = 3m (b)119889119888 = 8m and (c) 119889119888 = 15m where 119875119904 = 2W 120578 = 06 and 120572 = 05
worse For example considering that the value of 119889119888changes from 3m to 15m in CFP scheme the degreeofweakening is (214minus41)214times100 = 808whenconsidering the effect of parameter119875119904 but the value ofthe degree of weakening is (103 minus 6)103 times 100 =2718 when considering the effect of parameter119873119903
Therefore for improving the multihop capabilitiesincreasing the value of parameter119873119903 is more effective
According to the abovementioned results and analysiswe can obtain the important conclusions as follows (1) themultihop capability of CFP is better than CFIP and DFIP
10 Wireless Communications and Mobile Computing
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Ps
4
6
8
10
12
14
16
18
20
22
24
26Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
7
8
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 6 Numerical results for the impact of parameter119875119904 on themultihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8mand (c) 119889119888 = 15m where 120578 = 06 120572 = 05 and119873119903 = 20
(2) all of the parameters 119875119904 120578 120572 119873119903 and 119889119888 can affectthe multihop capability of the three schemes where theparameter 119889119888 can produce an important effect and (3) forimproving the multihop capability it is best effective toincrease the value of parameter119873119903 Of course we can furtherimprove the multihop capability by simultaneously adjustingthe values of parameters 119875119904 120578 and 120572
7 Conclusions
In this paper we study SWIPT in multihop wireless coop-erative networks where the multihop capabilities of CFPCFIP and DFIP schemes are analyzed For this purposewe construct analysis model to investigate the multihopcapabilities of CFP CFIP and DFIP schemes respectively
Wireless Communications and Mobile Computing 11
Finally numerical results show that the multihop capabilityof CFP is better than CFIP and DFIP and for improvingthe multihop capabilities it is best effective to increase theaverage number of relay nodes in cooperative set
Through the analysis model proposed in this paper theappropriate values of related parameters that is initial energyof source node the number of relay nodes the energyharvesting efficiency coefficient and power splitting coeffi-cient can be set to achieve the given transmission hops fromsource to destination
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work is funded by the China Postdoctoral Science Foun-dation (Grant no 2014M561627) the Natural Science Foun-dation ofAnhui Province (Grant no 1308085MF101) theNat-ural Science Foundation of Anhui Higher Education Insti-tutions (Grant no KJ2014A172) and the Science ResearchProject of Chaohu University (Grant no XLZ-201703)
References
[1] L R Varshney ldquoTransporting information and energy simul-taneouslyrdquo in Proceedings of the IEEE International Symposiumon Information Theory (ISIT rsquo08) pp 1612ndash1616 IEEE TorontoCanada July 2008
[2] P Grover and A Sahai ldquoShannonmeets tesla wireless informa-tion andpower transferrdquo inProceedings of the IEEE InternationalSymposium on Information Theory (ISIT rsquo10) pp 2363ndash2367Austin Tex USA June 2010
[3] R Zhang and C K Ho ldquoMIMO broadcasting for simultaneouswireless information and power transferrdquo IEEE Transactions onWireless Communications vol 12 no 5 pp 1989ndash2001 2013
[4] J N LanemanDN Tse andGWornell ldquoCooperative diversityin wireless networks efficient protocols and outage behaviorrdquoInstitute of Electrical and Electronics Engineers Transactions onInformation Theory vol 50 no 12 pp 3062ndash3080 2004
[5] A A Nasir X Zhou S Durrani and R A Kennedy ldquoWireless-powered relays in cooperative communications time-switchingrelaying protocols and throughput analysisrdquo IEEE Transactionson Communications vol 63 no 5 pp 1607ndash1622 2015
[6] E Chen M Xia D B da Costa and S Aissa ldquoMulti-Hopcooperative relaying with energy harvesting from cochannelinterferencesrdquo IEEE Communications Letters vol 21 no 5 pp1199ndash1202 2017
[7] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4761 2013
[8] L Liu R Zhang and K-C Chua ldquoWireless information trans-fer with opportunistic energy harvestingrdquo IEEE Transactions onWireless Communications vol 12 no 1 pp 288ndash300 2013
[9] L Liu R Zhang and K C Chua ldquoWireless information andpower transfer a dynamic power splitting approachrdquo IEEETransactions on Communications vol 61 no 9 pp 3990ndash40012013
[10] H Ju and R Zhang ldquoThroughput maximization in wire-less powered communication networksrdquo IEEE Transactions onWireless Communications vol 13 no 1 pp 418ndash428 2014
[11] R Morsi D S Michalopoulos and R Schober ldquoMultiuserscheduling schemes for simultaneous wireless information andpower transfer over fading channelsrdquo IEEE Transactions onWireless Communications vol 14 no 4 pp 1967ndash1982 2015
[12] C Zhong X Chen Z Zhang and G K Karagiannidis ldquoWire-less-powered communications performance analysis and opti-mizationrdquo IEEE Transactions on Communications vol 63 no12 pp 5178ndash5190 2015
[13] N Zhao F R Yu and V C M Leung ldquoOpportunistic com-munications in interference alignment networks with wirelesspower transferrdquo IEEE Wireless Communications Magazine vol22 no 1 pp 88ndash95 2015
[14] N Zhao ldquoJoint optimization of power splitting and allocationfor SWIPT in interference alignment networksrdquo in v preprintpp 1701ndash01952 httpsarxivorgabs170101952 2017
[15] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[16] D-T Do ldquoTime power switching based relaying protocol inenergy harvesting mobile node optimal throughput analysisrdquoMobile Information Systems vol 2015 Article ID 769286 8pages 2015
[17] C Zhang and Y Chen ldquoWireless power transfer strategies forcooperative relay system tomaximize information throughputrdquoIEEE Access vol 5 pp 2573ndash2582 2017
[18] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[19] Y Liu LWangM Elkashlan T Q Duong andANallanathanldquoTwo-way relay networks with wireless power transfer designand performance analysisrdquo IET Communications vol 10 no 14pp 1810ndash1819 2016
[20] T P Do I Song and Y H Kim ldquoSimultaneous wireless transferof power and information in a decode-and-forward two-wayrelaying networkrdquo IEEE Transactions on Wireless Communica-tions vol 16 no 3 pp 1579ndash1592 2017
[21] C Zhong H A Suraweera G Zheng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[22] Y Zeng and R Zhang ldquoFull-duplex wireless-powered relay withself-energy recyclingrdquo IEEE Wireless Communications Lettersvol 4 no 2 pp 201ndash204 2015
