Research ArticlePerformance Analysis for Downlink MIMO-NOMA in MillimeterWave Cellular Network with D2D Communications
Jianguo Li Xiangming Li Aihua Wang and Neng Ye
School of Information and Electronics Beijing Institute of Technology Beijing China
Correspondence should be addressed to Xiangming Li xmlibiteducn
Received 4 April 2019 Accepted 3 June 2019 Published 19 June 2019
Guest Editor Xi Chen
Copyright copy 2019 Jianguo Li et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
Enabling nonorthogonal multiple access (NOMA) in device-to-device (D2D) communications under the millimeter wave(mmWave) multiple-input multiple-output (MIMO) cellular network is of critical importance for 5G wireless systems to supportlow latency high reliability and high throughput radio access In this paper the closed-form expressions for the outage probabilityand the ergodic capacity in downlinkMIMO-NOMAmmWave cellular network with D2D communications are considered whichindicates that NOMA outperforms TDMA The influencing factors of performance such as transmission power and antennanumber are also analyzed It is found that higher transmission power and more antennas in the base station can decrease theoutage probability and enhance the ergodic capacity of NOMA
1 Introduction
With the rapid growth of a variety of 5th-generation wirelesssystems commercial requirements like 8k video cloud VRunmanned driving smart city etc the demands on high datarates low latency and high reliability of wireless communica-tion are increasing rapidly As the core technologies of 5G thewide bandwidth and large scale antenna arrays can be usedby mmWave MIMO to provide high data rates MeanwhileNOMA can increase the spectral efficiency of transmissionso that more data is transmitted over the same bandwidthspectrum At the same time due to the short communicationdistance D2D communication can obtain lower transmissionpower and lower delay to ensure the battery availability andsystem reliability Therefore combined with MIMO-NOMAandmmWave inD2D communications the throughput of theentire cell system can be improved
D2D communication was noticed as a viable candidatefor some certain applications such as proximity servicescontent sharing multiparty games and coverage discoveredwith business purposes in the 3rd-Generation PartnershipProject (3GPP) Long-term Evolution (LTE) 12th and 13theditions [1 2] By sharing the same resource blocks withdownlink cellular users D2D communication is a usefultechnology which can enhance the spectrum efficiency and
system capacity successfully Due to the short communica-tion distance D2D pairs can communicate with each otherdirectly without being relayed by the base station which canreduce transmission power increase transmission reliabilityand extend system range [3 4] Since the cellular user andthe D2D user coexist if the D2D user and the cellular userare not well coordinated it will not bring any benefits andmay affect the communication of the normal cellular userAccording to the literature [5] based on the overlappingcoalition formation game theory the authors have proposeda method to conduct joint interference management andresource allocation in the D2D communications In additiona new interference management strategy has been discussedto enhance the overall sum rate of cellular networks andD2D pairs which has combined the conventional mechanismand 120575119863-interference limited area control scheme [6] Fur-thermore a graph theoretic approach for transmission-orderoptimization scheme in bidirectional D2D communicationsunderlaying cellular TDD networks has been introduced inthe [7] Meanwhile the authors in [8] have considered acontinuous beamforming vector design for all cellular usersand the D2D pairs association vector search algorithm tomaximize the capacity of the cellular users and D2D pairsIn order to reduce the interference between the cellular usersandD2Dpairs a combining call admission control andpower
HindawiWireless Communications and Mobile ComputingVolume 2019 Article ID 1914762 11 pageshttpsdoiorg10115520191914762
2 Wireless Communications and Mobile Computing
control scheme under guaranteeing QoS of every users inthe cellular network has been presented in [9] Besides it issignificant that the NOMA andMU-MIMO can also improvethe overall system throughput in the cellular network withunderlaid D2D communications which have been proposedin [10]
As the core technology of 5G NOMA can serve mul-tiple users in the same resource block such as a timeslot frequency channel or spreading code Compared tothe orthogonal multiple access NOMA can provide a setof visible benefits such as greater spectrum efficiency andhigher system throughout [11ndash15] There are two availableNOMA technology categories namely power-domain andcode-domain NOMA widely used in the cellular networkThis paper focuses on the power-domain NOMA whichdivides the users in power-domain On the transmitter sidessignals from multiple users are transmitted at the sameresource blocks On the receiver sides the multiuser detec-tion algorithms such as successive interference cancellationhave been utilized to detect the signal regarding the weaksignal as the interference and decode the strong signal whilecancelling the strong signal to detect the weak signal [16 17]Aiming at enhancing system capacity and user fairness theauthors have presented a novel resource and power allocationtechnique which can provide a flexible balancing betweencapacity and fairness maximization in [18] Meanwhile theoptimum received power levels of uplink NOMA signal havebeen proposed in [19] Furthermore comparing with OMAin massive connectivity NOMA can supply more users thanOMA because of the limited number of supported users bythe amount of the available resources [20ndash22] In additionthe analytical outage probability expression for each user hasbeen derived in the downlink cooperative NOMA networkover Nakagami-m fading channels in [23] Since the perfectchannel state information at the transmitter side is nearlyimpractical formany communication scenarios the literature[24] presented a practical downlink NOMA system over theNakagami-m fading channels with statistical CSI associatedwith each other At the same time the authors attempted tocombine the NOMA andMIMO to accomplish high spectralefficiency [25 26] Additionally the outage probability of themassiveMIMO-NOMAsystemhas been derivedwith perfectuser-ordering and limited feedback [27] Besides the schemediscussed in [28] required that the number of antennas at thereceiver is larger than that at the transmitter instead of theCSIat the transmitter In [29] the optimal and low complexitysuboptimal power allocation schemes have been proposedto maximize the ergodic capacity of MIMO-NOMA systemwith statistical channel state information in the transmitterover Rayleigh fading channel Also the authors in [30] haveproposed a cluster beamforming strategy which can optimizebeamforming vectors and power allocation coefficients inMIMO-NOMA system to decrease the total power In addi-tion NOMA can improve the achievable rate greatly in theD2D-aided cooperative relaying system in the literature [31]
Nowadays as spectrum resources become increasinglyscare the mmWave band with a wider spectrum becomes anatural choice for large-volume content services [32] Mean-while benefitting from the small wavelength of mmWave
the large scale antenna arrays can be adopted easily Com-bining the high gain directional antenna and beamformingtechnology enabled by massive antennas the high data ratescan be reached within a 200-metermmWave cellular networkwhich has high path loss in mmWave band [33] In theliterature [34] the authors have proposed that the base stationwhich is equipped with a large antenna array can servea set of users through the users precoding with massiveMIMO Furthermore the literature [35] has proved thatthe orders of magnitude are increased in spectral efficiencywith massive MIMO which can offer more multiuser gainHowever as for MIMO in conventional cellular frequencyband the beamforming precoding is totally achieved in thedigital domain which can cancel the interference betweendifferent beams In order to realize the precoder in the digitaldomain a dedicated RF chain is needed by every antennaBut it is difficult for the mmWave base station with large scaleantennas whose energy consumption is a large part of thetotal energy consumption at mmWave frequencies due to thewide bandwidth [36] At the same time the authors in [36]have discussed a successive interference cancellation-basedhybrid precoding method with near-optimal performanceand low complexity which can maximize the achievablesubrate of each subantenna array and avoid the need forsingular value decomposition and matrix inversion Addi-tionally the literature [37] has proposed an interference-aware beam selection which can avoid serious multiuserinterferences to reduce obvious performance loss Besidesthe authors in [38] have proposed a practical design of hybridprecoders and combiners with low-resolution phase shiftersin mmWave MIMO systems adopting an iterative algorithmfor hybrid precoders and combiners to optimize the spectralefficiency Moreover the MIMO capacity has been computedover the Nakagami-m fading channel in [39] and the closed-form expressions for outage probabilities achieved byNOMAusers in a multicell downlink mmWave network have beenobtained over a Poisson cluster point process Moreovera fine-grained performance analysis over Poisson bipolarmodel of the mmWave D2D communication networks wasprovided in [40] The literature [41] has presented an in-depth capacity analysis for the integrated NOMA mmWave-massive-MIMO systems which can achieve significant capac-ity improvements
Because of the large link attenuation and weak coveragein the MIMO-NOMA cellular network the D2D communi-cation can be used to enhance service for cell edge users Inthis paper the outage probability and the ergodic capacity areproposed in the downlink MIMO-NOMA cellular networkwith D2D communicationsThe remaining part of this paperis organized as follows In Section 2 we introduce a systemmodel of the downlink MIMO-NOMA cellular networkwith multiple direct D2D pairs underlaying communicationThe closed-form expressions of the performance analysisincluding the outage probability and the ergodic capacityare given in Section 3 Finally the numerical results inSection 4 validate the theoretical analysis and demonstratethat the system capacity can be improved by the inte-grated MIMO-NOMA in the mmWave network with D2Dcommunications
Wireless Communications and Mobile Computing 3
Digital
RF chain
RF chainprecoder
＄５1
＄５2
＄５3
＄５4
＄５P
＄５P-1
CU2
CU1
CU3
CU4
CUQ
CUQ-1
Figure 1 System model of D2D-aided mmWave MIMO-NOMA
2 System Model
The paper considers a downlink NOMA MU-MIMOmmWave cellular network with multiple direct D2D pairsunderlaying communications where the cellular users arerandomly distributed The same mmWave resources are usedby the cellular user andD2DpairswithNOMAThemmWaveMIMO-NOMAD2D communication systemmodel is shownin Figure 1 The base station is equipped with multipleantennas which can generate high directional and high gainbeams for cellular usersThere are119876 cellular users with signalantenna and 119875 D2D users with signal antenna in the cellu-lar network which are denoted as 1198621198801 1198621198802 119862119880119876 and1198631198801 1198631198802 119863119880119875TheD2Dpairs are randomly distributedin the edge of the cellular network and there is no direct linkbetween the base station and the D2D pairs [10]
21 NOMA Signal In beam 119899 we assume that 119906(119899 1)119906(119899 2) 119906(119899 119870) are scheduled on the same radio resourcewithNOMA119870 ge 2 where119862119880 of 119896119905ℎ in the beam 119899 is denotedas 119906(119899 119896) 119909119899 is the transmitted signal by the base station inthe beam 119899 which is the sum of all K user signals
where 120582119906(119899119896) is the power ratio of 119896119905ℎ user 120582119906(1198991) le120582119906(1198992) le 120582119906(119899119870) andsum119870119896=1 120582119906(119899119896) = 1119875119899 is the total power
in the beam 119899 119878119906(119899119896) is the normalized transmitted signal of119896119905ℎ user in the beam 119899 and E(119878119906(119899119896)2) = 122 Channel Model As for the large scale fading themmWave link is similar to that used in [33] the large scalefading 119871(119903) in dB is modeled as119871 (119903) = 120588 + 10120572 log (119903) (2)
where 120588 = 324 + 20 log(119891119888) 119891119888 is the carrier frequency 120572 isthe path loss exponents and 119903 is the distance from transmitterto receiver
As for the small scale fading the Nakagami-m fading isconsidered for each link ℎ119906(119899119896) ℎ119901119906(119899119896) ℎ1199011015840119901 are donated asthe link of base station to cellular user D2D user to cellularuser and D2D user to D2D user whose modular square isnormalized Gamma random variable [39] And when 119867 isnormalized Gamma random variable which is denoted as119867 sim 119866119886119898119898119886(120596 120595) the probability density function 119891(119909)and Cumulative Distribution Function 119865(119909) of H are
1119895120595119895119909119895119890minus119909120595 119909 ge 0
0 otherwise (4)
23 Directional Beamforming The base station withmmWave band is equipped with multiple antennas whichcan generate high directional and high gain beamsThe actualantenna pattern is modeled as the sectorized antenna modelapproximately for the sake of mathematical tractability [42]Generally the maximum power gain is adopted to replacethe array gain within the half-power beam width (main lobegain) and the first minor maximum gain is used to replacethe gains of the other DoAs (side lobe gain) According tothe literature [39 40] when the antenna pattern is a planarsquare the total array gain from base station to the user is119866(119899119896) where
where 119879 = 119871 120591 = 1sin2(31205872radic119871) and 119871 is the number ofantennas
24 Received Signal For downlinkMIMO-NOMA transmis-sion the cellular user 119906(119899 119870) will receive the sum of signalfrom base station and the signal from D2D transmitter atthe same time In addition to receiving the D2D transmittedsignal theD2D receiver119863119880119875will also receive the interferencesignal from the other D2D users Without loss of generalitywe assume there are119873 beams and119872D2Dpairs in the cellularnetwork then the received signal of cellular user 119910119906(119899119896) andthe received signal of D2D user 119910119863119901 can be formulated as
where ℎ119906(119899119896) is the channel gain for downlink 119906(119899 119870)ℎ119906(1198991) ge ℎ119906(1198992) ge ℎ119906(119899119870) ℎ119901119906(119899119896) is the channelgain between 119863119880119875 and 119906(119899 119870) and ℎ1199011015840119901 is the channel gainfrom 1198631198801199011015840 transmitter to 119863119880119901 receiver 119866(119899119896) is the totalbeamforming array gain frombase station to 119906(119899119870)119909119899 is thesuperimposed signal by the total K 119906(119899 119896) in the beam 119899 119875119863is the transmitted power of119863119880119875 119878119901 is the signal transmittedby119863119880119875 and E(1198781199012) = 1 Meanwhile 119899119906(119899119896) and 119899119863119901 are theiid white Gaussian noise with zero mean and one varianceat cellular user 119906(119899 119896) and D2D user 119863119880119875 which is denotedas 119899119906(119899119896) 119899119863119901 sim C119873(0 1)
We denote the SINRs of 119906(119899 119896) and119863119880119875 in the downlinkNOMA-MIMO cellular network as 120574119906(119899119896) 120574119863119880119901
Without lossof generality the interbeam interference is ignored in thispaper In the meantime the perfect SIC is used to preventerror propagation in the NOMA users in the paper Using (1)in (6) and (7) 120574119906(119899119896) and 120574119863119880119901
In this section we present the performance analysis ofD2D-aidedmmWaveMIMO-NOMAsystem Specifically theclosed-form expressions for the performancemetrics (ie theoutage probability and the ergodic capacity) are presentedin the following Without loss of generality in the beam119899 119896-th 119862119880119904 are adopted with NOMA in one beam 119896 isin1 2ℎ119906(1198991) ge ℎ119906(1198992) and one119863119880 is randomly distributedat the edge of the beam Three events are considered in thissystem