[23] D Wang R Zhang X Cheng and L Yang ldquoCapacity-enhancing full-duplex relay networks based on power-splitting(PS-)SWIPTrdquo IEEE Transactions on Vehicular Technology vol66 no 6 pp 5445ndash5450 2017
[24] ZDing I Krikidis B Sharif andHV Poor ldquoWireless informa-tion and power transfer in cooperative networks with spatiallyrandom relaysrdquo IEEETransactions onWireless Communicationsvol 13 no 8 pp 4440ndash4453 2014
[25] M Haghifam B Makki M Nasiri-Kenari and T SvenssonOn wireless energy and information transfer in relay networkshttpsarxivorgabs160707087 2016
12 Wireless Communications and Mobile Computing
[26] Y Liu ldquoWireless information and power transfer formultirelay-assisted cooperative communicationrdquo IEEE CommunicationsLetters vol 20 no 4 pp 784ndash787 2016
[27] J N Laneman and G W Wornell ldquoDistributed space-timecoded protocols for exploiting cooperative diversity in wirelessnetworksrdquo Institute of Electrical and Electronics Engineers Trans-actions on Information Theory vol 49 no 10 pp 2415ndash24252003
[28] IEEE Std IEEE Standard for Wireless LAN Medium AccessControl (MAC) and Physical Layer (PHY) Specifications(1999)
[29] N T Do V N Q Bao and B An ldquoOutage performance analysisof relay selection schemes in wireless energy harvesting coop-erative networks over non-identical rayleigh fading channelsrdquoSensors vol 16 no 3 article no 295 2016
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
Wireless Communications and Mobile Computing 7
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
02 03 04 05 06 07 08010
5
10
15
20
25
30
35
40
45
50Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
02 03 04 05 06 07 08011
2
3
4
5
6
7
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
1
2
3
4
5
The l
arge
st nu
mbe
r of h
ops
02 03 04 05 06 07 0801
(c)
Figure 3 Numerical results for the impact of parameter 120578 on themultihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8mand (c) 119889119888 = 15m where 119875119904 = 2W 120572 = 05 and119873119903 = 20
increases it is because119873119903 has a larger range value andcan affect the values of 119871cfpmax 119871cfipmax and 119871dfipmax in (8)(13) and (17) obviously
In Figure 6 we investigate the impact of parameter 119875119904on the numerical results with considering the effect of 119889119888 Inorder to compare the results with parameter 119873119903 in a larger
range of values we also let a numerical value 119909 on the 119909-axisof Figure 6 only denote an exponential quantity where thecorresponding value of 119875119904 is equal to lfloor119889119909119888 rfloor From Figure 6 wecan observe the following
(1) With the increase of 119875119904 the multihop capabilitiesof the three schemes are improved correspondingly
8 Wireless Communications and Mobile Computing
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
02 03 04 05 06 07 08 09012
4
6
8
10
12
14
16
18
20
22Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
02 03 04 05 06 07 08 09011
2
3
4
5
6
7
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
02 03 04 05 06 07 08 0901 1
2
3
4
5
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 4 Numerical results for the impact of parameter 120572 on the multihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8m(c) and 119889119888 = 15m where 119875119904 = 2W 120578 = 06 and119873119903 = 20
and the multihop capability of CFP is better thanCFIP and DFIP However with the increase of 119889119888the multihop capabilities of the three schemes areweakened correspondingly Specifically when 119889119888 =3m the average largest number of hops of CFP CFIPand DFIP is 214 99 and 55 respectively when
119889119888 = 8m the average values are 59 48 and 34respectively when 119889119888 = 15m the average values are41 36 and 28 respectively
(2) Compared with the case of considering the effectof parameter 119873119903 the degree of weakening is much
Wireless Communications and Mobile Computing 9
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
18
20Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
18
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 5 Numerical results for the impact of parameter 119873119903 on the multihop capability with different values of CTD (a) 119889119888 = 3m (b)119889119888 = 8m and (c) 119889119888 = 15m where 119875119904 = 2W 120578 = 06 and 120572 = 05
worse For example considering that the value of 119889119888changes from 3m to 15m in CFP scheme the degreeofweakening is (214minus41)214times100 = 808whenconsidering the effect of parameter119875119904 but the value ofthe degree of weakening is (103 minus 6)103 times 100 =2718 when considering the effect of parameter119873119903
Therefore for improving the multihop capabilitiesincreasing the value of parameter119873119903 is more effective
According to the abovementioned results and analysiswe can obtain the important conclusions as follows (1) themultihop capability of CFP is better than CFIP and DFIP
10 Wireless Communications and Mobile Computing
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Ps
4
6
8
10
12
14
16
18
20
22
24
26Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
7
8
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 6 Numerical results for the impact of parameter119875119904 on themultihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8mand (c) 119889119888 = 15m where 120578 = 06 120572 = 05 and119873119903 = 20
(2) all of the parameters 119875119904 120578 120572 119873119903 and 119889119888 can affectthe multihop capability of the three schemes where theparameter 119889119888 can produce an important effect and (3) forimproving the multihop capability it is best effective toincrease the value of parameter119873119903 Of course we can furtherimprove the multihop capability by simultaneously adjustingthe values of parameters 119875119904 120578 and 120572
7 Conclusions
In this paper we study SWIPT in multihop wireless coop-erative networks where the multihop capabilities of CFPCFIP and DFIP schemes are analyzed For this purposewe construct analysis model to investigate the multihopcapabilities of CFP CFIP and DFIP schemes respectively
Wireless Communications and Mobile Computing 11
Finally numerical results show that the multihop capabilityof CFP is better than CFIP and DFIP and for improvingthe multihop capabilities it is best effective to increase theaverage number of relay nodes in cooperative set
Through the analysis model proposed in this paper theappropriate values of related parameters that is initial energyof source node the number of relay nodes the energyharvesting efficiency coefficient and power splitting coeffi-cient can be set to achieve the given transmission hops fromsource to destination
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work is funded by the China Postdoctoral Science Foun-dation (Grant no 2014M561627) the Natural Science Foun-dation ofAnhui Province (Grant no 1308085MF101) theNat-ural Science Foundation of Anhui Higher Education Insti-tutions (Grant no KJ2014A172) and the Science ResearchProject of Chaohu University (Grant no XLZ-201703)
References
[1] L R Varshney ldquoTransporting information and energy simul-taneouslyrdquo in Proceedings of the IEEE International Symposiumon Information Theory (ISIT rsquo08) pp 1612ndash1616 IEEE TorontoCanada July 2008
[2] P Grover and A Sahai ldquoShannonmeets tesla wireless informa-tion andpower transferrdquo inProceedings of the IEEE InternationalSymposium on Information Theory (ISIT rsquo10) pp 2363ndash2367Austin Tex USA June 2010
[3] R Zhang and C K Ho ldquoMIMO broadcasting for simultaneouswireless information and power transferrdquo IEEE Transactions onWireless Communications vol 12 no 5 pp 1989ndash2001 2013
[4] J N LanemanDN Tse andGWornell ldquoCooperative diversityin wireless networks efficient protocols and outage behaviorrdquoInstitute of Electrical and Electronics Engineers Transactions onInformation Theory vol 50 no 12 pp 3062ndash3080 2004
[5] A A Nasir X Zhou S Durrani and R A Kennedy ldquoWireless-powered relays in cooperative communications time-switchingrelaying protocols and throughput analysisrdquo IEEE Transactionson Communications vol 63 no 5 pp 1607ndash1622 2015
[6] E Chen M Xia D B da Costa and S Aissa ldquoMulti-Hopcooperative relaying with energy harvesting from cochannelinterferencesrdquo IEEE Communications Letters vol 21 no 5 pp1199ndash1202 2017
[7] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4761 2013
[8] L Liu R Zhang and K-C Chua ldquoWireless information trans-fer with opportunistic energy harvestingrdquo IEEE Transactions onWireless Communications vol 12 no 1 pp 288ndash300 2013
[9] L Liu R Zhang and K C Chua ldquoWireless information andpower transfer a dynamic power splitting approachrdquo IEEETransactions on Communications vol 61 no 9 pp 3990ndash40012013
[10] H Ju and R Zhang ldquoThroughput maximization in wire-less powered communication networksrdquo IEEE Transactions onWireless Communications vol 13 no 1 pp 418ndash428 2014
[11] R Morsi D S Michalopoulos and R Schober ldquoMultiuserscheduling schemes for simultaneous wireless information andpower transfer over fading channelsrdquo IEEE Transactions onWireless Communications vol 14 no 4 pp 1967ndash1982 2015
[12] C Zhong X Chen Z Zhang and G K Karagiannidis ldquoWire-less-powered communications performance analysis and opti-mizationrdquo IEEE Transactions on Communications vol 63 no12 pp 5178ndash5190 2015
[13] N Zhao F R Yu and V C M Leung ldquoOpportunistic com-munications in interference alignment networks with wirelesspower transferrdquo IEEE Wireless Communications Magazine vol22 no 1 pp 88ndash95 2015
[14] N Zhao ldquoJoint optimization of power splitting and allocationfor SWIPT in interference alignment networksrdquo in v preprintpp 1701ndash01952 httpsarxivorgabs170101952 2017
[15] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[16] D-T Do ldquoTime power switching based relaying protocol inenergy harvesting mobile node optimal throughput analysisrdquoMobile Information Systems vol 2015 Article ID 769286 8pages 2015
[17] C Zhang and Y Chen ldquoWireless power transfer strategies forcooperative relay system tomaximize information throughputrdquoIEEE Access vol 5 pp 2573ndash2582 2017
[18] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[19] Y Liu LWangM Elkashlan T Q Duong andANallanathanldquoTwo-way relay networks with wireless power transfer designand performance analysisrdquo IET Communications vol 10 no 14pp 1810ndash1819 2016
[20] T P Do I Song and Y H Kim ldquoSimultaneous wireless transferof power and information in a decode-and-forward two-wayrelaying networkrdquo IEEE Transactions on Wireless Communica-tions vol 16 no 3 pp 1579ndash1592 2017
[21] C Zhong H A Suraweera G Zheng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[22] Y Zeng and R Zhang ldquoFull-duplex wireless-powered relay withself-energy recyclingrdquo IEEE Wireless Communications Lettersvol 4 no 2 pp 201ndash204 2015
[23] D Wang R Zhang X Cheng and L Yang ldquoCapacity-enhancing full-duplex relay networks based on power-splitting(PS-)SWIPTrdquo IEEE Transactions on Vehicular Technology vol66 no 6 pp 5445ndash5450 2017
[24] ZDing I Krikidis B Sharif andHV Poor ldquoWireless informa-tion and power transfer in cooperative networks with spatiallyrandom relaysrdquo IEEETransactions onWireless Communicationsvol 13 no 8 pp 4440ndash4453 2014
[25] M Haghifam B Makki M Nasiri-Kenari and T SvenssonOn wireless energy and information transfer in relay networkshttpsarxivorgabs160707087 2016
12 Wireless Communications and Mobile Computing
[26] Y Liu ldquoWireless information and power transfer formultirelay-assisted cooperative communicationrdquo IEEE CommunicationsLetters vol 20 no 4 pp 784ndash787 2016
[27] J N Laneman and G W Wornell ldquoDistributed space-timecoded protocols for exploiting cooperative diversity in wirelessnetworksrdquo Institute of Electrical and Electronics Engineers Trans-actions on Information Theory vol 49 no 10 pp 2415ndash24252003
[28] IEEE Std IEEE Standard for Wireless LAN Medium AccessControl (MAC) and Physical Layer (PHY) Specifications(1999)
[29] N T Do V N Q Bao and B An ldquoOutage performance analysisof relay selection schemes in wireless energy harvesting coop-erative networks over non-identical rayleigh fading channelsrdquoSensors vol 16 no 3 article no 295 2016
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
8 Wireless Communications and Mobile Computing
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
02 03 04 05 06 07 08 09012
4
6
8
10
12
14
16
18
20
22Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
02 03 04 05 06 07 08 09011
2
3
4
5
6
7
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
02 03 04 05 06 07 08 0901 1
2
3
4
5
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 4 Numerical results for the impact of parameter 120572 on the multihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8m(c) and 119889119888 = 15m where 119875119904 = 2W 120578 = 06 and119873119903 = 20