Event 1 According to the NOMA successive interferencecancellation (SIC) principle user 1 obtains the informationintended for user 2 with 1205741997888rarr2 and removes it Whendecoding the information intended for user 2 user 1 cancelsit successfully with 1205741
31 Outage Probability In this section we study the outageprobability of 119862119880 and119863119880 The outage probability of the user1 user 2 and119863119880 is given by 119875119900119906119905
where 1198771 1198772 119877119863 are the target rates of user 1 user 2 and119863119880Firstly we consider the outage probability of user 1 119875119900119906119905
1 then 119875(log(1 + 1205741997888rarr2) le 1198772) can be rewritten as 119875(1205741997888rarr2 le21198772 minus 1) so we set
119875 (1205741997888rarr2 le 21198772 minus 1) = 119865 (119898 119886 119887 119888 119889) = 1198651205741997888rarr2 (119898) (21)
where 119886 = 120582119906(1198992)119875119899119866(1198991)2 119887 = 120582119906(1198991)119875119899119866(1198991)2 119889 = 119875119863119888 = 1205902119899 119898 = 21198772 minus 1 and 1198671 = ℎ119906(1198991)2 sim 119866119886119898119898119886(120596 120595)1198672 = ℎ119901119906(1198991)2 sim 119866119886119898119898119886(120578 120579) then1198651205741997888rarr2 (119898) = 119875( 11988611986711198871198671 + 1198891198672 + 119888 le 119898)
= intinfin
0119875( 119886119910119887119910 + 1198891198672 + 119888 le 119898)1198911198671 (119910) 119889119910
= intinfin
0119875(119886119910 minus 119887119898119910 minus 119888119898119889119898 le 1198672)1198911198671 (119910) 119889119910
(22)
In order to determine if (119886119910 minus 119887119898119910 minus 119888119898)119889119898 le 0 we setΦ = 119888119898(119886 minus 119887119898) WhenΦ le 0 (119886119910 minus 119887119898119910minus 119888119898)119889119898 le 0 so119875((119886119910 minus 119887119898119910 minus 119888119898)119889119898 le 1198672) = 1 therefore1198651205741997888rarr2 (119898) = 1 (23)
When Φ gt 0 which is119898 lt 1198861198871198651205741997888rarr2 (119898) = intΦ
01198911198671 (119910) 119889119910
+ intinfin
Φ(1 minus 1198651198672 (119886119910 minus 119887119898119910 minus 119888119898119889119898 ))1198911198671 (119910) 119889119910
= intinfin
Φ
120578minus1sum119895=0
1119895120579119895 (119886 minus 119887119898119889119898 119910 minus 119888119889)119895
(119895119894) 120572119894120573119895minus119894sdot 119890minus120573120579 (minus119869(minus(120572120579 + 1120595) 120596 + 119895 minus 1Φ))+ 1120595120596Γ (120596) (119869 (minus( 1120595) 120596 minus 1Φ)minus 119869(minus( 1120595) 120596 minus 1 0))
(28)
Similarly by adopting different parameters with119886 119887 119888 119889 which is shown in Table 1 we can obtain1198651205741997888rarr2(119898) 1198651205741(119898) 1198651205742(119898)In addition when 1198673 = ℎ1199011199012 sim 119866119886119898119898119886(120596 120601)119875119863ℎ11990111990121205902119899 sim 119866119886119898119898119886(120596 (1198751198631205902119899)120601) Hence 119865120574119863(119898) is
denoted as
119865120574119863 (119898) = 1 minus 120596minus1sum119869=0
Finally the outage probability of user 1 user 2 and 119863119880can be evaluated by 1198651205741997888rarr2(119898) 1198651205741(119898) 1198651205742(119898) 119865120574119863(119898) whichare formulated as
1198751199001199061199051 = 1 minus (1 minus 1198651205741997888rarr2 (21198772 minus 1))
lowast (1 minus 1198651205741 (21198771 minus 1)) (30)
1198751199001199061199052 = 1198651205742 (21198772 minus 1) (31)
119875119900119906119905119863 = 119865120574119863 (2119877119863 minus 1) (32)
32 Ergodic Capacity The ergodic capacity is the averagecapacity of channel which can be defined as the instantaneousend-to-end mutual information expectations and denoted as
119862119890119903119892 = E [log2 (1 + 1205741)] + E [log2 (1 + 1205742)]+ E [log2 (1 + 120574119863)] (33)
6 Wireless Communications and Mobile Computing
Table 1 Parameters of the outage probability
a b c d1198651205741997888rarr2 (119898) 120582119906(1198991)119875119899 1003817100381710038171003817119866(1198991)10038171003817100381710038172 120582119906(1198992)119875119899 1003817100381710038171003817119866(1198992)
In order to compute (34) we first compute the first itemofthe formula As we set before 119886 = 120582119906(1198991)119875119899119866(1198991)2 119889 = 119875119863119888 = 1205902119899 1198671 = ℎ119906(1198991)2 sim 119866119886119898119898119886(120596 120595) 1198672 = ℎ119901119906(1198991)2 sim119866119886119898119898119886(120578 120579) we can get
Similarly we can set a b c d as different parametersto obtain the other items of the formula (34) and then pulleverything together The asymptotic result for the ergodiccapacity of the consider system can be obtained
Wireless Communications and Mobile Computing 7
4 Numerical Results
In this section the outage probability and the ergodic capacityof MIMO-NOMA mmWave cellular network with D2Dcommunications are investigated The effects of differentparameters on the probability of outage and ergodic capacityare analyzed such as the base station transmission power thenumber of base station antennas the power ratio of NOMAuser and the distance between D2D users In order to verifythe performance of the system the traditional TDMA themeis adopted as the comparison between the two users of eachbeam In particular the time slot is equally divided by the twousers Hence the capacity of this theme is 119877119879119863119872119860 which isdenoted as
A simplified cellular network system is discussed for theperformance analyzed here The carrier frequency is 28GHzwhich is commonly used for wireless broadband serviceThere are 16 antennas in the base station whose coverageradius is 100m There is single antenna with D2D user Andthe distance between D2D users is 30m Meanwhile thetransmission power of base station and D2D users is 5 dbmIn addition there are 8 NOMA users and 4 D2D usersin the cellular network The path loss exponent is set as3 Furthermore the small scale fading is denoted as 119867 sim119866119886119898119898119886(2 1) which is simplified for the simulation
41 Outage Probability In this section we consider theoutage probability of the NOMA far user and near user
Figure 2 depicts the outage probability in the differentbase station transmission power with 1198771 = 5 bitsHz and1198772 = 332 bitsHz As the base station transmission powerincreases it can be seen that the outage probability of theNOMA users decreases with the exponential form Further-more the performance of each userrsquos outage probability inthe NOMA scheme is significantly better than the TDMAand the closed-form solution obtained is consistent with theMonte Carlo simulation results
In Figure 3 the impact of antenna number in the basestation on the outage probability (1198771 = 564 bitsHz and 1198772
= 4 bitsHz) is presented The simulation results effectivelyverify that the number of antennas of the base stationcan decrease the usersrsquo outage probability in the MIMO-NOMA mmWave cellular network thereby improving thethroughput of the system under the limited time-frequencyresources As can be seen from Figure 3 the number ofantennas has a greater impact on user 2 than user 1When thenumber of antennas is 36 the outage probability of the systemis satisfied which can balance the number of RF chains andthe system performance Then the NOMA scheme performsbetter than the traditional TDMA in the mmWave MIMOcellular network with D2D communications
In Figure 4 we discuss the influence of the power ratiocoefficient in the cellular network between the NOMA usersIt can be seen that the outage probability (1198771 = 4 bitsHz and1198772 = 3 bitsHz) of the two users in NOMA is balanced whenthe power ratio coefficient is approximately 02
Analysis result User 1Numerical result User 1TDMA User 1Analysis result User 2Numerical result User 2TDMA User 2
10minus2
10minus1
100
Out
age p
roba
bilit
y
10 15 20 255Transmission Power (dbm)
Figure 2 Impact of transmission power on outage probability
Analysis result User 1Numerical result User 1TDMA User 1Analysis result User 2Numerical result User 2TDMA User 2
10minus2
10minus1
100
Out
age p
roba
bilit
y
10 15 20 25 30 355Antenna Number
Figure 3 Impact of antenna number on outage probability
In Figure 5 the effect of the distance between D2D usersis consideredThe figure indicates that the outage probability(1198771 = 5 bitsHz and1198772 = 332 bitsHz) of the NOMAusers isreduced in the formof an exponent when the distance ofD2Duser is linear growth Since the distance betweenD2Dusers isincreasing the interference from the D2D transmitter to theNOMA user is weak Hence the throughput of the NOMAusers is improved while the outage probability is dropping
8 Wireless Communications and Mobile Computing
Analysis result User 1Numerical result User 1Analysis result User 2Numerical result User 2
01 015 02 025 03 035 04 045005Power ratio coefficient
10minus3
10minus2
10minus1
100
Out
age p
roba
bilit
y
Figure 4 Impact of power ratio coefficient on outage probability
Analysis result User 1Numerical result User 1Analysis result User 2Numerical result User 2
30 40 50 60 70 8020D2D Distance (m)
10minus2
10minus1
100
Out
age p
roba
bilit
y
Figure 5 Impact of D2D distance on outage probability
42 Ergodic Capacity In this section the total ergodiccapacity is considered in the MIMO-NOMA mmWave cel-lular network with D2D communications It can be seenthat the numerical results are consistent with the closed-form solution which is better than the traditional TDMAMeanwhile the transmission power and the number of basestation antennas have a greater impact and the power ratiocoefficient and the distance between D2D users have lesseffect
In Figure 6 the impact of the transmission power of basestation on the ergodic capacity is considered in the MIMO-NOMA mmWave cellular network with D2D communica-tions It is shown that the ergodic capacity is growing linearly
Analysis resultNumerical resultTDMA
10 15 20 255Transmission Power (dbm)
8
10
12
14
16
18
Syste
m C
apac
ityFigure 6 Impact of transmission power on ergodic capacity
with the increase of transmission power In addition theergodic capacity of the systemwe proposed is higher than thetraditional TDMA Hence in order to improve the ergodiccapacity of the system we can increase the base stationtransmission power as much as possible without affectingothers
As the number of the base station antennas is increasingit is indicated that the ergodic capacity can be improvedbetter than the traditional TDMA in Figure 7 Benefitingfrom the length of mmWave more and more antennas canbe equipped for the base station At the same time we needto balance the improvement in ergodic capacity brought bythe increasing of the number of antennas and the powerconsumption and hardware requirements of the increase inRF chains to determine the final number of antennas
In Figure 8 the ergodic capacity is affected by thechange of the power ratio coefficient of the NOMA usersin the MIMO-NOMA mmWave cellular network with D2Dcommunications It can be seen that the total ergodic capacitychanges slowly with the increase of power ratio
In Figure 9 since the interference from the D2D users isdecreasing the total ergodic capacity is improved with theincrease of the distance between theD2Dusers in theMIMO-NOMA mmWave cellular network It can also be seen thatthe ergodic capacity in the MIMO-NOMAmmWave cellularnetwork is always better than the traditional TDMA
5 Conclusion
In this paper the outage probability and the ergodic capacityof the NOMA in the MIMO-NOMA mmWave cellularnetwork with D2D communications are studied The closed-form solutions of the outage probability and the ergodiccapacity are obtained which are consistent with the numeri-cal results Meanwhile the performance of NOMA is shown
Wireless Communications and Mobile Computing 9
Analysis resultNumerical resultTDMA
4
6
8
10
12
14
16
Syste
m C
apac
ity
10 15 20 25 30 355Antenna Number
Figure 7 Impact of antenna number on ergodic capacity
Analysis resultNumerical resultTDMA
01 015 02 025 03 035 04 045005Power Ratio Coefficient
6
7
8
9
10
11
12
Syste
m C
apac
ity
Figure 8 Impact of power ratio coefficient on ergodic capacity
to be better than traditional TDMA in the MIMO mmWavecellular network with D2D communications Furthermorethe higher transmission power of base station and the largerantenna array can also improve system performance
Data Availability
No data were used to support this study
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Analysis resultNumerical resultTDMA
6
7
8
9
10
11
12
13
Syste
m C
apac
ity
30 40 50 60 70 8020D2D Distance (m)
Figure 9 Impact of D2D distance on ergodic capacity
Acknowledgments
This work was supported by Advance Research Projects of13th Five-Year Plan of Civil Aerospace Technology (B0105)and the National Natural Science Foundation of China(61771051)
References
[1] M Tehrani M Uysal and H Yanikomeroglu ldquoDevice-to-device communication in 5G cellular networks challengessolutions and future directionsrdquo IEEE Communications Mag-azine vol 52 no 5 pp 86ndash92 2014
[2] S-Y Lien C-C Chien G S-T Liu H-L Tsai R Li and YJ Wang ldquoEnhanced LTE device-to-device proximity servicesrdquoIEEE Communications Magazine vol 54 no 12 pp 174ndash1822016
[3] L Lei ZD ZhongC Lin andXM Shen ldquoOperator controlleddevice-to-device communications in LTE-advanced networksrdquoIEEEWireless Communications Magazine vol 19 no 3 pp 96ndash104 2012
[4] A Asadi and V Mancuso ldquoNetwork-assisted outband D2D-clustering in 5G cellular networks theory and practicerdquo IEEETransactions onMobile Computing vol 16 no 8 pp 2246ndash22592017
[5] J HuW Heng Y Zhu GWang X Li and JWu ldquoOverlappingcoalition formation games for joint interference managementand resource allocation in D2D communicationsrdquo IEEE Accessvol 6 pp 6341ndash6349 2018
[6] H Min J Lee S Park and D Hong ldquoCapacity enhancementusing an interference limited area for device-to-device uplinkunderlaying cellular networksrdquo IEEE Transactions on WirelessCommunications vol 10 no 12 pp 3995ndash4000 2011
[7] Z Uykan and R Jantti ldquoTransmission-order optimization forbidirectional device-to-device (D2D) communications under-laying cellular TDD networksmdasha graph theoretic approachrdquoIEEE Journal on Selected Areas in Communications vol 34 no1 pp 1ndash14 2016
10 Wireless Communications and Mobile Computing
[8] L L Wei R Q Hu T He and Y Qian ldquoDevice-to-device(d2d)communications underlaying MU-MIMO cellular networksrdquoin Proceedings of the IEEE Global Communications Conference(GLOBECOM rsquo13) pp 4902ndash4907 IEEE Atlanta Ga USADecember 2013
[9] X Li W Zhang H Zhang andW Li ldquoA combining call admis-sion control and power control scheme for D2D communica-tions underlaying cellular networksrdquo China Communicationsvol 13 no 10 pp 137ndash145 2016
[10] H Sun Y Xu and R Q Hu ldquoA NOMA and MU-MIMOsupported cellular network with underlaid D2D communica-tionsrdquo in Proceedings of the 2016 IEEE 83rd Vehicular TechnologyConference (VTC Spring) pp 1ndash5 Nanjing China May 2016
[11] Z Ding X Lei G K Karagiannidis R Schober J Yuan andV K Bhargava ldquoA survey on non-orthogonal multiple accessfor 5G networks research challenges and future trendsrdquo IEEEJournal on Selected Areas in Communications vol 35 no 10 pp2181ndash2195 2017
[12] N Ye X Li H Yu AWangW Liu andXHou ldquoDeep learningaided grant-free noma towards reliable low-latency access intactile internet of thingsrdquo IEEE Transactions on IndustrialInformatics vol 15 no 5 pp 2995ndash3005 2019
[13] J An K Yang J Wu N Ye S Guo and Z Liao ldquoAchievingsustainable ultra-dense heterogeneous networks for 5Grdquo IEEECommunications Magazine vol 55 no 12 pp 84ndash90 2017
[14] N Ye AWang X Li H Yu A Li andH Jiang ldquoA randomnon-orthogonal multiple access scheme for mmtcrdquo in Proceedingsof the 2017 IEEE 85th Vehicular Technology Conference (VTCSpring) pp 1ndash6 June 2017
[15] K Yang N Yang N Ye M Jia Z Gao and R Fan ldquoNon-orthogonal multiple access achieving sustainable future radioaccessrdquo IEEE Communications Magazine vol 57 no 2 pp 116ndash121 2019