and the multihop capability of CFP is better thanCFIP and DFIP However with the increase of 119889119888the multihop capabilities of the three schemes areweakened correspondingly Specifically when 119889119888 =3m the average largest number of hops of CFP CFIPand DFIP is 214 99 and 55 respectively when
119889119888 = 8m the average values are 59 48 and 34respectively when 119889119888 = 15m the average values are41 36 and 28 respectively
(2) Compared with the case of considering the effectof parameter 119873119903 the degree of weakening is much
Wireless Communications and Mobile Computing 9
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
18
20Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
18
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 5 Numerical results for the impact of parameter 119873119903 on the multihop capability with different values of CTD (a) 119889119888 = 3m (b)119889119888 = 8m and (c) 119889119888 = 15m where 119875119904 = 2W 120578 = 06 and 120572 = 05
worse For example considering that the value of 119889119888changes from 3m to 15m in CFP scheme the degreeofweakening is (214minus41)214times100 = 808whenconsidering the effect of parameter119875119904 but the value ofthe degree of weakening is (103 minus 6)103 times 100 =2718 when considering the effect of parameter119873119903
Therefore for improving the multihop capabilitiesincreasing the value of parameter119873119903 is more effective
According to the abovementioned results and analysiswe can obtain the important conclusions as follows (1) themultihop capability of CFP is better than CFIP and DFIP
10 Wireless Communications and Mobile Computing
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Ps
4
6
8
10
12
14
16
18
20
22
24
26Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
7
8
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 6 Numerical results for the impact of parameter119875119904 on themultihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8mand (c) 119889119888 = 15m where 120578 = 06 120572 = 05 and119873119903 = 20
(2) all of the parameters 119875119904 120578 120572 119873119903 and 119889119888 can affectthe multihop capability of the three schemes where theparameter 119889119888 can produce an important effect and (3) forimproving the multihop capability it is best effective toincrease the value of parameter119873119903 Of course we can furtherimprove the multihop capability by simultaneously adjustingthe values of parameters 119875119904 120578 and 120572
7 Conclusions
In this paper we study SWIPT in multihop wireless coop-erative networks where the multihop capabilities of CFPCFIP and DFIP schemes are analyzed For this purposewe construct analysis model to investigate the multihopcapabilities of CFP CFIP and DFIP schemes respectively
Wireless Communications and Mobile Computing 11
Finally numerical results show that the multihop capabilityof CFP is better than CFIP and DFIP and for improvingthe multihop capabilities it is best effective to increase theaverage number of relay nodes in cooperative set
Through the analysis model proposed in this paper theappropriate values of related parameters that is initial energyof source node the number of relay nodes the energyharvesting efficiency coefficient and power splitting coeffi-cient can be set to achieve the given transmission hops fromsource to destination
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work is funded by the China Postdoctoral Science Foun-dation (Grant no 2014M561627) the Natural Science Foun-dation ofAnhui Province (Grant no 1308085MF101) theNat-ural Science Foundation of Anhui Higher Education Insti-tutions (Grant no KJ2014A172) and the Science ResearchProject of Chaohu University (Grant no XLZ-201703)
References
[1] L R Varshney ldquoTransporting information and energy simul-taneouslyrdquo in Proceedings of the IEEE International Symposiumon Information Theory (ISIT rsquo08) pp 1612ndash1616 IEEE TorontoCanada July 2008
[2] P Grover and A Sahai ldquoShannonmeets tesla wireless informa-tion andpower transferrdquo inProceedings of the IEEE InternationalSymposium on Information Theory (ISIT rsquo10) pp 2363ndash2367Austin Tex USA June 2010
[3] R Zhang and C K Ho ldquoMIMO broadcasting for simultaneouswireless information and power transferrdquo IEEE Transactions onWireless Communications vol 12 no 5 pp 1989ndash2001 2013
[4] J N LanemanDN Tse andGWornell ldquoCooperative diversityin wireless networks efficient protocols and outage behaviorrdquoInstitute of Electrical and Electronics Engineers Transactions onInformation Theory vol 50 no 12 pp 3062ndash3080 2004
[5] A A Nasir X Zhou S Durrani and R A Kennedy ldquoWireless-powered relays in cooperative communications time-switchingrelaying protocols and throughput analysisrdquo IEEE Transactionson Communications vol 63 no 5 pp 1607ndash1622 2015
[6] E Chen M Xia D B da Costa and S Aissa ldquoMulti-Hopcooperative relaying with energy harvesting from cochannelinterferencesrdquo IEEE Communications Letters vol 21 no 5 pp1199ndash1202 2017
[7] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4761 2013
[8] L Liu R Zhang and K-C Chua ldquoWireless information trans-fer with opportunistic energy harvestingrdquo IEEE Transactions onWireless Communications vol 12 no 1 pp 288ndash300 2013
[9] L Liu R Zhang and K C Chua ldquoWireless information andpower transfer a dynamic power splitting approachrdquo IEEETransactions on Communications vol 61 no 9 pp 3990ndash40012013
[10] H Ju and R Zhang ldquoThroughput maximization in wire-less powered communication networksrdquo IEEE Transactions onWireless Communications vol 13 no 1 pp 418ndash428 2014
[11] R Morsi D S Michalopoulos and R Schober ldquoMultiuserscheduling schemes for simultaneous wireless information andpower transfer over fading channelsrdquo IEEE Transactions onWireless Communications vol 14 no 4 pp 1967ndash1982 2015
[12] C Zhong X Chen Z Zhang and G K Karagiannidis ldquoWire-less-powered communications performance analysis and opti-mizationrdquo IEEE Transactions on Communications vol 63 no12 pp 5178ndash5190 2015
[13] N Zhao F R Yu and V C M Leung ldquoOpportunistic com-munications in interference alignment networks with wirelesspower transferrdquo IEEE Wireless Communications Magazine vol22 no 1 pp 88ndash95 2015
[14] N Zhao ldquoJoint optimization of power splitting and allocationfor SWIPT in interference alignment networksrdquo in v preprintpp 1701ndash01952 httpsarxivorgabs170101952 2017
[15] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[16] D-T Do ldquoTime power switching based relaying protocol inenergy harvesting mobile node optimal throughput analysisrdquoMobile Information Systems vol 2015 Article ID 769286 8pages 2015
[17] C Zhang and Y Chen ldquoWireless power transfer strategies forcooperative relay system tomaximize information throughputrdquoIEEE Access vol 5 pp 2573ndash2582 2017
[18] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[19] Y Liu LWangM Elkashlan T Q Duong andANallanathanldquoTwo-way relay networks with wireless power transfer designand performance analysisrdquo IET Communications vol 10 no 14pp 1810ndash1819 2016
[20] T P Do I Song and Y H Kim ldquoSimultaneous wireless transferof power and information in a decode-and-forward two-wayrelaying networkrdquo IEEE Transactions on Wireless Communica-tions vol 16 no 3 pp 1579ndash1592 2017
[21] C Zhong H A Suraweera G Zheng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[22] Y Zeng and R Zhang ldquoFull-duplex wireless-powered relay withself-energy recyclingrdquo IEEE Wireless Communications Lettersvol 4 no 2 pp 201ndash204 2015
[23] D Wang R Zhang X Cheng and L Yang ldquoCapacity-enhancing full-duplex relay networks based on power-splitting(PS-)SWIPTrdquo IEEE Transactions on Vehicular Technology vol66 no 6 pp 5445ndash5450 2017
[24] ZDing I Krikidis B Sharif andHV Poor ldquoWireless informa-tion and power transfer in cooperative networks with spatiallyrandom relaysrdquo IEEETransactions onWireless Communicationsvol 13 no 8 pp 4440ndash4453 2014
[25] M Haghifam B Makki M Nasiri-Kenari and T SvenssonOn wireless energy and information transfer in relay networkshttpsarxivorgabs160707087 2016
12 Wireless Communications and Mobile Computing
[26] Y Liu ldquoWireless information and power transfer formultirelay-assisted cooperative communicationrdquo IEEE CommunicationsLetters vol 20 no 4 pp 784ndash787 2016
[27] J N Laneman and G W Wornell ldquoDistributed space-timecoded protocols for exploiting cooperative diversity in wirelessnetworksrdquo Institute of Electrical and Electronics Engineers Trans-actions on Information Theory vol 49 no 10 pp 2415ndash24252003
[28] IEEE Std IEEE Standard for Wireless LAN Medium AccessControl (MAC) and Physical Layer (PHY) Specifications(1999)
[29] N T Do V N Q Bao and B An ldquoOutage performance analysisof relay selection schemes in wireless energy harvesting coop-erative networks over non-identical rayleigh fading channelsrdquoSensors vol 16 no 3 article no 295 2016
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
Wireless Communications and Mobile Computing 9
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
18
20Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
18
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Nr
0
2
4
6
8
10
12
14
16
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 5 Numerical results for the impact of parameter 119873119903 on the multihop capability with different values of CTD (a) 119889119888 = 3m (b)119889119888 = 8m and (c) 119889119888 = 15m where 119875119904 = 2W 120578 = 06 and 120572 = 05
worse For example considering that the value of 119889119888changes from 3m to 15m in CFP scheme the degreeofweakening is (214minus41)214times100 = 808whenconsidering the effect of parameter119875119904 but the value ofthe degree of weakening is (103 minus 6)103 times 100 =2718 when considering the effect of parameter119873119903
Therefore for improving the multihop capabilitiesincreasing the value of parameter119873119903 is more effective
According to the abovementioned results and analysiswe can obtain the important conclusions as follows (1) themultihop capability of CFP is better than CFIP and DFIP
10 Wireless Communications and Mobile Computing
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Ps
4
6
8
10
12
14
16
18
20
22
24
26Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
7
8
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 6 Numerical results for the impact of parameter119875119904 on themultihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8mand (c) 119889119888 = 15m where 120578 = 06 120572 = 05 and119873119903 = 20
(2) all of the parameters 119875119904 120578 120572 119873119903 and 119889119888 can affectthe multihop capability of the three schemes where theparameter 119889119888 can produce an important effect and (3) forimproving the multihop capability it is best effective toincrease the value of parameter119873119903 Of course we can furtherimprove the multihop capability by simultaneously adjustingthe values of parameters 119875119904 120578 and 120572
7 Conclusions
In this paper we study SWIPT in multihop wireless coop-erative networks where the multihop capabilities of CFPCFIP and DFIP schemes are analyzed For this purposewe construct analysis model to investigate the multihopcapabilities of CFP CFIP and DFIP schemes respectively
Wireless Communications and Mobile Computing 11
Finally numerical results show that the multihop capabilityof CFP is better than CFIP and DFIP and for improvingthe multihop capabilities it is best effective to increase theaverage number of relay nodes in cooperative set
Through the analysis model proposed in this paper theappropriate values of related parameters that is initial energyof source node the number of relay nodes the energyharvesting efficiency coefficient and power splitting coeffi-cient can be set to achieve the given transmission hops fromsource to destination
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work is funded by the China Postdoctoral Science Foun-dation (Grant no 2014M561627) the Natural Science Foun-dation ofAnhui Province (Grant no 1308085MF101) theNat-ural Science Foundation of Anhui Higher Education Insti-tutions (Grant no KJ2014A172) and the Science ResearchProject of Chaohu University (Grant no XLZ-201703)
References
[1] L R Varshney ldquoTransporting information and energy simul-taneouslyrdquo in Proceedings of the IEEE International Symposiumon Information Theory (ISIT rsquo08) pp 1612ndash1616 IEEE TorontoCanada July 2008
[2] P Grover and A Sahai ldquoShannonmeets tesla wireless informa-tion andpower transferrdquo inProceedings of the IEEE InternationalSymposium on Information Theory (ISIT rsquo10) pp 2363ndash2367Austin Tex USA June 2010
[3] R Zhang and C K Ho ldquoMIMO broadcasting for simultaneouswireless information and power transferrdquo IEEE Transactions onWireless Communications vol 12 no 5 pp 1989ndash2001 2013
[4] J N LanemanDN Tse andGWornell ldquoCooperative diversityin wireless networks efficient protocols and outage behaviorrdquoInstitute of Electrical and Electronics Engineers Transactions onInformation Theory vol 50 no 12 pp 3062ndash3080 2004
[5] A A Nasir X Zhou S Durrani and R A Kennedy ldquoWireless-powered relays in cooperative communications time-switchingrelaying protocols and throughput analysisrdquo IEEE Transactionson Communications vol 63 no 5 pp 1607ndash1622 2015