[16] S M R Islam N Avazov O A Dobre and K-S KwakldquoPower-domain non-orthogonal multiple access (NOMA) in5G systems potentials and challengesrdquo IEEE CommunicationsSurveys amp Tutorials vol 19 no 2 pp 721ndash742 2017
[17] N Ye AWang X Li W Liu X Hou and H Yu ldquoOn constella-tion rotation of noma with sic receiverrdquo IEEE CommunicationsLetters vol 22 no 3 pp 514ndash517 2018
[18] MHojeij C A Nour J Farah and C Douillard ldquoJoint resourceand power allocation technique for downlink power-domainnon-orthogonalmultiple accessrdquo inProceedings of the 2018 IEEEConference on Antenna Measurements amp Applications (CAMA)pp 1ndash4 September 2018
[19] F A Rabee K Davaslioglu and R Gitlin ldquoThe optimumreceived power levels of uplink non-orthogonal multiple access(NOMA) signalsrdquo in Proceedings of the 18th IEEE Wireless andMicrowave Technology Conference WAMICON 2017 pp 1ndash4USA April 2017
[20] Y Li andG A A Baduge ldquoNoma-aided cell-freemassivemimosystemsrdquo IEEEWireless Communications Letters vol 7 pp 950ndash953 2018
[21] N Ye A Wang X Li et al ldquoRate-adaptive multiple access foruplink grant-free transmissionrdquo Wireless Communications andMobile Computing vol 2018 Article ID 8978207 21 pages 2018
[22] N Ye H Han L Zhao and A-H Wang ldquoUplink nonorthogo-nal multiple access technologies toward 5G a surveyrdquo WirelessCommunications and Mobile Computing vol 2018 Article ID6187580 26 pages 2018
[23] Y LiuW-J Lu S Shi et al ldquoPerformance analysis of a downlinkcooperative noma network over nakagami-m fading channelsrdquoIEEE Access vol 6 pp 53034ndash53043 2018
[24] X Wang J Wang L He and J Song ldquoOutage analysis fordownlink noma with statistical channel state informationrdquoIEEEWireless Communications Letters vol 7 no 2 pp 142ndash1452018
[25] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAnoverview ofMIMOcommunicationsmdasha key to gigabit wirelessrdquoProceedings of the IEEE vol 92 no 2 pp 198ndash217 2004
[26] W Cai C Chen L Bai Y Jin and J Choi ldquoUser selectionand power allocation schemes for downlink NOMA systemswith imperfect CSIrdquo in Proceedings of the 2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp 1ndash5 MontrealQC Canada September 2016
[27] Z Ding and H V Poor ldquoDesign of massive-MIMO-NOMAwith limited feedbackrdquo IEEE Signal Processing Letters vol 23no 5 pp 629ndash633 2016
[28] Z Ding F Adachi andHV Poor ldquoThe application ofMIMO tonon-orthogonal multiple accessrdquo IEEE Transactions onWirelessCommunications vol 15 no 1 pp 537ndash552 2016
[29] Q Sun SHan I Chin-Lin andZ Pan ldquoOn the ergodic capacityof MIMO NOMA systemsrdquo IEEE Wireless CommunicationsLetters vol 4 no 4 pp 405ndash408 2015
[30] J Ding J Cai and C Yi ldquoAn improved coalition game approachfor MIMO-NOMA clustering integrating beamforming andpower allocationrdquo IEEE Transactions on Vehicular Technologyvol 68 no 2 pp 1672ndash1687 2019
[31] J-B Kim I-H Lee and J Lee ldquoCapacity scaling for D2D aidedcooperative relaying systems using NOMArdquo IEEE WirelessCommunications Letters vol 7 no 1 pp 42ndash45 2018
[32] S Papaioannou G Kalfas C Vagionas et al ldquo5G mm WaveNetworks Leveraging Enhanced Fiber-Wireless Convergencefor High-Density Environments The 5G-PHOS Approachrdquoin Proceedings of the 2018 IEEE International Symposium onBroadband Multimedia Systems and Broadcasting (BMSB) pp1ndash5 Valencia Spain June 2018
[33] SANaqvi and SAHassan ldquoCombiningNOMAandmmWavetechnology for cellular communicationrdquo in Proceedings of the2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp1ndash5 Montreal QC Canada September 2016
[34] F Rusek D Persson B K Lau et al ldquoScaling up MIMOopportunities and challenges with very large arraysrdquo IEEESignal Processing Magazine vol 30 no 1 pp 40ndash60 2013
[35] T Bai A Alkhateeb and R W Heath ldquoCoverage and capacityof millimeter-wave cellular networksrdquo IEEE CommunicationsMagazine vol 52 no 9 pp 70ndash77 2014
[36] X Gao L Dai S Han I Chih-Lin and R W Heath ldquoEnergy-efficient hybrid analog and digital precoding for MmWaveMIMO systems with large antenna arraysrdquo IEEE Journal onSelected Areas in Communications vol 34 no 4 pp 998ndash10092016
[37] X Gao L Dai Z Chen Z Wang and Z Zhang ldquoNear-optimal beam selection for beamspace mmwave massive mimosystemsrdquo IEEE Communications Letters vol 20 no 5 pp 1054ndash1057 2016
[38] Z Wang M Li Q Liu and A L Swindlehurst ldquoHybrid pre-coder and combiner design with low-resolution phase shiftersin mmWave MIMO systemsrdquo IEEE Journal of Selected Topics inSignal Processing vol 12 no 2 pp 256ndash269 2018
Wireless Communications and Mobile Computing 11
[39] Y Sun Z Ding and X Dai ldquoOn the performance of downlinkNOMA in multi-cell mmWave networksrdquo IEEE Communica-tions Letters vol 22 no 11 pp 2366ndash2369 2018
[40] NDeng andMHaenggi ldquoAfine-grained analysis ofmillimeter-wave device-to-device networksrdquo IEEE Transactions on Com-munications vol 65 no 11 pp 4940ndash4954 2017
[41] D Zhang Z Zhou C Xu Y Zhang J Rodriguez and T SatoldquoCapacity analysis of NOMA with mmWave massive MIMOsystemsrdquo IEEE Journal on Selected Areas in Communicationsvol 35 no 7 pp 1606ndash1618 2017
[42] S Singh M N Kulkarni A Ghosh and J G AndrewsldquoTractable model for rate in self-backhauled millimeter wavecellular networksrdquo IEEE Journal on Selected Areas in Commu-nications vol 33 no 10 pp 2191ndash2211 2015
[43] X Yan H Xiao C-X Wang and K An ldquoOn the ergodiccapacity of NOMA-based cognitive hybrid satellite terrestrialnetworksrdquo in Proceedings of the 2017 IEEECIC InternationalConference on Communications in China ICCC 2017 pp 1ndash5China October 2017
[44] Y Huang F Al-Qahtani C Zhong Q Wu J Wang and HAlnuweiri ldquoPerformance analysis ofmultiusermultiple antennarelaying networks with co-channel interference and feedbackdelayrdquo IEEE Transactions on Communications vol 62 no 1 pp59ndash73 2014
Chemical EngineeringInternational Journal of Antennas and
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2 Wireless Communications and Mobile Computing
control scheme under guaranteeing QoS of every users inthe cellular network has been presented in [9] Besides it issignificant that the NOMA andMU-MIMO can also improvethe overall system throughput in the cellular network withunderlaid D2D communications which have been proposedin [10]
As the core technology of 5G NOMA can serve mul-tiple users in the same resource block such as a timeslot frequency channel or spreading code Compared tothe orthogonal multiple access NOMA can provide a setof visible benefits such as greater spectrum efficiency andhigher system throughout [11ndash15] There are two availableNOMA technology categories namely power-domain andcode-domain NOMA widely used in the cellular networkThis paper focuses on the power-domain NOMA whichdivides the users in power-domain On the transmitter sidessignals from multiple users are transmitted at the sameresource blocks On the receiver sides the multiuser detec-tion algorithms such as successive interference cancellationhave been utilized to detect the signal regarding the weaksignal as the interference and decode the strong signal whilecancelling the strong signal to detect the weak signal [16 17]Aiming at enhancing system capacity and user fairness theauthors have presented a novel resource and power allocationtechnique which can provide a flexible balancing betweencapacity and fairness maximization in [18] Meanwhile theoptimum received power levels of uplink NOMA signal havebeen proposed in [19] Furthermore comparing with OMAin massive connectivity NOMA can supply more users thanOMA because of the limited number of supported users bythe amount of the available resources [20ndash22] In additionthe analytical outage probability expression for each user hasbeen derived in the downlink cooperative NOMA networkover Nakagami-m fading channels in [23] Since the perfectchannel state information at the transmitter side is nearlyimpractical formany communication scenarios the literature[24] presented a practical downlink NOMA system over theNakagami-m fading channels with statistical CSI associatedwith each other At the same time the authors attempted tocombine the NOMA andMIMO to accomplish high spectralefficiency [25 26] Additionally the outage probability of themassiveMIMO-NOMAsystemhas been derivedwith perfectuser-ordering and limited feedback [27] Besides the schemediscussed in [28] required that the number of antennas at thereceiver is larger than that at the transmitter instead of theCSIat the transmitter In [29] the optimal and low complexitysuboptimal power allocation schemes have been proposedto maximize the ergodic capacity of MIMO-NOMA systemwith statistical channel state information in the transmitterover Rayleigh fading channel Also the authors in [30] haveproposed a cluster beamforming strategy which can optimizebeamforming vectors and power allocation coefficients inMIMO-NOMA system to decrease the total power In addi-tion NOMA can improve the achievable rate greatly in theD2D-aided cooperative relaying system in the literature [31]
Nowadays as spectrum resources become increasinglyscare the mmWave band with a wider spectrum becomes anatural choice for large-volume content services [32] Mean-while benefitting from the small wavelength of mmWave
the large scale antenna arrays can be adopted easily Com-bining the high gain directional antenna and beamformingtechnology enabled by massive antennas the high data ratescan be reached within a 200-metermmWave cellular networkwhich has high path loss in mmWave band [33] In theliterature [34] the authors have proposed that the base stationwhich is equipped with a large antenna array can servea set of users through the users precoding with massiveMIMO Furthermore the literature [35] has proved thatthe orders of magnitude are increased in spectral efficiencywith massive MIMO which can offer more multiuser gainHowever as for MIMO in conventional cellular frequencyband the beamforming precoding is totally achieved in thedigital domain which can cancel the interference betweendifferent beams In order to realize the precoder in the digitaldomain a dedicated RF chain is needed by every antennaBut it is difficult for the mmWave base station with large scaleantennas whose energy consumption is a large part of thetotal energy consumption at mmWave frequencies due to thewide bandwidth [36] At the same time the authors in [36]have discussed a successive interference cancellation-basedhybrid precoding method with near-optimal performanceand low complexity which can maximize the achievablesubrate of each subantenna array and avoid the need forsingular value decomposition and matrix inversion Addi-tionally the literature [37] has proposed an interference-aware beam selection which can avoid serious multiuserinterferences to reduce obvious performance loss Besidesthe authors in [38] have proposed a practical design of hybridprecoders and combiners with low-resolution phase shiftersin mmWave MIMO systems adopting an iterative algorithmfor hybrid precoders and combiners to optimize the spectralefficiency Moreover the MIMO capacity has been computedover the Nakagami-m fading channel in [39] and the closed-form expressions for outage probabilities achieved byNOMAusers in a multicell downlink mmWave network have beenobtained over a Poisson cluster point process Moreovera fine-grained performance analysis over Poisson bipolarmodel of the mmWave D2D communication networks wasprovided in [40] The literature [41] has presented an in-depth capacity analysis for the integrated NOMA mmWave-massive-MIMO systems which can achieve significant capac-ity improvements
Because of the large link attenuation and weak coveragein the MIMO-NOMA cellular network the D2D communi-cation can be used to enhance service for cell edge users Inthis paper the outage probability and the ergodic capacity areproposed in the downlink MIMO-NOMA cellular networkwith D2D communicationsThe remaining part of this paperis organized as follows In Section 2 we introduce a systemmodel of the downlink MIMO-NOMA cellular networkwith multiple direct D2D pairs underlaying communicationThe closed-form expressions of the performance analysisincluding the outage probability and the ergodic capacityare given in Section 3 Finally the numerical results inSection 4 validate the theoretical analysis and demonstratethat the system capacity can be improved by the inte-grated MIMO-NOMA in the mmWave network with D2Dcommunications
Wireless Communications and Mobile Computing 3
Digital
RF chain
RF chainprecoder
＄５1
＄５2
＄５3
＄５4
＄５P
＄５P-1
CU2
CU1
CU3
CU4
CUQ
CUQ-1
Figure 1 System model of D2D-aided mmWave MIMO-NOMA
2 System Model
The paper considers a downlink NOMA MU-MIMOmmWave cellular network with multiple direct D2D pairsunderlaying communications where the cellular users arerandomly distributed The same mmWave resources are usedby the cellular user andD2DpairswithNOMAThemmWaveMIMO-NOMAD2D communication systemmodel is shownin Figure 1 The base station is equipped with multipleantennas which can generate high directional and high gainbeams for cellular usersThere are119876 cellular users with signalantenna and 119875 D2D users with signal antenna in the cellu-lar network which are denoted as 1198621198801 1198621198802 119862119880119876 and1198631198801 1198631198802 119863119880119875TheD2Dpairs are randomly distributedin the edge of the cellular network and there is no direct linkbetween the base station and the D2D pairs [10]
21 NOMA Signal In beam 119899 we assume that 119906(119899 1)119906(119899 2) 119906(119899 119870) are scheduled on the same radio resourcewithNOMA119870 ge 2 where119862119880 of 119896119905ℎ in the beam 119899 is denotedas 119906(119899 119896) 119909119899 is the transmitted signal by the base station inthe beam 119899 which is the sum of all K user signals
where 120582119906(119899119896) is the power ratio of 119896119905ℎ user 120582119906(1198991) le120582119906(1198992) le 120582119906(119899119870) andsum119870119896=1 120582119906(119899119896) = 1119875119899 is the total power
in the beam 119899 119878119906(119899119896) is the normalized transmitted signal of119896119905ℎ user in the beam 119899 and E(119878119906(119899119896)2) = 122 Channel Model As for the large scale fading themmWave link is similar to that used in [33] the large scalefading 119871(119903) in dB is modeled as119871 (119903) = 120588 + 10120572 log (119903) (2)
where 120588 = 324 + 20 log(119891119888) 119891119888 is the carrier frequency 120572 isthe path loss exponents and 119903 is the distance from transmitterto receiver
As for the small scale fading the Nakagami-m fading isconsidered for each link ℎ119906(119899119896) ℎ119901119906(119899119896) ℎ1199011015840119901 are donated asthe link of base station to cellular user D2D user to cellularuser and D2D user to D2D user whose modular square isnormalized Gamma random variable [39] And when 119867 isnormalized Gamma random variable which is denoted as119867 sim 119866119886119898119898119886(120596 120595) the probability density function 119891(119909)and Cumulative Distribution Function 119865(119909) of H are
1119895120595119895119909119895119890minus119909120595 119909 ge 0
0 otherwise (4)
23 Directional Beamforming The base station withmmWave band is equipped with multiple antennas whichcan generate high directional and high gain beamsThe actualantenna pattern is modeled as the sectorized antenna modelapproximately for the sake of mathematical tractability [42]Generally the maximum power gain is adopted to replacethe array gain within the half-power beam width (main lobegain) and the first minor maximum gain is used to replacethe gains of the other DoAs (side lobe gain) According tothe literature [39 40] when the antenna pattern is a planarsquare the total array gain from base station to the user is119866(119899119896) where
where 119879 = 119871 120591 = 1sin2(31205872radic119871) and 119871 is the number ofantennas
24 Received Signal For downlinkMIMO-NOMA transmis-sion the cellular user 119906(119899 119870) will receive the sum of signalfrom base station and the signal from D2D transmitter atthe same time In addition to receiving the D2D transmittedsignal theD2D receiver119863119880119875will also receive the interferencesignal from the other D2D users Without loss of generalitywe assume there are119873 beams and119872D2Dpairs in the cellularnetwork then the received signal of cellular user 119910119906(119899119896) andthe received signal of D2D user 119910119863119901 can be formulated as