[6] E Chen M Xia D B da Costa and S Aissa ldquoMulti-Hopcooperative relaying with energy harvesting from cochannelinterferencesrdquo IEEE Communications Letters vol 21 no 5 pp1199ndash1202 2017
[7] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4761 2013
[8] L Liu R Zhang and K-C Chua ldquoWireless information trans-fer with opportunistic energy harvestingrdquo IEEE Transactions onWireless Communications vol 12 no 1 pp 288ndash300 2013
[9] L Liu R Zhang and K C Chua ldquoWireless information andpower transfer a dynamic power splitting approachrdquo IEEETransactions on Communications vol 61 no 9 pp 3990ndash40012013
[10] H Ju and R Zhang ldquoThroughput maximization in wire-less powered communication networksrdquo IEEE Transactions onWireless Communications vol 13 no 1 pp 418ndash428 2014
[11] R Morsi D S Michalopoulos and R Schober ldquoMultiuserscheduling schemes for simultaneous wireless information andpower transfer over fading channelsrdquo IEEE Transactions onWireless Communications vol 14 no 4 pp 1967ndash1982 2015
[12] C Zhong X Chen Z Zhang and G K Karagiannidis ldquoWire-less-powered communications performance analysis and opti-mizationrdquo IEEE Transactions on Communications vol 63 no12 pp 5178ndash5190 2015
[13] N Zhao F R Yu and V C M Leung ldquoOpportunistic com-munications in interference alignment networks with wirelesspower transferrdquo IEEE Wireless Communications Magazine vol22 no 1 pp 88ndash95 2015
[14] N Zhao ldquoJoint optimization of power splitting and allocationfor SWIPT in interference alignment networksrdquo in v preprintpp 1701ndash01952 httpsarxivorgabs170101952 2017
[15] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[16] D-T Do ldquoTime power switching based relaying protocol inenergy harvesting mobile node optimal throughput analysisrdquoMobile Information Systems vol 2015 Article ID 769286 8pages 2015
[17] C Zhang and Y Chen ldquoWireless power transfer strategies forcooperative relay system tomaximize information throughputrdquoIEEE Access vol 5 pp 2573ndash2582 2017
[18] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[19] Y Liu LWangM Elkashlan T Q Duong andANallanathanldquoTwo-way relay networks with wireless power transfer designand performance analysisrdquo IET Communications vol 10 no 14pp 1810ndash1819 2016
[20] T P Do I Song and Y H Kim ldquoSimultaneous wireless transferof power and information in a decode-and-forward two-wayrelaying networkrdquo IEEE Transactions on Wireless Communica-tions vol 16 no 3 pp 1579ndash1592 2017
[21] C Zhong H A Suraweera G Zheng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[22] Y Zeng and R Zhang ldquoFull-duplex wireless-powered relay withself-energy recyclingrdquo IEEE Wireless Communications Lettersvol 4 no 2 pp 201ndash204 2015
[23] D Wang R Zhang X Cheng and L Yang ldquoCapacity-enhancing full-duplex relay networks based on power-splitting(PS-)SWIPTrdquo IEEE Transactions on Vehicular Technology vol66 no 6 pp 5445ndash5450 2017
[24] ZDing I Krikidis B Sharif andHV Poor ldquoWireless informa-tion and power transfer in cooperative networks with spatiallyrandom relaysrdquo IEEETransactions onWireless Communicationsvol 13 no 8 pp 4440ndash4453 2014
[25] M Haghifam B Makki M Nasiri-Kenari and T SvenssonOn wireless energy and information transfer in relay networkshttpsarxivorgabs160707087 2016
12 Wireless Communications and Mobile Computing
[26] Y Liu ldquoWireless information and power transfer formultirelay-assisted cooperative communicationrdquo IEEE CommunicationsLetters vol 20 no 4 pp 784ndash787 2016
[27] J N Laneman and G W Wornell ldquoDistributed space-timecoded protocols for exploiting cooperative diversity in wirelessnetworksrdquo Institute of Electrical and Electronics Engineers Trans-actions on Information Theory vol 49 no 10 pp 2415ndash24252003
[28] IEEE Std IEEE Standard for Wireless LAN Medium AccessControl (MAC) and Physical Layer (PHY) Specifications(1999)
[29] N T Do V N Q Bao and B An ldquoOutage performance analysisof relay selection schemes in wireless energy harvesting coop-erative networks over non-identical rayleigh fading channelsrdquoSensors vol 16 no 3 article no 295 2016
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
10 Wireless Communications and Mobile Computing
Analysis results for CFPSimulation results for CFPAnalysis results for CFIPSimulation results for CFIPAnalysis results for DFIPSimulation results for DFIP
09 12 15 18 21 24 2706Ps
4
6
8
10
12
14
16
18
20
22
24
26Th
e lar
gest
num
ber o
f hop
s
(a)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
7
8
The l
arge
st nu
mbe
r of h
ops
(b)
CFPCIFPDIFP
09 12 15 18 21 24 2706Ps
1
2
3
4
5
6
The l
arge
st nu
mbe
r of h
ops
(c)
Figure 6 Numerical results for the impact of parameter119875119904 on themultihop capability with different values of CTD (a) 119889119888 = 3m (b) 119889119888 = 8mand (c) 119889119888 = 15m where 120578 = 06 120572 = 05 and119873119903 = 20
(2) all of the parameters 119875119904 120578 120572 119873119903 and 119889119888 can affectthe multihop capability of the three schemes where theparameter 119889119888 can produce an important effect and (3) forimproving the multihop capability it is best effective toincrease the value of parameter119873119903 Of course we can furtherimprove the multihop capability by simultaneously adjustingthe values of parameters 119875119904 120578 and 120572
7 Conclusions
In this paper we study SWIPT in multihop wireless coop-erative networks where the multihop capabilities of CFPCFIP and DFIP schemes are analyzed For this purposewe construct analysis model to investigate the multihopcapabilities of CFP CFIP and DFIP schemes respectively
Wireless Communications and Mobile Computing 11
Finally numerical results show that the multihop capabilityof CFP is better than CFIP and DFIP and for improvingthe multihop capabilities it is best effective to increase theaverage number of relay nodes in cooperative set
Through the analysis model proposed in this paper theappropriate values of related parameters that is initial energyof source node the number of relay nodes the energyharvesting efficiency coefficient and power splitting coeffi-cient can be set to achieve the given transmission hops fromsource to destination
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work is funded by the China Postdoctoral Science Foun-dation (Grant no 2014M561627) the Natural Science Foun-dation ofAnhui Province (Grant no 1308085MF101) theNat-ural Science Foundation of Anhui Higher Education Insti-tutions (Grant no KJ2014A172) and the Science ResearchProject of Chaohu University (Grant no XLZ-201703)