where ℎ119906(119899119896) is the channel gain for downlink 119906(119899 119870)ℎ119906(1198991) ge ℎ119906(1198992) ge ℎ119906(119899119870) ℎ119901119906(119899119896) is the channelgain between 119863119880119875 and 119906(119899 119870) and ℎ1199011015840119901 is the channel gainfrom 1198631198801199011015840 transmitter to 119863119880119901 receiver 119866(119899119896) is the totalbeamforming array gain frombase station to 119906(119899119870)119909119899 is thesuperimposed signal by the total K 119906(119899 119896) in the beam 119899 119875119863is the transmitted power of119863119880119875 119878119901 is the signal transmittedby119863119880119875 and E(1198781199012) = 1 Meanwhile 119899119906(119899119896) and 119899119863119901 are theiid white Gaussian noise with zero mean and one varianceat cellular user 119906(119899 119896) and D2D user 119863119880119875 which is denotedas 119899119906(119899119896) 119899119863119901 sim C119873(0 1)
We denote the SINRs of 119906(119899 119896) and119863119880119875 in the downlinkNOMA-MIMO cellular network as 120574119906(119899119896) 120574119863119880119901
Without lossof generality the interbeam interference is ignored in thispaper In the meantime the perfect SIC is used to preventerror propagation in the NOMA users in the paper Using (1)in (6) and (7) 120574119906(119899119896) and 120574119863119880119901
In this section we present the performance analysis ofD2D-aidedmmWaveMIMO-NOMAsystem Specifically theclosed-form expressions for the performancemetrics (ie theoutage probability and the ergodic capacity) are presentedin the following Without loss of generality in the beam119899 119896-th 119862119880119904 are adopted with NOMA in one beam 119896 isin1 2ℎ119906(1198991) ge ℎ119906(1198992) and one119863119880 is randomly distributedat the edge of the beam Three events are considered in thissystem
Event 1 According to the NOMA successive interferencecancellation (SIC) principle user 1 obtains the informationintended for user 2 with 1205741997888rarr2 and removes it Whendecoding the information intended for user 2 user 1 cancelsit successfully with 1205741
31 Outage Probability In this section we study the outageprobability of 119862119880 and119863119880 The outage probability of the user1 user 2 and119863119880 is given by 119875119900119906119905
where 1198771 1198772 119877119863 are the target rates of user 1 user 2 and119863119880Firstly we consider the outage probability of user 1 119875119900119906119905
1 then 119875(log(1 + 1205741997888rarr2) le 1198772) can be rewritten as 119875(1205741997888rarr2 le21198772 minus 1) so we set
119875 (1205741997888rarr2 le 21198772 minus 1) = 119865 (119898 119886 119887 119888 119889) = 1198651205741997888rarr2 (119898) (21)
where 119886 = 120582119906(1198992)119875119899119866(1198991)2 119887 = 120582119906(1198991)119875119899119866(1198991)2 119889 = 119875119863119888 = 1205902119899 119898 = 21198772 minus 1 and 1198671 = ℎ119906(1198991)2 sim 119866119886119898119898119886(120596 120595)1198672 = ℎ119901119906(1198991)2 sim 119866119886119898119898119886(120578 120579) then1198651205741997888rarr2 (119898) = 119875( 11988611986711198871198671 + 1198891198672 + 119888 le 119898)
= intinfin
0119875( 119886119910119887119910 + 1198891198672 + 119888 le 119898)1198911198671 (119910) 119889119910
= intinfin
0119875(119886119910 minus 119887119898119910 minus 119888119898119889119898 le 1198672)1198911198671 (119910) 119889119910
(22)
In order to determine if (119886119910 minus 119887119898119910 minus 119888119898)119889119898 le 0 we setΦ = 119888119898(119886 minus 119887119898) WhenΦ le 0 (119886119910 minus 119887119898119910minus 119888119898)119889119898 le 0 so119875((119886119910 minus 119887119898119910 minus 119888119898)119889119898 le 1198672) = 1 therefore1198651205741997888rarr2 (119898) = 1 (23)
When Φ gt 0 which is119898 lt 1198861198871198651205741997888rarr2 (119898) = intΦ
01198911198671 (119910) 119889119910
+ intinfin
Φ(1 minus 1198651198672 (119886119910 minus 119887119898119910 minus 119888119898119889119898 ))1198911198671 (119910) 119889119910
= intinfin
Φ
120578minus1sum119895=0
1119895120579119895 (119886 minus 119887119898119889119898 119910 minus 119888119889)119895
(119895119894) 120572119894120573119895minus119894sdot 119890minus120573120579 (minus119869(minus(120572120579 + 1120595) 120596 + 119895 minus 1Φ))+ 1120595120596Γ (120596) (119869 (minus( 1120595) 120596 minus 1Φ)minus 119869(minus( 1120595) 120596 minus 1 0))
(28)
Similarly by adopting different parameters with119886 119887 119888 119889 which is shown in Table 1 we can obtain1198651205741997888rarr2(119898) 1198651205741(119898) 1198651205742(119898)In addition when 1198673 = ℎ1199011199012 sim 119866119886119898119898119886(120596 120601)119875119863ℎ11990111990121205902119899 sim 119866119886119898119898119886(120596 (1198751198631205902119899)120601) Hence 119865120574119863(119898) is
denoted as
119865120574119863 (119898) = 1 minus 120596minus1sum119869=0
Finally the outage probability of user 1 user 2 and 119863119880can be evaluated by 1198651205741997888rarr2(119898) 1198651205741(119898) 1198651205742(119898) 119865120574119863(119898) whichare formulated as
1198751199001199061199051 = 1 minus (1 minus 1198651205741997888rarr2 (21198772 minus 1))
lowast (1 minus 1198651205741 (21198771 minus 1)) (30)
1198751199001199061199052 = 1198651205742 (21198772 minus 1) (31)
119875119900119906119905119863 = 119865120574119863 (2119877119863 minus 1) (32)
32 Ergodic Capacity The ergodic capacity is the averagecapacity of channel which can be defined as the instantaneousend-to-end mutual information expectations and denoted as
119862119890119903119892 = E [log2 (1 + 1205741)] + E [log2 (1 + 1205742)]+ E [log2 (1 + 120574119863)] (33)
6 Wireless Communications and Mobile Computing
Table 1 Parameters of the outage probability
a b c d1198651205741997888rarr2 (119898) 120582119906(1198991)119875119899 1003817100381710038171003817119866(1198991)10038171003817100381710038172 120582119906(1198992)119875119899 1003817100381710038171003817119866(1198992)
In order to compute (34) we first compute the first itemofthe formula As we set before 119886 = 120582119906(1198991)119875119899119866(1198991)2 119889 = 119875119863119888 = 1205902119899 1198671 = ℎ119906(1198991)2 sim 119866119886119898119898119886(120596 120595) 1198672 = ℎ119901119906(1198991)2 sim119866119886119898119898119886(120578 120579) we can get
Similarly we can set a b c d as different parametersto obtain the other items of the formula (34) and then pulleverything together The asymptotic result for the ergodiccapacity of the consider system can be obtained
Wireless Communications and Mobile Computing 7
4 Numerical Results
In this section the outage probability and the ergodic capacityof MIMO-NOMA mmWave cellular network with D2Dcommunications are investigated The effects of differentparameters on the probability of outage and ergodic capacityare analyzed such as the base station transmission power thenumber of base station antennas the power ratio of NOMAuser and the distance between D2D users In order to verifythe performance of the system the traditional TDMA themeis adopted as the comparison between the two users of eachbeam In particular the time slot is equally divided by the twousers Hence the capacity of this theme is 119877119879119863119872119860 which isdenoted as
A simplified cellular network system is discussed for theperformance analyzed here The carrier frequency is 28GHzwhich is commonly used for wireless broadband serviceThere are 16 antennas in the base station whose coverageradius is 100m There is single antenna with D2D user Andthe distance between D2D users is 30m Meanwhile thetransmission power of base station and D2D users is 5 dbmIn addition there are 8 NOMA users and 4 D2D usersin the cellular network The path loss exponent is set as3 Furthermore the small scale fading is denoted as 119867 sim119866119886119898119898119886(2 1) which is simplified for the simulation
41 Outage Probability In this section we consider theoutage probability of the NOMA far user and near user
Figure 2 depicts the outage probability in the differentbase station transmission power with 1198771 = 5 bitsHz and1198772 = 332 bitsHz As the base station transmission powerincreases it can be seen that the outage probability of theNOMA users decreases with the exponential form Further-more the performance of each userrsquos outage probability inthe NOMA scheme is significantly better than the TDMAand the closed-form solution obtained is consistent with theMonte Carlo simulation results
In Figure 3 the impact of antenna number in the basestation on the outage probability (1198771 = 564 bitsHz and 1198772
= 4 bitsHz) is presented The simulation results effectivelyverify that the number of antennas of the base stationcan decrease the usersrsquo outage probability in the MIMO-NOMA mmWave cellular network thereby improving thethroughput of the system under the limited time-frequencyresources As can be seen from Figure 3 the number ofantennas has a greater impact on user 2 than user 1When thenumber of antennas is 36 the outage probability of the systemis satisfied which can balance the number of RF chains andthe system performance Then the NOMA scheme performsbetter than the traditional TDMA in the mmWave MIMOcellular network with D2D communications
In Figure 4 we discuss the influence of the power ratiocoefficient in the cellular network between the NOMA usersIt can be seen that the outage probability (1198771 = 4 bitsHz and1198772 = 3 bitsHz) of the two users in NOMA is balanced whenthe power ratio coefficient is approximately 02
Analysis result User 1Numerical result User 1TDMA User 1Analysis result User 2Numerical result User 2TDMA User 2
10minus2
10minus1
100
Out
age p
roba
bilit
y
10 15 20 255Transmission Power (dbm)
Figure 2 Impact of transmission power on outage probability
Analysis result User 1Numerical result User 1TDMA User 1Analysis result User 2Numerical result User 2TDMA User 2
10minus2
10minus1
100
Out
age p
roba
bilit
y
10 15 20 25 30 355Antenna Number
Figure 3 Impact of antenna number on outage probability
In Figure 5 the effect of the distance between D2D usersis consideredThe figure indicates that the outage probability(1198771 = 5 bitsHz and1198772 = 332 bitsHz) of the NOMAusers isreduced in the formof an exponent when the distance ofD2Duser is linear growth Since the distance betweenD2Dusers isincreasing the interference from the D2D transmitter to theNOMA user is weak Hence the throughput of the NOMAusers is improved while the outage probability is dropping
8 Wireless Communications and Mobile Computing
Analysis result User 1Numerical result User 1Analysis result User 2Numerical result User 2
01 015 02 025 03 035 04 045005Power ratio coefficient
10minus3
10minus2
10minus1
100
Out
age p
roba
bilit
y
Figure 4 Impact of power ratio coefficient on outage probability
Analysis result User 1Numerical result User 1Analysis result User 2Numerical result User 2
30 40 50 60 70 8020D2D Distance (m)
10minus2
10minus1
100
Out
age p
roba
bilit
y
Figure 5 Impact of D2D distance on outage probability
42 Ergodic Capacity In this section the total ergodiccapacity is considered in the MIMO-NOMA mmWave cel-lular network with D2D communications It can be seenthat the numerical results are consistent with the closed-form solution which is better than the traditional TDMAMeanwhile the transmission power and the number of basestation antennas have a greater impact and the power ratiocoefficient and the distance between D2D users have lesseffect
In Figure 6 the impact of the transmission power of basestation on the ergodic capacity is considered in the MIMO-NOMA mmWave cellular network with D2D communica-tions It is shown that the ergodic capacity is growing linearly
Analysis resultNumerical resultTDMA
10 15 20 255Transmission Power (dbm)
8
10
12
14
16
18
Syste
m C
apac
ityFigure 6 Impact of transmission power on ergodic capacity
with the increase of transmission power In addition theergodic capacity of the systemwe proposed is higher than thetraditional TDMA Hence in order to improve the ergodiccapacity of the system we can increase the base stationtransmission power as much as possible without affectingothers
As the number of the base station antennas is increasingit is indicated that the ergodic capacity can be improvedbetter than the traditional TDMA in Figure 7 Benefitingfrom the length of mmWave more and more antennas canbe equipped for the base station At the same time we needto balance the improvement in ergodic capacity brought bythe increasing of the number of antennas and the powerconsumption and hardware requirements of the increase inRF chains to determine the final number of antennas
In Figure 8 the ergodic capacity is affected by thechange of the power ratio coefficient of the NOMA usersin the MIMO-NOMA mmWave cellular network with D2Dcommunications It can be seen that the total ergodic capacitychanges slowly with the increase of power ratio
In Figure 9 since the interference from the D2D users isdecreasing the total ergodic capacity is improved with theincrease of the distance between theD2Dusers in theMIMO-NOMA mmWave cellular network It can also be seen thatthe ergodic capacity in the MIMO-NOMAmmWave cellularnetwork is always better than the traditional TDMA
5 Conclusion
In this paper the outage probability and the ergodic capacityof the NOMA in the MIMO-NOMA mmWave cellularnetwork with D2D communications are studied The closed-form solutions of the outage probability and the ergodiccapacity are obtained which are consistent with the numeri-cal results Meanwhile the performance of NOMA is shown
Wireless Communications and Mobile Computing 9
Analysis resultNumerical resultTDMA
4
6
8
10
12
14
16
Syste
m C
apac
ity
10 15 20 25 30 355Antenna Number
Figure 7 Impact of antenna number on ergodic capacity
Analysis resultNumerical resultTDMA
01 015 02 025 03 035 04 045005Power Ratio Coefficient
6
7
8
9
10
11
12
Syste
m C
apac
ity
Figure 8 Impact of power ratio coefficient on ergodic capacity
to be better than traditional TDMA in the MIMO mmWavecellular network with D2D communications Furthermorethe higher transmission power of base station and the largerantenna array can also improve system performance
Data Availability
No data were used to support this study
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Analysis resultNumerical resultTDMA
6
7
8
9
10
11
12
13
Syste
m C
apac
ity
30 40 50 60 70 8020D2D Distance (m)
Figure 9 Impact of D2D distance on ergodic capacity
Acknowledgments
This work was supported by Advance Research Projects of13th Five-Year Plan of Civil Aerospace Technology (B0105)and the National Natural Science Foundation of China(61771051)
References
[1] M Tehrani M Uysal and H Yanikomeroglu ldquoDevice-to-device communication in 5G cellular networks challengessolutions and future directionsrdquo IEEE Communications Mag-azine vol 52 no 5 pp 86ndash92 2014
[2] S-Y Lien C-C Chien G S-T Liu H-L Tsai R Li and YJ Wang ldquoEnhanced LTE device-to-device proximity servicesrdquoIEEE Communications Magazine vol 54 no 12 pp 174ndash1822016
[3] L Lei ZD ZhongC Lin andXM Shen ldquoOperator controlleddevice-to-device communications in LTE-advanced networksrdquoIEEEWireless Communications Magazine vol 19 no 3 pp 96ndash104 2012
[4] A Asadi and V Mancuso ldquoNetwork-assisted outband D2D-clustering in 5G cellular networks theory and practicerdquo IEEETransactions onMobile Computing vol 16 no 8 pp 2246ndash22592017
[5] J HuW Heng Y Zhu GWang X Li and JWu ldquoOverlappingcoalition formation games for joint interference managementand resource allocation in D2D communicationsrdquo IEEE Accessvol 6 pp 6341ndash6349 2018
[6] H Min J Lee S Park and D Hong ldquoCapacity enhancementusing an interference limited area for device-to-device uplinkunderlaying cellular networksrdquo IEEE Transactions on WirelessCommunications vol 10 no 12 pp 3995ndash4000 2011
[7] Z Uykan and R Jantti ldquoTransmission-order optimization forbidirectional device-to-device (D2D) communications under-laying cellular TDD networksmdasha graph theoretic approachrdquoIEEE Journal on Selected Areas in Communications vol 34 no1 pp 1ndash14 2016
10 Wireless Communications and Mobile Computing
[8] L L Wei R Q Hu T He and Y Qian ldquoDevice-to-device(d2d)communications underlaying MU-MIMO cellular networksrdquoin Proceedings of the IEEE Global Communications Conference(GLOBECOM rsquo13) pp 4902ndash4907 IEEE Atlanta Ga USADecember 2013
[9] X Li W Zhang H Zhang andW Li ldquoA combining call admis-sion control and power control scheme for D2D communica-tions underlaying cellular networksrdquo China Communicationsvol 13 no 10 pp 137ndash145 2016
[10] H Sun Y Xu and R Q Hu ldquoA NOMA and MU-MIMOsupported cellular network with underlaid D2D communica-tionsrdquo in Proceedings of the 2016 IEEE 83rd Vehicular TechnologyConference (VTC Spring) pp 1ndash5 Nanjing China May 2016
[11] Z Ding X Lei G K Karagiannidis R Schober J Yuan andV K Bhargava ldquoA survey on non-orthogonal multiple accessfor 5G networks research challenges and future trendsrdquo IEEEJournal on Selected Areas in Communications vol 35 no 10 pp2181ndash2195 2017
[12] N Ye X Li H Yu AWangW Liu andXHou ldquoDeep learningaided grant-free noma towards reliable low-latency access intactile internet of thingsrdquo IEEE Transactions on IndustrialInformatics vol 15 no 5 pp 2995ndash3005 2019
[13] J An K Yang J Wu N Ye S Guo and Z Liao ldquoAchievingsustainable ultra-dense heterogeneous networks for 5Grdquo IEEECommunications Magazine vol 55 no 12 pp 84ndash90 2017
[14] N Ye AWang X Li H Yu A Li andH Jiang ldquoA randomnon-orthogonal multiple access scheme for mmtcrdquo in Proceedingsof the 2017 IEEE 85th Vehicular Technology Conference (VTCSpring) pp 1ndash6 June 2017
[15] K Yang N Yang N Ye M Jia Z Gao and R Fan ldquoNon-orthogonal multiple access achieving sustainable future radioaccessrdquo IEEE Communications Magazine vol 57 no 2 pp 116ndash121 2019
[16] S M R Islam N Avazov O A Dobre and K-S KwakldquoPower-domain non-orthogonal multiple access (NOMA) in5G systems potentials and challengesrdquo IEEE CommunicationsSurveys amp Tutorials vol 19 no 2 pp 721ndash742 2017
[17] N Ye AWang X Li W Liu X Hou and H Yu ldquoOn constella-tion rotation of noma with sic receiverrdquo IEEE CommunicationsLetters vol 22 no 3 pp 514ndash517 2018
[18] MHojeij C A Nour J Farah and C Douillard ldquoJoint resourceand power allocation technique for downlink power-domainnon-orthogonalmultiple accessrdquo inProceedings of the 2018 IEEEConference on Antenna Measurements amp Applications (CAMA)pp 1ndash4 September 2018
[19] F A Rabee K Davaslioglu and R Gitlin ldquoThe optimumreceived power levels of uplink non-orthogonal multiple access(NOMA) signalsrdquo in Proceedings of the 18th IEEE Wireless andMicrowave Technology Conference WAMICON 2017 pp 1ndash4USA April 2017
[20] Y Li andG A A Baduge ldquoNoma-aided cell-freemassivemimosystemsrdquo IEEEWireless Communications Letters vol 7 pp 950ndash953 2018
[21] N Ye A Wang X Li et al ldquoRate-adaptive multiple access foruplink grant-free transmissionrdquo Wireless Communications andMobile Computing vol 2018 Article ID 8978207 21 pages 2018
[22] N Ye H Han L Zhao and A-H Wang ldquoUplink nonorthogo-nal multiple access technologies toward 5G a surveyrdquo WirelessCommunications and Mobile Computing vol 2018 Article ID6187580 26 pages 2018
[23] Y LiuW-J Lu S Shi et al ldquoPerformance analysis of a downlinkcooperative noma network over nakagami-m fading channelsrdquoIEEE Access vol 6 pp 53034ndash53043 2018
[24] X Wang J Wang L He and J Song ldquoOutage analysis fordownlink noma with statistical channel state informationrdquoIEEEWireless Communications Letters vol 7 no 2 pp 142ndash1452018
[25] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAnoverview ofMIMOcommunicationsmdasha key to gigabit wirelessrdquoProceedings of the IEEE vol 92 no 2 pp 198ndash217 2004
[26] W Cai C Chen L Bai Y Jin and J Choi ldquoUser selectionand power allocation schemes for downlink NOMA systemswith imperfect CSIrdquo in Proceedings of the 2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp 1ndash5 MontrealQC Canada September 2016
[27] Z Ding and H V Poor ldquoDesign of massive-MIMO-NOMAwith limited feedbackrdquo IEEE Signal Processing Letters vol 23no 5 pp 629ndash633 2016
[28] Z Ding F Adachi andHV Poor ldquoThe application ofMIMO tonon-orthogonal multiple accessrdquo IEEE Transactions onWirelessCommunications vol 15 no 1 pp 537ndash552 2016
[29] Q Sun SHan I Chin-Lin andZ Pan ldquoOn the ergodic capacityof MIMO NOMA systemsrdquo IEEE Wireless CommunicationsLetters vol 4 no 4 pp 405ndash408 2015
[30] J Ding J Cai and C Yi ldquoAn improved coalition game approachfor MIMO-NOMA clustering integrating beamforming andpower allocationrdquo IEEE Transactions on Vehicular Technologyvol 68 no 2 pp 1672ndash1687 2019
[31] J-B Kim I-H Lee and J Lee ldquoCapacity scaling for D2D aidedcooperative relaying systems using NOMArdquo IEEE WirelessCommunications Letters vol 7 no 1 pp 42ndash45 2018
[32] S Papaioannou G Kalfas C Vagionas et al ldquo5G mm WaveNetworks Leveraging Enhanced Fiber-Wireless Convergencefor High-Density Environments The 5G-PHOS Approachrdquoin Proceedings of the 2018 IEEE International Symposium onBroadband Multimedia Systems and Broadcasting (BMSB) pp1ndash5 Valencia Spain June 2018
[33] SANaqvi and SAHassan ldquoCombiningNOMAandmmWavetechnology for cellular communicationrdquo in Proceedings of the2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp1ndash5 Montreal QC Canada September 2016
[34] F Rusek D Persson B K Lau et al ldquoScaling up MIMOopportunities and challenges with very large arraysrdquo IEEESignal Processing Magazine vol 30 no 1 pp 40ndash60 2013
[35] T Bai A Alkhateeb and R W Heath ldquoCoverage and capacityof millimeter-wave cellular networksrdquo IEEE CommunicationsMagazine vol 52 no 9 pp 70ndash77 2014
[36] X Gao L Dai S Han I Chih-Lin and R W Heath ldquoEnergy-efficient hybrid analog and digital precoding for MmWaveMIMO systems with large antenna arraysrdquo IEEE Journal onSelected Areas in Communications vol 34 no 4 pp 998ndash10092016
[37] X Gao L Dai Z Chen Z Wang and Z Zhang ldquoNear-optimal beam selection for beamspace mmwave massive mimosystemsrdquo IEEE Communications Letters vol 20 no 5 pp 1054ndash1057 2016
[38] Z Wang M Li Q Liu and A L Swindlehurst ldquoHybrid pre-coder and combiner design with low-resolution phase shiftersin mmWave MIMO systemsrdquo IEEE Journal of Selected Topics inSignal Processing vol 12 no 2 pp 256ndash269 2018
Wireless Communications and Mobile Computing 11
[39] Y Sun Z Ding and X Dai ldquoOn the performance of downlinkNOMA in multi-cell mmWave networksrdquo IEEE Communica-tions Letters vol 22 no 11 pp 2366ndash2369 2018
[40] NDeng andMHaenggi ldquoAfine-grained analysis ofmillimeter-wave device-to-device networksrdquo IEEE Transactions on Com-munications vol 65 no 11 pp 4940ndash4954 2017
[41] D Zhang Z Zhou C Xu Y Zhang J Rodriguez and T SatoldquoCapacity analysis of NOMA with mmWave massive MIMOsystemsrdquo IEEE Journal on Selected Areas in Communicationsvol 35 no 7 pp 1606ndash1618 2017
[42] S Singh M N Kulkarni A Ghosh and J G AndrewsldquoTractable model for rate in self-backhauled millimeter wavecellular networksrdquo IEEE Journal on Selected Areas in Commu-nications vol 33 no 10 pp 2191ndash2211 2015
[43] X Yan H Xiao C-X Wang and K An ldquoOn the ergodiccapacity of NOMA-based cognitive hybrid satellite terrestrialnetworksrdquo in Proceedings of the 2017 IEEECIC InternationalConference on Communications in China ICCC 2017 pp 1ndash5China October 2017
[44] Y Huang F Al-Qahtani C Zhong Q Wu J Wang and HAlnuweiri ldquoPerformance analysis ofmultiusermultiple antennarelaying networks with co-channel interference and feedbackdelayrdquo IEEE Transactions on Communications vol 62 no 1 pp59ndash73 2014
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 3
Digital
RF chain
RF chainprecoder
＄５1
＄５2
＄５3
＄５4
＄５P
＄５P-1
CU2
CU1
CU3
CU4
CUQ
CUQ-1
Figure 1 System model of D2D-aided mmWave MIMO-NOMA
2 System Model
The paper considers a downlink NOMA MU-MIMOmmWave cellular network with multiple direct D2D pairsunderlaying communications where the cellular users arerandomly distributed The same mmWave resources are usedby the cellular user andD2DpairswithNOMAThemmWaveMIMO-NOMAD2D communication systemmodel is shownin Figure 1 The base station is equipped with multipleantennas which can generate high directional and high gainbeams for cellular usersThere are119876 cellular users with signalantenna and 119875 D2D users with signal antenna in the cellu-lar network which are denoted as 1198621198801 1198621198802 119862119880119876 and1198631198801 1198631198802 119863119880119875TheD2Dpairs are randomly distributedin the edge of the cellular network and there is no direct linkbetween the base station and the D2D pairs [10]
21 NOMA Signal In beam 119899 we assume that 119906(119899 1)119906(119899 2) 119906(119899 119870) are scheduled on the same radio resourcewithNOMA119870 ge 2 where119862119880 of 119896119905ℎ in the beam 119899 is denotedas 119906(119899 119896) 119909119899 is the transmitted signal by the base station inthe beam 119899 which is the sum of all K user signals
where 120582119906(119899119896) is the power ratio of 119896119905ℎ user 120582119906(1198991) le120582119906(1198992) le 120582119906(119899119870) andsum119870119896=1 120582119906(119899119896) = 1119875119899 is the total power
in the beam 119899 119878119906(119899119896) is the normalized transmitted signal of119896119905ℎ user in the beam 119899 and E(119878119906(119899119896)2) = 122 Channel Model As for the large scale fading themmWave link is similar to that used in [33] the large scalefading 119871(119903) in dB is modeled as119871 (119903) = 120588 + 10120572 log (119903) (2)
where 120588 = 324 + 20 log(119891119888) 119891119888 is the carrier frequency 120572 isthe path loss exponents and 119903 is the distance from transmitterto receiver
As for the small scale fading the Nakagami-m fading isconsidered for each link ℎ119906(119899119896) ℎ119901119906(119899119896) ℎ1199011015840119901 are donated asthe link of base station to cellular user D2D user to cellularuser and D2D user to D2D user whose modular square isnormalized Gamma random variable [39] And when 119867 isnormalized Gamma random variable which is denoted as119867 sim 119866119886119898119898119886(120596 120595) the probability density function 119891(119909)and Cumulative Distribution Function 119865(119909) of H are
1119895120595119895119909119895119890minus119909120595 119909 ge 0
0 otherwise (4)
23 Directional Beamforming The base station withmmWave band is equipped with multiple antennas whichcan generate high directional and high gain beamsThe actualantenna pattern is modeled as the sectorized antenna modelapproximately for the sake of mathematical tractability [42]Generally the maximum power gain is adopted to replacethe array gain within the half-power beam width (main lobegain) and the first minor maximum gain is used to replacethe gains of the other DoAs (side lobe gain) According tothe literature [39 40] when the antenna pattern is a planarsquare the total array gain from base station to the user is119866(119899119896) where
where 119879 = 119871 120591 = 1sin2(31205872radic119871) and 119871 is the number ofantennas
24 Received Signal For downlinkMIMO-NOMA transmis-sion the cellular user 119906(119899 119870) will receive the sum of signalfrom base station and the signal from D2D transmitter atthe same time In addition to receiving the D2D transmittedsignal theD2D receiver119863119880119875will also receive the interferencesignal from the other D2D users Without loss of generalitywe assume there are119873 beams and119872D2Dpairs in the cellularnetwork then the received signal of cellular user 119910119906(119899119896) andthe received signal of D2D user 119910119863119901 can be formulated as
where ℎ119906(119899119896) is the channel gain for downlink 119906(119899 119870)ℎ119906(1198991) ge ℎ119906(1198992) ge ℎ119906(119899119870) ℎ119901119906(119899119896) is the channelgain between 119863119880119875 and 119906(119899 119870) and ℎ1199011015840119901 is the channel gainfrom 1198631198801199011015840 transmitter to 119863119880119901 receiver 119866(119899119896) is the totalbeamforming array gain frombase station to 119906(119899119870)119909119899 is thesuperimposed signal by the total K 119906(119899 119896) in the beam 119899 119875119863is the transmitted power of119863119880119875 119878119901 is the signal transmittedby119863119880119875 and E(1198781199012) = 1 Meanwhile 119899119906(119899119896) and 119899119863119901 are theiid white Gaussian noise with zero mean and one varianceat cellular user 119906(119899 119896) and D2D user 119863119880119875 which is denotedas 119899119906(119899119896) 119899119863119901 sim C119873(0 1)
We denote the SINRs of 119906(119899 119896) and119863119880119875 in the downlinkNOMA-MIMO cellular network as 120574119906(119899119896) 120574119863119880119901
Without lossof generality the interbeam interference is ignored in thispaper In the meantime the perfect SIC is used to preventerror propagation in the NOMA users in the paper Using (1)in (6) and (7) 120574119906(119899119896) and 120574119863119880119901
In this section we present the performance analysis ofD2D-aidedmmWaveMIMO-NOMAsystem Specifically theclosed-form expressions for the performancemetrics (ie theoutage probability and the ergodic capacity) are presentedin the following Without loss of generality in the beam119899 119896-th 119862119880119904 are adopted with NOMA in one beam 119896 isin1 2ℎ119906(1198991) ge ℎ119906(1198992) and one119863119880 is randomly distributedat the edge of the beam Three events are considered in thissystem
Event 1 According to the NOMA successive interferencecancellation (SIC) principle user 1 obtains the informationintended for user 2 with 1205741997888rarr2 and removes it Whendecoding the information intended for user 2 user 1 cancelsit successfully with 1205741
31 Outage Probability In this section we study the outageprobability of 119862119880 and119863119880 The outage probability of the user1 user 2 and119863119880 is given by 119875119900119906119905
where 1198771 1198772 119877119863 are the target rates of user 1 user 2 and119863119880Firstly we consider the outage probability of user 1 119875119900119906119905
1 then 119875(log(1 + 1205741997888rarr2) le 1198772) can be rewritten as 119875(1205741997888rarr2 le21198772 minus 1) so we set
119875 (1205741997888rarr2 le 21198772 minus 1) = 119865 (119898 119886 119887 119888 119889) = 1198651205741997888rarr2 (119898) (21)
where 119886 = 120582119906(1198992)119875119899119866(1198991)2 119887 = 120582119906(1198991)119875119899119866(1198991)2 119889 = 119875119863119888 = 1205902119899 119898 = 21198772 minus 1 and 1198671 = ℎ119906(1198991)2 sim 119866119886119898119898119886(120596 120595)1198672 = ℎ119901119906(1198991)2 sim 119866119886119898119898119886(120578 120579) then1198651205741997888rarr2 (119898) = 119875( 11988611986711198871198671 + 1198891198672 + 119888 le 119898)
= intinfin
0119875( 119886119910119887119910 + 1198891198672 + 119888 le 119898)1198911198671 (119910) 119889119910
= intinfin
0119875(119886119910 minus 119887119898119910 minus 119888119898119889119898 le 1198672)1198911198671 (119910) 119889119910
(22)
In order to determine if (119886119910 minus 119887119898119910 minus 119888119898)119889119898 le 0 we setΦ = 119888119898(119886 minus 119887119898) WhenΦ le 0 (119886119910 minus 119887119898119910minus 119888119898)119889119898 le 0 so119875((119886119910 minus 119887119898119910 minus 119888119898)119889119898 le 1198672) = 1 therefore1198651205741997888rarr2 (119898) = 1 (23)
When Φ gt 0 which is119898 lt 1198861198871198651205741997888rarr2 (119898) = intΦ
01198911198671 (119910) 119889119910
+ intinfin
Φ(1 minus 1198651198672 (119886119910 minus 119887119898119910 minus 119888119898119889119898 ))1198911198671 (119910) 119889119910
= intinfin
Φ
120578minus1sum119895=0
1119895120579119895 (119886 minus 119887119898119889119898 119910 minus 119888119889)119895