References
[1] L R Varshney ldquoTransporting information and energy simul-taneouslyrdquo in Proceedings of the IEEE International Symposiumon Information Theory (ISIT rsquo08) pp 1612ndash1616 IEEE TorontoCanada July 2008
[2] P Grover and A Sahai ldquoShannonmeets tesla wireless informa-tion andpower transferrdquo inProceedings of the IEEE InternationalSymposium on Information Theory (ISIT rsquo10) pp 2363ndash2367Austin Tex USA June 2010
[3] R Zhang and C K Ho ldquoMIMO broadcasting for simultaneouswireless information and power transferrdquo IEEE Transactions onWireless Communications vol 12 no 5 pp 1989ndash2001 2013
[4] J N LanemanDN Tse andGWornell ldquoCooperative diversityin wireless networks efficient protocols and outage behaviorrdquoInstitute of Electrical and Electronics Engineers Transactions onInformation Theory vol 50 no 12 pp 3062ndash3080 2004
[5] A A Nasir X Zhou S Durrani and R A Kennedy ldquoWireless-powered relays in cooperative communications time-switchingrelaying protocols and throughput analysisrdquo IEEE Transactionson Communications vol 63 no 5 pp 1607ndash1622 2015
[6] E Chen M Xia D B da Costa and S Aissa ldquoMulti-Hopcooperative relaying with energy harvesting from cochannelinterferencesrdquo IEEE Communications Letters vol 21 no 5 pp1199ndash1202 2017
[7] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4761 2013
[8] L Liu R Zhang and K-C Chua ldquoWireless information trans-fer with opportunistic energy harvestingrdquo IEEE Transactions onWireless Communications vol 12 no 1 pp 288ndash300 2013
[9] L Liu R Zhang and K C Chua ldquoWireless information andpower transfer a dynamic power splitting approachrdquo IEEETransactions on Communications vol 61 no 9 pp 3990ndash40012013
[10] H Ju and R Zhang ldquoThroughput maximization in wire-less powered communication networksrdquo IEEE Transactions onWireless Communications vol 13 no 1 pp 418ndash428 2014
[11] R Morsi D S Michalopoulos and R Schober ldquoMultiuserscheduling schemes for simultaneous wireless information andpower transfer over fading channelsrdquo IEEE Transactions onWireless Communications vol 14 no 4 pp 1967ndash1982 2015
[12] C Zhong X Chen Z Zhang and G K Karagiannidis ldquoWire-less-powered communications performance analysis and opti-mizationrdquo IEEE Transactions on Communications vol 63 no12 pp 5178ndash5190 2015
[13] N Zhao F R Yu and V C M Leung ldquoOpportunistic com-munications in interference alignment networks with wirelesspower transferrdquo IEEE Wireless Communications Magazine vol22 no 1 pp 88ndash95 2015
[14] N Zhao ldquoJoint optimization of power splitting and allocationfor SWIPT in interference alignment networksrdquo in v preprintpp 1701ndash01952 httpsarxivorgabs170101952 2017
[15] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[16] D-T Do ldquoTime power switching based relaying protocol inenergy harvesting mobile node optimal throughput analysisrdquoMobile Information Systems vol 2015 Article ID 769286 8pages 2015
[17] C Zhang and Y Chen ldquoWireless power transfer strategies forcooperative relay system tomaximize information throughputrdquoIEEE Access vol 5 pp 2573ndash2582 2017
[18] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[19] Y Liu LWangM Elkashlan T Q Duong andANallanathanldquoTwo-way relay networks with wireless power transfer designand performance analysisrdquo IET Communications vol 10 no 14pp 1810ndash1819 2016
[20] T P Do I Song and Y H Kim ldquoSimultaneous wireless transferof power and information in a decode-and-forward two-wayrelaying networkrdquo IEEE Transactions on Wireless Communica-tions vol 16 no 3 pp 1579ndash1592 2017
[21] C Zhong H A Suraweera G Zheng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[22] Y Zeng and R Zhang ldquoFull-duplex wireless-powered relay withself-energy recyclingrdquo IEEE Wireless Communications Lettersvol 4 no 2 pp 201ndash204 2015
[23] D Wang R Zhang X Cheng and L Yang ldquoCapacity-enhancing full-duplex relay networks based on power-splitting(PS-)SWIPTrdquo IEEE Transactions on Vehicular Technology vol66 no 6 pp 5445ndash5450 2017
[24] ZDing I Krikidis B Sharif andHV Poor ldquoWireless informa-tion and power transfer in cooperative networks with spatiallyrandom relaysrdquo IEEETransactions onWireless Communicationsvol 13 no 8 pp 4440ndash4453 2014
[25] M Haghifam B Makki M Nasiri-Kenari and T SvenssonOn wireless energy and information transfer in relay networkshttpsarxivorgabs160707087 2016
12 Wireless Communications and Mobile Computing
[26] Y Liu ldquoWireless information and power transfer formultirelay-assisted cooperative communicationrdquo IEEE CommunicationsLetters vol 20 no 4 pp 784ndash787 2016
[27] J N Laneman and G W Wornell ldquoDistributed space-timecoded protocols for exploiting cooperative diversity in wirelessnetworksrdquo Institute of Electrical and Electronics Engineers Trans-actions on Information Theory vol 49 no 10 pp 2415ndash24252003
[28] IEEE Std IEEE Standard for Wireless LAN Medium AccessControl (MAC) and Physical Layer (PHY) Specifications(1999)
[29] N T Do V N Q Bao and B An ldquoOutage performance analysisof relay selection schemes in wireless energy harvesting coop-erative networks over non-identical rayleigh fading channelsrdquoSensors vol 16 no 3 article no 295 2016
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
Wireless Communications and Mobile Computing 11
Finally numerical results show that the multihop capabilityof CFP is better than CFIP and DFIP and for improvingthe multihop capabilities it is best effective to increase theaverage number of relay nodes in cooperative set
Through the analysis model proposed in this paper theappropriate values of related parameters that is initial energyof source node the number of relay nodes the energyharvesting efficiency coefficient and power splitting coeffi-cient can be set to achieve the given transmission hops fromsource to destination
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Acknowledgments
This work is funded by the China Postdoctoral Science Foun-dation (Grant no 2014M561627) the Natural Science Foun-dation ofAnhui Province (Grant no 1308085MF101) theNat-ural Science Foundation of Anhui Higher Education Insti-tutions (Grant no KJ2014A172) and the Science ResearchProject of Chaohu University (Grant no XLZ-201703)
References
[1] L R Varshney ldquoTransporting information and energy simul-taneouslyrdquo in Proceedings of the IEEE International Symposiumon Information Theory (ISIT rsquo08) pp 1612ndash1616 IEEE TorontoCanada July 2008