(119895119894) 120572119894120573119895minus119894sdot 119890minus120573120579 (minus119869(minus(120572120579 + 1120595) 120596 + 119895 minus 1Φ))+ 1120595120596Γ (120596) (119869 (minus( 1120595) 120596 minus 1Φ)minus 119869(minus( 1120595) 120596 minus 1 0))
(28)
Similarly by adopting different parameters with119886 119887 119888 119889 which is shown in Table 1 we can obtain1198651205741997888rarr2(119898) 1198651205741(119898) 1198651205742(119898)In addition when 1198673 = ℎ1199011199012 sim 119866119886119898119898119886(120596 120601)119875119863ℎ11990111990121205902119899 sim 119866119886119898119898119886(120596 (1198751198631205902119899)120601) Hence 119865120574119863(119898) is
denoted as
119865120574119863 (119898) = 1 minus 120596minus1sum119869=0
Finally the outage probability of user 1 user 2 and 119863119880can be evaluated by 1198651205741997888rarr2(119898) 1198651205741(119898) 1198651205742(119898) 119865120574119863(119898) whichare formulated as
1198751199001199061199051 = 1 minus (1 minus 1198651205741997888rarr2 (21198772 minus 1))
lowast (1 minus 1198651205741 (21198771 minus 1)) (30)
1198751199001199061199052 = 1198651205742 (21198772 minus 1) (31)
119875119900119906119905119863 = 119865120574119863 (2119877119863 minus 1) (32)
32 Ergodic Capacity The ergodic capacity is the averagecapacity of channel which can be defined as the instantaneousend-to-end mutual information expectations and denoted as
119862119890119903119892 = E [log2 (1 + 1205741)] + E [log2 (1 + 1205742)]+ E [log2 (1 + 120574119863)] (33)
6 Wireless Communications and Mobile Computing
Table 1 Parameters of the outage probability
a b c d1198651205741997888rarr2 (119898) 120582119906(1198991)119875119899 1003817100381710038171003817119866(1198991)10038171003817100381710038172 120582119906(1198992)119875119899 1003817100381710038171003817119866(1198992)
In order to compute (34) we first compute the first itemofthe formula As we set before 119886 = 120582119906(1198991)119875119899119866(1198991)2 119889 = 119875119863119888 = 1205902119899 1198671 = ℎ119906(1198991)2 sim 119866119886119898119898119886(120596 120595) 1198672 = ℎ119901119906(1198991)2 sim119866119886119898119898119886(120578 120579) we can get
Similarly we can set a b c d as different parametersto obtain the other items of the formula (34) and then pulleverything together The asymptotic result for the ergodiccapacity of the consider system can be obtained
Wireless Communications and Mobile Computing 7
4 Numerical Results
In this section the outage probability and the ergodic capacityof MIMO-NOMA mmWave cellular network with D2Dcommunications are investigated The effects of differentparameters on the probability of outage and ergodic capacityare analyzed such as the base station transmission power thenumber of base station antennas the power ratio of NOMAuser and the distance between D2D users In order to verifythe performance of the system the traditional TDMA themeis adopted as the comparison between the two users of eachbeam In particular the time slot is equally divided by the twousers Hence the capacity of this theme is 119877119879119863119872119860 which isdenoted as
A simplified cellular network system is discussed for theperformance analyzed here The carrier frequency is 28GHzwhich is commonly used for wireless broadband serviceThere are 16 antennas in the base station whose coverageradius is 100m There is single antenna with D2D user Andthe distance between D2D users is 30m Meanwhile thetransmission power of base station and D2D users is 5 dbmIn addition there are 8 NOMA users and 4 D2D usersin the cellular network The path loss exponent is set as3 Furthermore the small scale fading is denoted as 119867 sim119866119886119898119898119886(2 1) which is simplified for the simulation
41 Outage Probability In this section we consider theoutage probability of the NOMA far user and near user
Figure 2 depicts the outage probability in the differentbase station transmission power with 1198771 = 5 bitsHz and1198772 = 332 bitsHz As the base station transmission powerincreases it can be seen that the outage probability of theNOMA users decreases with the exponential form Further-more the performance of each userrsquos outage probability inthe NOMA scheme is significantly better than the TDMAand the closed-form solution obtained is consistent with theMonte Carlo simulation results
In Figure 3 the impact of antenna number in the basestation on the outage probability (1198771 = 564 bitsHz and 1198772
= 4 bitsHz) is presented The simulation results effectivelyverify that the number of antennas of the base stationcan decrease the usersrsquo outage probability in the MIMO-NOMA mmWave cellular network thereby improving thethroughput of the system under the limited time-frequencyresources As can be seen from Figure 3 the number ofantennas has a greater impact on user 2 than user 1When thenumber of antennas is 36 the outage probability of the systemis satisfied which can balance the number of RF chains andthe system performance Then the NOMA scheme performsbetter than the traditional TDMA in the mmWave MIMOcellular network with D2D communications
In Figure 4 we discuss the influence of the power ratiocoefficient in the cellular network between the NOMA usersIt can be seen that the outage probability (1198771 = 4 bitsHz and1198772 = 3 bitsHz) of the two users in NOMA is balanced whenthe power ratio coefficient is approximately 02
Analysis result User 1Numerical result User 1TDMA User 1Analysis result User 2Numerical result User 2TDMA User 2
10minus2
10minus1
100
Out
age p
roba
bilit
y
10 15 20 255Transmission Power (dbm)
Figure 2 Impact of transmission power on outage probability
Analysis result User 1Numerical result User 1TDMA User 1Analysis result User 2Numerical result User 2TDMA User 2
10minus2
10minus1
100
Out
age p
roba
bilit
y
10 15 20 25 30 355Antenna Number
Figure 3 Impact of antenna number on outage probability
In Figure 5 the effect of the distance between D2D usersis consideredThe figure indicates that the outage probability(1198771 = 5 bitsHz and1198772 = 332 bitsHz) of the NOMAusers isreduced in the formof an exponent when the distance ofD2Duser is linear growth Since the distance betweenD2Dusers isincreasing the interference from the D2D transmitter to theNOMA user is weak Hence the throughput of the NOMAusers is improved while the outage probability is dropping
8 Wireless Communications and Mobile Computing
Analysis result User 1Numerical result User 1Analysis result User 2Numerical result User 2
01 015 02 025 03 035 04 045005Power ratio coefficient
10minus3
10minus2
10minus1
100
Out
age p
roba
bilit
y
Figure 4 Impact of power ratio coefficient on outage probability
Analysis result User 1Numerical result User 1Analysis result User 2Numerical result User 2
30 40 50 60 70 8020D2D Distance (m)
10minus2
10minus1
100
Out
age p
roba
bilit
y
Figure 5 Impact of D2D distance on outage probability
42 Ergodic Capacity In this section the total ergodiccapacity is considered in the MIMO-NOMA mmWave cel-lular network with D2D communications It can be seenthat the numerical results are consistent with the closed-form solution which is better than the traditional TDMAMeanwhile the transmission power and the number of basestation antennas have a greater impact and the power ratiocoefficient and the distance between D2D users have lesseffect
In Figure 6 the impact of the transmission power of basestation on the ergodic capacity is considered in the MIMO-NOMA mmWave cellular network with D2D communica-tions It is shown that the ergodic capacity is growing linearly
Analysis resultNumerical resultTDMA
10 15 20 255Transmission Power (dbm)
8
10
12
14
16
18
Syste
m C
apac
ityFigure 6 Impact of transmission power on ergodic capacity
with the increase of transmission power In addition theergodic capacity of the systemwe proposed is higher than thetraditional TDMA Hence in order to improve the ergodiccapacity of the system we can increase the base stationtransmission power as much as possible without affectingothers
As the number of the base station antennas is increasingit is indicated that the ergodic capacity can be improvedbetter than the traditional TDMA in Figure 7 Benefitingfrom the length of mmWave more and more antennas canbe equipped for the base station At the same time we needto balance the improvement in ergodic capacity brought bythe increasing of the number of antennas and the powerconsumption and hardware requirements of the increase inRF chains to determine the final number of antennas
In Figure 8 the ergodic capacity is affected by thechange of the power ratio coefficient of the NOMA usersin the MIMO-NOMA mmWave cellular network with D2Dcommunications It can be seen that the total ergodic capacitychanges slowly with the increase of power ratio
In Figure 9 since the interference from the D2D users isdecreasing the total ergodic capacity is improved with theincrease of the distance between theD2Dusers in theMIMO-NOMA mmWave cellular network It can also be seen thatthe ergodic capacity in the MIMO-NOMAmmWave cellularnetwork is always better than the traditional TDMA
5 Conclusion
In this paper the outage probability and the ergodic capacityof the NOMA in the MIMO-NOMA mmWave cellularnetwork with D2D communications are studied The closed-form solutions of the outage probability and the ergodiccapacity are obtained which are consistent with the numeri-cal results Meanwhile the performance of NOMA is shown
Wireless Communications and Mobile Computing 9
Analysis resultNumerical resultTDMA
4
6
8
10
12
14
16
Syste
m C
apac
ity
10 15 20 25 30 355Antenna Number
Figure 7 Impact of antenna number on ergodic capacity
Analysis resultNumerical resultTDMA
01 015 02 025 03 035 04 045005Power Ratio Coefficient
6
7
8
9
10
11
12
Syste
m C
apac
ity
Figure 8 Impact of power ratio coefficient on ergodic capacity
to be better than traditional TDMA in the MIMO mmWavecellular network with D2D communications Furthermorethe higher transmission power of base station and the largerantenna array can also improve system performance
Data Availability
No data were used to support this study
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Analysis resultNumerical resultTDMA
6
7
8
9
10
11
12
13
Syste
m C
apac
ity
30 40 50 60 70 8020D2D Distance (m)
Figure 9 Impact of D2D distance on ergodic capacity
Acknowledgments
This work was supported by Advance Research Projects of13th Five-Year Plan of Civil Aerospace Technology (B0105)and the National Natural Science Foundation of China(61771051)
References
[1] M Tehrani M Uysal and H Yanikomeroglu ldquoDevice-to-device communication in 5G cellular networks challengessolutions and future directionsrdquo IEEE Communications Mag-azine vol 52 no 5 pp 86ndash92 2014
[2] S-Y Lien C-C Chien G S-T Liu H-L Tsai R Li and YJ Wang ldquoEnhanced LTE device-to-device proximity servicesrdquoIEEE Communications Magazine vol 54 no 12 pp 174ndash1822016
[3] L Lei ZD ZhongC Lin andXM Shen ldquoOperator controlleddevice-to-device communications in LTE-advanced networksrdquoIEEEWireless Communications Magazine vol 19 no 3 pp 96ndash104 2012
[4] A Asadi and V Mancuso ldquoNetwork-assisted outband D2D-clustering in 5G cellular networks theory and practicerdquo IEEETransactions onMobile Computing vol 16 no 8 pp 2246ndash22592017
[5] J HuW Heng Y Zhu GWang X Li and JWu ldquoOverlappingcoalition formation games for joint interference managementand resource allocation in D2D communicationsrdquo IEEE Accessvol 6 pp 6341ndash6349 2018
[6] H Min J Lee S Park and D Hong ldquoCapacity enhancementusing an interference limited area for device-to-device uplinkunderlaying cellular networksrdquo IEEE Transactions on WirelessCommunications vol 10 no 12 pp 3995ndash4000 2011
[7] Z Uykan and R Jantti ldquoTransmission-order optimization forbidirectional device-to-device (D2D) communications under-laying cellular TDD networksmdasha graph theoretic approachrdquoIEEE Journal on Selected Areas in Communications vol 34 no1 pp 1ndash14 2016
10 Wireless Communications and Mobile Computing
[8] L L Wei R Q Hu T He and Y Qian ldquoDevice-to-device(d2d)communications underlaying MU-MIMO cellular networksrdquoin Proceedings of the IEEE Global Communications Conference(GLOBECOM rsquo13) pp 4902ndash4907 IEEE Atlanta Ga USADecember 2013
[9] X Li W Zhang H Zhang andW Li ldquoA combining call admis-sion control and power control scheme for D2D communica-tions underlaying cellular networksrdquo China Communicationsvol 13 no 10 pp 137ndash145 2016
[10] H Sun Y Xu and R Q Hu ldquoA NOMA and MU-MIMOsupported cellular network with underlaid D2D communica-tionsrdquo in Proceedings of the 2016 IEEE 83rd Vehicular TechnologyConference (VTC Spring) pp 1ndash5 Nanjing China May 2016
[11] Z Ding X Lei G K Karagiannidis R Schober J Yuan andV K Bhargava ldquoA survey on non-orthogonal multiple accessfor 5G networks research challenges and future trendsrdquo IEEEJournal on Selected Areas in Communications vol 35 no 10 pp2181ndash2195 2017
[12] N Ye X Li H Yu AWangW Liu andXHou ldquoDeep learningaided grant-free noma towards reliable low-latency access intactile internet of thingsrdquo IEEE Transactions on IndustrialInformatics vol 15 no 5 pp 2995ndash3005 2019
[13] J An K Yang J Wu N Ye S Guo and Z Liao ldquoAchievingsustainable ultra-dense heterogeneous networks for 5Grdquo IEEECommunications Magazine vol 55 no 12 pp 84ndash90 2017
[14] N Ye AWang X Li H Yu A Li andH Jiang ldquoA randomnon-orthogonal multiple access scheme for mmtcrdquo in Proceedingsof the 2017 IEEE 85th Vehicular Technology Conference (VTCSpring) pp 1ndash6 June 2017
[15] K Yang N Yang N Ye M Jia Z Gao and R Fan ldquoNon-orthogonal multiple access achieving sustainable future radioaccessrdquo IEEE Communications Magazine vol 57 no 2 pp 116ndash121 2019
[16] S M R Islam N Avazov O A Dobre and K-S KwakldquoPower-domain non-orthogonal multiple access (NOMA) in5G systems potentials and challengesrdquo IEEE CommunicationsSurveys amp Tutorials vol 19 no 2 pp 721ndash742 2017
[17] N Ye AWang X Li W Liu X Hou and H Yu ldquoOn constella-tion rotation of noma with sic receiverrdquo IEEE CommunicationsLetters vol 22 no 3 pp 514ndash517 2018
[18] MHojeij C A Nour J Farah and C Douillard ldquoJoint resourceand power allocation technique for downlink power-domainnon-orthogonalmultiple accessrdquo inProceedings of the 2018 IEEEConference on Antenna Measurements amp Applications (CAMA)pp 1ndash4 September 2018
[19] F A Rabee K Davaslioglu and R Gitlin ldquoThe optimumreceived power levels of uplink non-orthogonal multiple access(NOMA) signalsrdquo in Proceedings of the 18th IEEE Wireless andMicrowave Technology Conference WAMICON 2017 pp 1ndash4USA April 2017
[20] Y Li andG A A Baduge ldquoNoma-aided cell-freemassivemimosystemsrdquo IEEEWireless Communications Letters vol 7 pp 950ndash953 2018
[21] N Ye A Wang X Li et al ldquoRate-adaptive multiple access foruplink grant-free transmissionrdquo Wireless Communications andMobile Computing vol 2018 Article ID 8978207 21 pages 2018
[22] N Ye H Han L Zhao and A-H Wang ldquoUplink nonorthogo-nal multiple access technologies toward 5G a surveyrdquo WirelessCommunications and Mobile Computing vol 2018 Article ID6187580 26 pages 2018
[23] Y LiuW-J Lu S Shi et al ldquoPerformance analysis of a downlinkcooperative noma network over nakagami-m fading channelsrdquoIEEE Access vol 6 pp 53034ndash53043 2018
[24] X Wang J Wang L He and J Song ldquoOutage analysis fordownlink noma with statistical channel state informationrdquoIEEEWireless Communications Letters vol 7 no 2 pp 142ndash1452018
[25] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAnoverview ofMIMOcommunicationsmdasha key to gigabit wirelessrdquoProceedings of the IEEE vol 92 no 2 pp 198ndash217 2004
[26] W Cai C Chen L Bai Y Jin and J Choi ldquoUser selectionand power allocation schemes for downlink NOMA systemswith imperfect CSIrdquo in Proceedings of the 2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp 1ndash5 MontrealQC Canada September 2016
[27] Z Ding and H V Poor ldquoDesign of massive-MIMO-NOMAwith limited feedbackrdquo IEEE Signal Processing Letters vol 23no 5 pp 629ndash633 2016
[28] Z Ding F Adachi andHV Poor ldquoThe application ofMIMO tonon-orthogonal multiple accessrdquo IEEE Transactions onWirelessCommunications vol 15 no 1 pp 537ndash552 2016
[29] Q Sun SHan I Chin-Lin andZ Pan ldquoOn the ergodic capacityof MIMO NOMA systemsrdquo IEEE Wireless CommunicationsLetters vol 4 no 4 pp 405ndash408 2015
[30] J Ding J Cai and C Yi ldquoAn improved coalition game approachfor MIMO-NOMA clustering integrating beamforming andpower allocationrdquo IEEE Transactions on Vehicular Technologyvol 68 no 2 pp 1672ndash1687 2019
[31] J-B Kim I-H Lee and J Lee ldquoCapacity scaling for D2D aidedcooperative relaying systems using NOMArdquo IEEE WirelessCommunications Letters vol 7 no 1 pp 42ndash45 2018
[32] S Papaioannou G Kalfas C Vagionas et al ldquo5G mm WaveNetworks Leveraging Enhanced Fiber-Wireless Convergencefor High-Density Environments The 5G-PHOS Approachrdquoin Proceedings of the 2018 IEEE International Symposium onBroadband Multimedia Systems and Broadcasting (BMSB) pp1ndash5 Valencia Spain June 2018
[33] SANaqvi and SAHassan ldquoCombiningNOMAandmmWavetechnology for cellular communicationrdquo in Proceedings of the2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp1ndash5 Montreal QC Canada September 2016
[34] F Rusek D Persson B K Lau et al ldquoScaling up MIMOopportunities and challenges with very large arraysrdquo IEEESignal Processing Magazine vol 30 no 1 pp 40ndash60 2013
[35] T Bai A Alkhateeb and R W Heath ldquoCoverage and capacityof millimeter-wave cellular networksrdquo IEEE CommunicationsMagazine vol 52 no 9 pp 70ndash77 2014
[36] X Gao L Dai S Han I Chih-Lin and R W Heath ldquoEnergy-efficient hybrid analog and digital precoding for MmWaveMIMO systems with large antenna arraysrdquo IEEE Journal onSelected Areas in Communications vol 34 no 4 pp 998ndash10092016
[37] X Gao L Dai Z Chen Z Wang and Z Zhang ldquoNear-optimal beam selection for beamspace mmwave massive mimosystemsrdquo IEEE Communications Letters vol 20 no 5 pp 1054ndash1057 2016
[38] Z Wang M Li Q Liu and A L Swindlehurst ldquoHybrid pre-coder and combiner design with low-resolution phase shiftersin mmWave MIMO systemsrdquo IEEE Journal of Selected Topics inSignal Processing vol 12 no 2 pp 256ndash269 2018
Wireless Communications and Mobile Computing 11
[39] Y Sun Z Ding and X Dai ldquoOn the performance of downlinkNOMA in multi-cell mmWave networksrdquo IEEE Communica-tions Letters vol 22 no 11 pp 2366ndash2369 2018
[40] NDeng andMHaenggi ldquoAfine-grained analysis ofmillimeter-wave device-to-device networksrdquo IEEE Transactions on Com-munications vol 65 no 11 pp 4940ndash4954 2017
[41] D Zhang Z Zhou C Xu Y Zhang J Rodriguez and T SatoldquoCapacity analysis of NOMA with mmWave massive MIMOsystemsrdquo IEEE Journal on Selected Areas in Communicationsvol 35 no 7 pp 1606ndash1618 2017
[42] S Singh M N Kulkarni A Ghosh and J G AndrewsldquoTractable model for rate in self-backhauled millimeter wavecellular networksrdquo IEEE Journal on Selected Areas in Commu-nications vol 33 no 10 pp 2191ndash2211 2015
[43] X Yan H Xiao C-X Wang and K An ldquoOn the ergodiccapacity of NOMA-based cognitive hybrid satellite terrestrialnetworksrdquo in Proceedings of the 2017 IEEECIC InternationalConference on Communications in China ICCC 2017 pp 1ndash5China October 2017
[44] Y Huang F Al-Qahtani C Zhong Q Wu J Wang and HAlnuweiri ldquoPerformance analysis ofmultiusermultiple antennarelaying networks with co-channel interference and feedbackdelayrdquo IEEE Transactions on Communications vol 62 no 1 pp59ndash73 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
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Submit your manuscripts atwwwhindawicom
4 Wireless Communications and Mobile Computing
where 119879 = 119871 120591 = 1sin2(31205872radic119871) and 119871 is the number ofantennas
24 Received Signal For downlinkMIMO-NOMA transmis-sion the cellular user 119906(119899 119870) will receive the sum of signalfrom base station and the signal from D2D transmitter atthe same time In addition to receiving the D2D transmittedsignal theD2D receiver119863119880119875will also receive the interferencesignal from the other D2D users Without loss of generalitywe assume there are119873 beams and119872D2Dpairs in the cellularnetwork then the received signal of cellular user 119910119906(119899119896) andthe received signal of D2D user 119910119863119901 can be formulated as
where ℎ119906(119899119896) is the channel gain for downlink 119906(119899 119870)ℎ119906(1198991) ge ℎ119906(1198992) ge ℎ119906(119899119870) ℎ119901119906(119899119896) is the channelgain between 119863119880119875 and 119906(119899 119870) and ℎ1199011015840119901 is the channel gainfrom 1198631198801199011015840 transmitter to 119863119880119901 receiver 119866(119899119896) is the totalbeamforming array gain frombase station to 119906(119899119870)119909119899 is thesuperimposed signal by the total K 119906(119899 119896) in the beam 119899 119875119863is the transmitted power of119863119880119875 119878119901 is the signal transmittedby119863119880119875 and E(1198781199012) = 1 Meanwhile 119899119906(119899119896) and 119899119863119901 are theiid white Gaussian noise with zero mean and one varianceat cellular user 119906(119899 119896) and D2D user 119863119880119875 which is denotedas 119899119906(119899119896) 119899119863119901 sim C119873(0 1)
We denote the SINRs of 119906(119899 119896) and119863119880119875 in the downlinkNOMA-MIMO cellular network as 120574119906(119899119896) 120574119863119880119901
Without lossof generality the interbeam interference is ignored in thispaper In the meantime the perfect SIC is used to preventerror propagation in the NOMA users in the paper Using (1)in (6) and (7) 120574119906(119899119896) and 120574119863119880119901
In this section we present the performance analysis ofD2D-aidedmmWaveMIMO-NOMAsystem Specifically theclosed-form expressions for the performancemetrics (ie theoutage probability and the ergodic capacity) are presentedin the following Without loss of generality in the beam119899 119896-th 119862119880119904 are adopted with NOMA in one beam 119896 isin1 2ℎ119906(1198991) ge ℎ119906(1198992) and one119863119880 is randomly distributedat the edge of the beam Three events are considered in thissystem
Event 1 According to the NOMA successive interferencecancellation (SIC) principle user 1 obtains the informationintended for user 2 with 1205741997888rarr2 and removes it Whendecoding the information intended for user 2 user 1 cancelsit successfully with 1205741
31 Outage Probability In this section we study the outageprobability of 119862119880 and119863119880 The outage probability of the user1 user 2 and119863119880 is given by 119875119900119906119905
where 1198771 1198772 119877119863 are the target rates of user 1 user 2 and119863119880Firstly we consider the outage probability of user 1 119875119900119906119905
1 then 119875(log(1 + 1205741997888rarr2) le 1198772) can be rewritten as 119875(1205741997888rarr2 le21198772 minus 1) so we set
119875 (1205741997888rarr2 le 21198772 minus 1) = 119865 (119898 119886 119887 119888 119889) = 1198651205741997888rarr2 (119898) (21)
where 119886 = 120582119906(1198992)119875119899119866(1198991)2 119887 = 120582119906(1198991)119875119899119866(1198991)2 119889 = 119875119863119888 = 1205902119899 119898 = 21198772 minus 1 and 1198671 = ℎ119906(1198991)2 sim 119866119886119898119898119886(120596 120595)1198672 = ℎ119901119906(1198991)2 sim 119866119886119898119898119886(120578 120579) then1198651205741997888rarr2 (119898) = 119875( 11988611986711198871198671 + 1198891198672 + 119888 le 119898)
= intinfin
0119875( 119886119910119887119910 + 1198891198672 + 119888 le 119898)1198911198671 (119910) 119889119910
= intinfin
0119875(119886119910 minus 119887119898119910 minus 119888119898119889119898 le 1198672)1198911198671 (119910) 119889119910
(22)
In order to determine if (119886119910 minus 119887119898119910 minus 119888119898)119889119898 le 0 we setΦ = 119888119898(119886 minus 119887119898) WhenΦ le 0 (119886119910 minus 119887119898119910minus 119888119898)119889119898 le 0 so119875((119886119910 minus 119887119898119910 minus 119888119898)119889119898 le 1198672) = 1 therefore1198651205741997888rarr2 (119898) = 1 (23)
When Φ gt 0 which is119898 lt 1198861198871198651205741997888rarr2 (119898) = intΦ
01198911198671 (119910) 119889119910
+ intinfin
Φ(1 minus 1198651198672 (119886119910 minus 119887119898119910 minus 119888119898119889119898 ))1198911198671 (119910) 119889119910
= intinfin
Φ
120578minus1sum119895=0
1119895120579119895 (119886 minus 119887119898119889119898 119910 minus 119888119889)119895
(119895119894) 120572119894120573119895minus119894sdot 119890minus120573120579 (minus119869(minus(120572120579 + 1120595) 120596 + 119895 minus 1Φ))+ 1120595120596Γ (120596) (119869 (minus( 1120595) 120596 minus 1Φ)minus 119869(minus( 1120595) 120596 minus 1 0))
(28)
Similarly by adopting different parameters with119886 119887 119888 119889 which is shown in Table 1 we can obtain1198651205741997888rarr2(119898) 1198651205741(119898) 1198651205742(119898)In addition when 1198673 = ℎ1199011199012 sim 119866119886119898119898119886(120596 120601)119875119863ℎ11990111990121205902119899 sim 119866119886119898119898119886(120596 (1198751198631205902119899)120601) Hence 119865120574119863(119898) is
denoted as
119865120574119863 (119898) = 1 minus 120596minus1sum119869=0
Finally the outage probability of user 1 user 2 and 119863119880can be evaluated by 1198651205741997888rarr2(119898) 1198651205741(119898) 1198651205742(119898) 119865120574119863(119898) whichare formulated as
1198751199001199061199051 = 1 minus (1 minus 1198651205741997888rarr2 (21198772 minus 1))
lowast (1 minus 1198651205741 (21198771 minus 1)) (30)
1198751199001199061199052 = 1198651205742 (21198772 minus 1) (31)
119875119900119906119905119863 = 119865120574119863 (2119877119863 minus 1) (32)
32 Ergodic Capacity The ergodic capacity is the averagecapacity of channel which can be defined as the instantaneousend-to-end mutual information expectations and denoted as
119862119890119903119892 = E [log2 (1 + 1205741)] + E [log2 (1 + 1205742)]+ E [log2 (1 + 120574119863)] (33)
6 Wireless Communications and Mobile Computing
Table 1 Parameters of the outage probability
a b c d1198651205741997888rarr2 (119898) 120582119906(1198991)119875119899 1003817100381710038171003817119866(1198991)10038171003817100381710038172 120582119906(1198992)119875119899 1003817100381710038171003817119866(1198992)
In order to compute (34) we first compute the first itemofthe formula As we set before 119886 = 120582119906(1198991)119875119899119866(1198991)2 119889 = 119875119863119888 = 1205902119899 1198671 = ℎ119906(1198991)2 sim 119866119886119898119898119886(120596 120595) 1198672 = ℎ119901119906(1198991)2 sim119866119886119898119898119886(120578 120579) we can get
Similarly we can set a b c d as different parametersto obtain the other items of the formula (34) and then pulleverything together The asymptotic result for the ergodiccapacity of the consider system can be obtained
Wireless Communications and Mobile Computing 7
4 Numerical Results
In this section the outage probability and the ergodic capacityof MIMO-NOMA mmWave cellular network with D2Dcommunications are investigated The effects of differentparameters on the probability of outage and ergodic capacityare analyzed such as the base station transmission power thenumber of base station antennas the power ratio of NOMAuser and the distance between D2D users In order to verifythe performance of the system the traditional TDMA themeis adopted as the comparison between the two users of eachbeam In particular the time slot is equally divided by the twousers Hence the capacity of this theme is 119877119879119863119872119860 which isdenoted as
A simplified cellular network system is discussed for theperformance analyzed here The carrier frequency is 28GHzwhich is commonly used for wireless broadband serviceThere are 16 antennas in the base station whose coverageradius is 100m There is single antenna with D2D user Andthe distance between D2D users is 30m Meanwhile thetransmission power of base station and D2D users is 5 dbmIn addition there are 8 NOMA users and 4 D2D usersin the cellular network The path loss exponent is set as3 Furthermore the small scale fading is denoted as 119867 sim119866119886119898119898119886(2 1) which is simplified for the simulation
41 Outage Probability In this section we consider theoutage probability of the NOMA far user and near user
Figure 2 depicts the outage probability in the differentbase station transmission power with 1198771 = 5 bitsHz and1198772 = 332 bitsHz As the base station transmission powerincreases it can be seen that the outage probability of theNOMA users decreases with the exponential form Further-more the performance of each userrsquos outage probability inthe NOMA scheme is significantly better than the TDMAand the closed-form solution obtained is consistent with theMonte Carlo simulation results
In Figure 3 the impact of antenna number in the basestation on the outage probability (1198771 = 564 bitsHz and 1198772
= 4 bitsHz) is presented The simulation results effectivelyverify that the number of antennas of the base stationcan decrease the usersrsquo outage probability in the MIMO-NOMA mmWave cellular network thereby improving thethroughput of the system under the limited time-frequencyresources As can be seen from Figure 3 the number ofantennas has a greater impact on user 2 than user 1When thenumber of antennas is 36 the outage probability of the systemis satisfied which can balance the number of RF chains andthe system performance Then the NOMA scheme performsbetter than the traditional TDMA in the mmWave MIMOcellular network with D2D communications
In Figure 4 we discuss the influence of the power ratiocoefficient in the cellular network between the NOMA usersIt can be seen that the outage probability (1198771 = 4 bitsHz and1198772 = 3 bitsHz) of the two users in NOMA is balanced whenthe power ratio coefficient is approximately 02
Analysis result User 1Numerical result User 1TDMA User 1Analysis result User 2Numerical result User 2TDMA User 2
10minus2
10minus1
100
Out
age p
roba
bilit
y
10 15 20 255Transmission Power (dbm)
Figure 2 Impact of transmission power on outage probability
Analysis result User 1Numerical result User 1TDMA User 1Analysis result User 2Numerical result User 2TDMA User 2
10minus2
10minus1
100
Out
age p
roba
bilit
y
10 15 20 25 30 355Antenna Number
Figure 3 Impact of antenna number on outage probability
In Figure 5 the effect of the distance between D2D usersis consideredThe figure indicates that the outage probability(1198771 = 5 bitsHz and1198772 = 332 bitsHz) of the NOMAusers isreduced in the formof an exponent when the distance ofD2Duser is linear growth Since the distance betweenD2Dusers isincreasing the interference from the D2D transmitter to theNOMA user is weak Hence the throughput of the NOMAusers is improved while the outage probability is dropping
8 Wireless Communications and Mobile Computing
Analysis result User 1Numerical result User 1Analysis result User 2Numerical result User 2
01 015 02 025 03 035 04 045005Power ratio coefficient
10minus3
10minus2
10minus1
100
Out
age p
roba
bilit
y
Figure 4 Impact of power ratio coefficient on outage probability
Analysis result User 1Numerical result User 1Analysis result User 2Numerical result User 2
30 40 50 60 70 8020D2D Distance (m)
10minus2
10minus1
100
Out
age p
roba
bilit
y
Figure 5 Impact of D2D distance on outage probability
42 Ergodic Capacity In this section the total ergodiccapacity is considered in the MIMO-NOMA mmWave cel-lular network with D2D communications It can be seenthat the numerical results are consistent with the closed-form solution which is better than the traditional TDMAMeanwhile the transmission power and the number of basestation antennas have a greater impact and the power ratiocoefficient and the distance between D2D users have lesseffect
In Figure 6 the impact of the transmission power of basestation on the ergodic capacity is considered in the MIMO-NOMA mmWave cellular network with D2D communica-tions It is shown that the ergodic capacity is growing linearly
Analysis resultNumerical resultTDMA
10 15 20 255Transmission Power (dbm)
8
10
12
14
16
18
Syste
m C
apac
ityFigure 6 Impact of transmission power on ergodic capacity
with the increase of transmission power In addition theergodic capacity of the systemwe proposed is higher than thetraditional TDMA Hence in order to improve the ergodiccapacity of the system we can increase the base stationtransmission power as much as possible without affectingothers