[2] P Grover and A Sahai ldquoShannonmeets tesla wireless informa-tion andpower transferrdquo inProceedings of the IEEE InternationalSymposium on Information Theory (ISIT rsquo10) pp 2363ndash2367Austin Tex USA June 2010
[3] R Zhang and C K Ho ldquoMIMO broadcasting for simultaneouswireless information and power transferrdquo IEEE Transactions onWireless Communications vol 12 no 5 pp 1989ndash2001 2013
[4] J N LanemanDN Tse andGWornell ldquoCooperative diversityin wireless networks efficient protocols and outage behaviorrdquoInstitute of Electrical and Electronics Engineers Transactions onInformation Theory vol 50 no 12 pp 3062ndash3080 2004
[5] A A Nasir X Zhou S Durrani and R A Kennedy ldquoWireless-powered relays in cooperative communications time-switchingrelaying protocols and throughput analysisrdquo IEEE Transactionson Communications vol 63 no 5 pp 1607ndash1622 2015
[6] E Chen M Xia D B da Costa and S Aissa ldquoMulti-Hopcooperative relaying with energy harvesting from cochannelinterferencesrdquo IEEE Communications Letters vol 21 no 5 pp1199ndash1202 2017
[7] X Zhou R Zhang and C K Ho ldquoWireless information andpower transfer architecture design and rate-energy tradeoffrdquoIEEE Transactions on Communications vol 61 no 11 pp 4754ndash4761 2013
[8] L Liu R Zhang and K-C Chua ldquoWireless information trans-fer with opportunistic energy harvestingrdquo IEEE Transactions onWireless Communications vol 12 no 1 pp 288ndash300 2013
[9] L Liu R Zhang and K C Chua ldquoWireless information andpower transfer a dynamic power splitting approachrdquo IEEETransactions on Communications vol 61 no 9 pp 3990ndash40012013
[10] H Ju and R Zhang ldquoThroughput maximization in wire-less powered communication networksrdquo IEEE Transactions onWireless Communications vol 13 no 1 pp 418ndash428 2014
[11] R Morsi D S Michalopoulos and R Schober ldquoMultiuserscheduling schemes for simultaneous wireless information andpower transfer over fading channelsrdquo IEEE Transactions onWireless Communications vol 14 no 4 pp 1967ndash1982 2015
[12] C Zhong X Chen Z Zhang and G K Karagiannidis ldquoWire-less-powered communications performance analysis and opti-mizationrdquo IEEE Transactions on Communications vol 63 no12 pp 5178ndash5190 2015
[13] N Zhao F R Yu and V C M Leung ldquoOpportunistic com-munications in interference alignment networks with wirelesspower transferrdquo IEEE Wireless Communications Magazine vol22 no 1 pp 88ndash95 2015
[14] N Zhao ldquoJoint optimization of power splitting and allocationfor SWIPT in interference alignment networksrdquo in v preprintpp 1701ndash01952 httpsarxivorgabs170101952 2017
[15] A A Nasir X Zhou S Durrani and R A Kennedy ldquoRelayingprotocols for wireless energy harvesting and information pro-cessingrdquo IEEETransactions onWireless Communications vol 12no 7 pp 3622ndash3636 2013
[16] D-T Do ldquoTime power switching based relaying protocol inenergy harvesting mobile node optimal throughput analysisrdquoMobile Information Systems vol 2015 Article ID 769286 8pages 2015
[17] C Zhang and Y Chen ldquoWireless power transfer strategies forcooperative relay system tomaximize information throughputrdquoIEEE Access vol 5 pp 2573ndash2582 2017
[18] Z Chen B Wang B Xia and H Liu ldquoWireless informationand power transfer in two-way amplify-and-forward relayingchannelsrdquo inProceedings of the IEEEGlobal Conference on Signaland Information Processing (GlobalSIP rsquo14) pp 168ndash172 AtlantaGa USA December 2014
[19] Y Liu LWangM Elkashlan T Q Duong andANallanathanldquoTwo-way relay networks with wireless power transfer designand performance analysisrdquo IET Communications vol 10 no 14pp 1810ndash1819 2016
[20] T P Do I Song and Y H Kim ldquoSimultaneous wireless transferof power and information in a decode-and-forward two-wayrelaying networkrdquo IEEE Transactions on Wireless Communica-tions vol 16 no 3 pp 1579ndash1592 2017
[21] C Zhong H A Suraweera G Zheng I Krikidis and Z ZhangldquoWireless information and power transfer with full duplexrelayingrdquo IEEE Transactions on Communications vol 62 no 10pp 3447ndash3461 2014
[22] Y Zeng and R Zhang ldquoFull-duplex wireless-powered relay withself-energy recyclingrdquo IEEE Wireless Communications Lettersvol 4 no 2 pp 201ndash204 2015
[23] D Wang R Zhang X Cheng and L Yang ldquoCapacity-enhancing full-duplex relay networks based on power-splitting(PS-)SWIPTrdquo IEEE Transactions on Vehicular Technology vol66 no 6 pp 5445ndash5450 2017
[24] ZDing I Krikidis B Sharif andHV Poor ldquoWireless informa-tion and power transfer in cooperative networks with spatiallyrandom relaysrdquo IEEETransactions onWireless Communicationsvol 13 no 8 pp 4440ndash4453 2014
[25] M Haghifam B Makki M Nasiri-Kenari and T SvenssonOn wireless energy and information transfer in relay networkshttpsarxivorgabs160707087 2016
12 Wireless Communications and Mobile Computing
[26] Y Liu ldquoWireless information and power transfer formultirelay-assisted cooperative communicationrdquo IEEE CommunicationsLetters vol 20 no 4 pp 784ndash787 2016
[27] J N Laneman and G W Wornell ldquoDistributed space-timecoded protocols for exploiting cooperative diversity in wirelessnetworksrdquo Institute of Electrical and Electronics Engineers Trans-actions on Information Theory vol 49 no 10 pp 2415ndash24252003
[28] IEEE Std IEEE Standard for Wireless LAN Medium AccessControl (MAC) and Physical Layer (PHY) Specifications(1999)
[29] N T Do V N Q Bao and B An ldquoOutage performance analysisof relay selection schemes in wireless energy harvesting coop-erative networks over non-identical rayleigh fading channelsrdquoSensors vol 16 no 3 article no 295 2016
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
International Journal of
Hindawi
wwwhindawicom Volume 2018
Advances in
Multimedia
Submit your manuscripts atwwwhindawicom
12 Wireless Communications and Mobile Computing
[26] Y Liu ldquoWireless information and power transfer formultirelay-assisted cooperative communicationrdquo IEEE CommunicationsLetters vol 20 no 4 pp 784ndash787 2016
[27] J N Laneman and G W Wornell ldquoDistributed space-timecoded protocols for exploiting cooperative diversity in wirelessnetworksrdquo Institute of Electrical and Electronics Engineers Trans-actions on Information Theory vol 49 no 10 pp 2415ndash24252003
[28] IEEE Std IEEE Standard for Wireless LAN Medium AccessControl (MAC) and Physical Layer (PHY) Specifications(1999)
[29] N T Do V N Q Bao and B An ldquoOutage performance analysisof relay selection schemes in wireless energy harvesting coop-erative networks over non-identical rayleigh fading channelsrdquoSensors vol 16 no 3 article no 295 2016