As the number of the base station antennas is increasingit is indicated that the ergodic capacity can be improvedbetter than the traditional TDMA in Figure 7 Benefitingfrom the length of mmWave more and more antennas canbe equipped for the base station At the same time we needto balance the improvement in ergodic capacity brought bythe increasing of the number of antennas and the powerconsumption and hardware requirements of the increase inRF chains to determine the final number of antennas
In Figure 8 the ergodic capacity is affected by thechange of the power ratio coefficient of the NOMA usersin the MIMO-NOMA mmWave cellular network with D2Dcommunications It can be seen that the total ergodic capacitychanges slowly with the increase of power ratio
In Figure 9 since the interference from the D2D users isdecreasing the total ergodic capacity is improved with theincrease of the distance between theD2Dusers in theMIMO-NOMA mmWave cellular network It can also be seen thatthe ergodic capacity in the MIMO-NOMAmmWave cellularnetwork is always better than the traditional TDMA
5 Conclusion
In this paper the outage probability and the ergodic capacityof the NOMA in the MIMO-NOMA mmWave cellularnetwork with D2D communications are studied The closed-form solutions of the outage probability and the ergodiccapacity are obtained which are consistent with the numeri-cal results Meanwhile the performance of NOMA is shown
Wireless Communications and Mobile Computing 9
Analysis resultNumerical resultTDMA
4
6
8
10
12
14
16
Syste
m C
apac
ity
10 15 20 25 30 355Antenna Number
Figure 7 Impact of antenna number on ergodic capacity
Analysis resultNumerical resultTDMA
01 015 02 025 03 035 04 045005Power Ratio Coefficient
6
7
8
9
10
11
12
Syste
m C
apac
ity
Figure 8 Impact of power ratio coefficient on ergodic capacity
to be better than traditional TDMA in the MIMO mmWavecellular network with D2D communications Furthermorethe higher transmission power of base station and the largerantenna array can also improve system performance
Data Availability
No data were used to support this study
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Analysis resultNumerical resultTDMA
6
7
8
9
10
11
12
13
Syste
m C
apac
ity
30 40 50 60 70 8020D2D Distance (m)
Figure 9 Impact of D2D distance on ergodic capacity
Acknowledgments
This work was supported by Advance Research Projects of13th Five-Year Plan of Civil Aerospace Technology (B0105)and the National Natural Science Foundation of China(61771051)
References
[1] M Tehrani M Uysal and H Yanikomeroglu ldquoDevice-to-device communication in 5G cellular networks challengessolutions and future directionsrdquo IEEE Communications Mag-azine vol 52 no 5 pp 86ndash92 2014
[2] S-Y Lien C-C Chien G S-T Liu H-L Tsai R Li and YJ Wang ldquoEnhanced LTE device-to-device proximity servicesrdquoIEEE Communications Magazine vol 54 no 12 pp 174ndash1822016
[3] L Lei ZD ZhongC Lin andXM Shen ldquoOperator controlleddevice-to-device communications in LTE-advanced networksrdquoIEEEWireless Communications Magazine vol 19 no 3 pp 96ndash104 2012
[4] A Asadi and V Mancuso ldquoNetwork-assisted outband D2D-clustering in 5G cellular networks theory and practicerdquo IEEETransactions onMobile Computing vol 16 no 8 pp 2246ndash22592017
[5] J HuW Heng Y Zhu GWang X Li and JWu ldquoOverlappingcoalition formation games for joint interference managementand resource allocation in D2D communicationsrdquo IEEE Accessvol 6 pp 6341ndash6349 2018
[6] H Min J Lee S Park and D Hong ldquoCapacity enhancementusing an interference limited area for device-to-device uplinkunderlaying cellular networksrdquo IEEE Transactions on WirelessCommunications vol 10 no 12 pp 3995ndash4000 2011
[7] Z Uykan and R Jantti ldquoTransmission-order optimization forbidirectional device-to-device (D2D) communications under-laying cellular TDD networksmdasha graph theoretic approachrdquoIEEE Journal on Selected Areas in Communications vol 34 no1 pp 1ndash14 2016
10 Wireless Communications and Mobile Computing
[8] L L Wei R Q Hu T He and Y Qian ldquoDevice-to-device(d2d)communications underlaying MU-MIMO cellular networksrdquoin Proceedings of the IEEE Global Communications Conference(GLOBECOM rsquo13) pp 4902ndash4907 IEEE Atlanta Ga USADecember 2013
[9] X Li W Zhang H Zhang andW Li ldquoA combining call admis-sion control and power control scheme for D2D communica-tions underlaying cellular networksrdquo China Communicationsvol 13 no 10 pp 137ndash145 2016
[10] H Sun Y Xu and R Q Hu ldquoA NOMA and MU-MIMOsupported cellular network with underlaid D2D communica-tionsrdquo in Proceedings of the 2016 IEEE 83rd Vehicular TechnologyConference (VTC Spring) pp 1ndash5 Nanjing China May 2016
[11] Z Ding X Lei G K Karagiannidis R Schober J Yuan andV K Bhargava ldquoA survey on non-orthogonal multiple accessfor 5G networks research challenges and future trendsrdquo IEEEJournal on Selected Areas in Communications vol 35 no 10 pp2181ndash2195 2017
[12] N Ye X Li H Yu AWangW Liu andXHou ldquoDeep learningaided grant-free noma towards reliable low-latency access intactile internet of thingsrdquo IEEE Transactions on IndustrialInformatics vol 15 no 5 pp 2995ndash3005 2019
[13] J An K Yang J Wu N Ye S Guo and Z Liao ldquoAchievingsustainable ultra-dense heterogeneous networks for 5Grdquo IEEECommunications Magazine vol 55 no 12 pp 84ndash90 2017
[14] N Ye AWang X Li H Yu A Li andH Jiang ldquoA randomnon-orthogonal multiple access scheme for mmtcrdquo in Proceedingsof the 2017 IEEE 85th Vehicular Technology Conference (VTCSpring) pp 1ndash6 June 2017
[15] K Yang N Yang N Ye M Jia Z Gao and R Fan ldquoNon-orthogonal multiple access achieving sustainable future radioaccessrdquo IEEE Communications Magazine vol 57 no 2 pp 116ndash121 2019
[16] S M R Islam N Avazov O A Dobre and K-S KwakldquoPower-domain non-orthogonal multiple access (NOMA) in5G systems potentials and challengesrdquo IEEE CommunicationsSurveys amp Tutorials vol 19 no 2 pp 721ndash742 2017
[17] N Ye AWang X Li W Liu X Hou and H Yu ldquoOn constella-tion rotation of noma with sic receiverrdquo IEEE CommunicationsLetters vol 22 no 3 pp 514ndash517 2018
[18] MHojeij C A Nour J Farah and C Douillard ldquoJoint resourceand power allocation technique for downlink power-domainnon-orthogonalmultiple accessrdquo inProceedings of the 2018 IEEEConference on Antenna Measurements amp Applications (CAMA)pp 1ndash4 September 2018
[19] F A Rabee K Davaslioglu and R Gitlin ldquoThe optimumreceived power levels of uplink non-orthogonal multiple access(NOMA) signalsrdquo in Proceedings of the 18th IEEE Wireless andMicrowave Technology Conference WAMICON 2017 pp 1ndash4USA April 2017
[20] Y Li andG A A Baduge ldquoNoma-aided cell-freemassivemimosystemsrdquo IEEEWireless Communications Letters vol 7 pp 950ndash953 2018
[21] N Ye A Wang X Li et al ldquoRate-adaptive multiple access foruplink grant-free transmissionrdquo Wireless Communications andMobile Computing vol 2018 Article ID 8978207 21 pages 2018
[22] N Ye H Han L Zhao and A-H Wang ldquoUplink nonorthogo-nal multiple access technologies toward 5G a surveyrdquo WirelessCommunications and Mobile Computing vol 2018 Article ID6187580 26 pages 2018
[23] Y LiuW-J Lu S Shi et al ldquoPerformance analysis of a downlinkcooperative noma network over nakagami-m fading channelsrdquoIEEE Access vol 6 pp 53034ndash53043 2018
[24] X Wang J Wang L He and J Song ldquoOutage analysis fordownlink noma with statistical channel state informationrdquoIEEEWireless Communications Letters vol 7 no 2 pp 142ndash1452018
[25] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAnoverview ofMIMOcommunicationsmdasha key to gigabit wirelessrdquoProceedings of the IEEE vol 92 no 2 pp 198ndash217 2004
[26] W Cai C Chen L Bai Y Jin and J Choi ldquoUser selectionand power allocation schemes for downlink NOMA systemswith imperfect CSIrdquo in Proceedings of the 2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp 1ndash5 MontrealQC Canada September 2016
[27] Z Ding and H V Poor ldquoDesign of massive-MIMO-NOMAwith limited feedbackrdquo IEEE Signal Processing Letters vol 23no 5 pp 629ndash633 2016
[28] Z Ding F Adachi andHV Poor ldquoThe application ofMIMO tonon-orthogonal multiple accessrdquo IEEE Transactions onWirelessCommunications vol 15 no 1 pp 537ndash552 2016
[29] Q Sun SHan I Chin-Lin andZ Pan ldquoOn the ergodic capacityof MIMO NOMA systemsrdquo IEEE Wireless CommunicationsLetters vol 4 no 4 pp 405ndash408 2015
[30] J Ding J Cai and C Yi ldquoAn improved coalition game approachfor MIMO-NOMA clustering integrating beamforming andpower allocationrdquo IEEE Transactions on Vehicular Technologyvol 68 no 2 pp 1672ndash1687 2019
[31] J-B Kim I-H Lee and J Lee ldquoCapacity scaling for D2D aidedcooperative relaying systems using NOMArdquo IEEE WirelessCommunications Letters vol 7 no 1 pp 42ndash45 2018
[32] S Papaioannou G Kalfas C Vagionas et al ldquo5G mm WaveNetworks Leveraging Enhanced Fiber-Wireless Convergencefor High-Density Environments The 5G-PHOS Approachrdquoin Proceedings of the 2018 IEEE International Symposium onBroadband Multimedia Systems and Broadcasting (BMSB) pp1ndash5 Valencia Spain June 2018
[33] SANaqvi and SAHassan ldquoCombiningNOMAandmmWavetechnology for cellular communicationrdquo in Proceedings of the2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp1ndash5 Montreal QC Canada September 2016
[34] F Rusek D Persson B K Lau et al ldquoScaling up MIMOopportunities and challenges with very large arraysrdquo IEEESignal Processing Magazine vol 30 no 1 pp 40ndash60 2013
[35] T Bai A Alkhateeb and R W Heath ldquoCoverage and capacityof millimeter-wave cellular networksrdquo IEEE CommunicationsMagazine vol 52 no 9 pp 70ndash77 2014
[36] X Gao L Dai S Han I Chih-Lin and R W Heath ldquoEnergy-efficient hybrid analog and digital precoding for MmWaveMIMO systems with large antenna arraysrdquo IEEE Journal onSelected Areas in Communications vol 34 no 4 pp 998ndash10092016
[37] X Gao L Dai Z Chen Z Wang and Z Zhang ldquoNear-optimal beam selection for beamspace mmwave massive mimosystemsrdquo IEEE Communications Letters vol 20 no 5 pp 1054ndash1057 2016
[38] Z Wang M Li Q Liu and A L Swindlehurst ldquoHybrid pre-coder and combiner design with low-resolution phase shiftersin mmWave MIMO systemsrdquo IEEE Journal of Selected Topics inSignal Processing vol 12 no 2 pp 256ndash269 2018
Wireless Communications and Mobile Computing 11
[39] Y Sun Z Ding and X Dai ldquoOn the performance of downlinkNOMA in multi-cell mmWave networksrdquo IEEE Communica-tions Letters vol 22 no 11 pp 2366ndash2369 2018
[40] NDeng andMHaenggi ldquoAfine-grained analysis ofmillimeter-wave device-to-device networksrdquo IEEE Transactions on Com-munications vol 65 no 11 pp 4940ndash4954 2017
[41] D Zhang Z Zhou C Xu Y Zhang J Rodriguez and T SatoldquoCapacity analysis of NOMA with mmWave massive MIMOsystemsrdquo IEEE Journal on Selected Areas in Communicationsvol 35 no 7 pp 1606ndash1618 2017
[42] S Singh M N Kulkarni A Ghosh and J G AndrewsldquoTractable model for rate in self-backhauled millimeter wavecellular networksrdquo IEEE Journal on Selected Areas in Commu-nications vol 33 no 10 pp 2191ndash2211 2015
[43] X Yan H Xiao C-X Wang and K An ldquoOn the ergodiccapacity of NOMA-based cognitive hybrid satellite terrestrialnetworksrdquo in Proceedings of the 2017 IEEECIC InternationalConference on Communications in China ICCC 2017 pp 1ndash5China October 2017
[44] Y Huang F Al-Qahtani C Zhong Q Wu J Wang and HAlnuweiri ldquoPerformance analysis ofmultiusermultiple antennarelaying networks with co-channel interference and feedbackdelayrdquo IEEE Transactions on Communications vol 62 no 1 pp59ndash73 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwwwhindawicom Volume 2018
Hindawiwwwhindawicom Volume 2018
Navigation and Observation
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Hindawi
wwwhindawicom Volume 2018
Advances in
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Submit your manuscripts atwwwhindawicom
Wireless Communications and Mobile Computing 5
According to (13)(20) we can get
119875 (1205741997888rarr2 le 21198772 minus 1) = 119865 (119898 119886 119887 119888 119889) = 1198651205741997888rarr2 (119898) (21)
where 119886 = 120582119906(1198992)119875119899119866(1198991)2 119887 = 120582119906(1198991)119875119899119866(1198991)2 119889 = 119875119863119888 = 1205902119899 119898 = 21198772 minus 1 and 1198671 = ℎ119906(1198991)2 sim 119866119886119898119898119886(120596 120595)1198672 = ℎ119901119906(1198991)2 sim 119866119886119898119898119886(120578 120579) then1198651205741997888rarr2 (119898) = 119875( 11988611986711198871198671 + 1198891198672 + 119888 le 119898)
= intinfin
0119875( 119886119910119887119910 + 1198891198672 + 119888 le 119898)1198911198671 (119910) 119889119910
= intinfin
0119875(119886119910 minus 119887119898119910 minus 119888119898119889119898 le 1198672)1198911198671 (119910) 119889119910
(22)
In order to determine if (119886119910 minus 119887119898119910 minus 119888119898)119889119898 le 0 we setΦ = 119888119898(119886 minus 119887119898) WhenΦ le 0 (119886119910 minus 119887119898119910minus 119888119898)119889119898 le 0 so119875((119886119910 minus 119887119898119910 minus 119888119898)119889119898 le 1198672) = 1 therefore1198651205741997888rarr2 (119898) = 1 (23)
When Φ gt 0 which is119898 lt 1198861198871198651205741997888rarr2 (119898) = intΦ
01198911198671 (119910) 119889119910
+ intinfin
Φ(1 minus 1198651198672 (119886119910 minus 119887119898119910 minus 119888119898119889119898 ))1198911198671 (119910) 119889119910
= intinfin
Φ
120578minus1sum119895=0
1119895120579119895 (119886 minus 119887119898119889119898 119910 minus 119888119889)119895
(119895119894) 120572119894120573119895minus119894sdot 119890minus120573120579 (minus119869(minus(120572120579 + 1120595) 120596 + 119895 minus 1Φ))+ 1120595120596Γ (120596) (119869 (minus( 1120595) 120596 minus 1Φ)minus 119869(minus( 1120595) 120596 minus 1 0))
(28)
Similarly by adopting different parameters with119886 119887 119888 119889 which is shown in Table 1 we can obtain1198651205741997888rarr2(119898) 1198651205741(119898) 1198651205742(119898)In addition when 1198673 = ℎ1199011199012 sim 119866119886119898119898119886(120596 120601)119875119863ℎ11990111990121205902119899 sim 119866119886119898119898119886(120596 (1198751198631205902119899)120601) Hence 119865120574119863(119898) is
denoted as
119865120574119863 (119898) = 1 minus 120596minus1sum119869=0
Finally the outage probability of user 1 user 2 and 119863119880can be evaluated by 1198651205741997888rarr2(119898) 1198651205741(119898) 1198651205742(119898) 119865120574119863(119898) whichare formulated as
1198751199001199061199051 = 1 minus (1 minus 1198651205741997888rarr2 (21198772 minus 1))
lowast (1 minus 1198651205741 (21198771 minus 1)) (30)
1198751199001199061199052 = 1198651205742 (21198772 minus 1) (31)
119875119900119906119905119863 = 119865120574119863 (2119877119863 minus 1) (32)
32 Ergodic Capacity The ergodic capacity is the averagecapacity of channel which can be defined as the instantaneousend-to-end mutual information expectations and denoted as
119862119890119903119892 = E [log2 (1 + 1205741)] + E [log2 (1 + 1205742)]+ E [log2 (1 + 120574119863)] (33)
6 Wireless Communications and Mobile Computing
Table 1 Parameters of the outage probability
a b c d1198651205741997888rarr2 (119898) 120582119906(1198991)119875119899 1003817100381710038171003817119866(1198991)10038171003817100381710038172 120582119906(1198992)119875119899 1003817100381710038171003817119866(1198992)
In order to compute (34) we first compute the first itemofthe formula As we set before 119886 = 120582119906(1198991)119875119899119866(1198991)2 119889 = 119875119863119888 = 1205902119899 1198671 = ℎ119906(1198991)2 sim 119866119886119898119898119886(120596 120595) 1198672 = ℎ119901119906(1198991)2 sim119866119886119898119898119886(120578 120579) we can get
Similarly we can set a b c d as different parametersto obtain the other items of the formula (34) and then pulleverything together The asymptotic result for the ergodiccapacity of the consider system can be obtained
Wireless Communications and Mobile Computing 7
4 Numerical Results
In this section the outage probability and the ergodic capacityof MIMO-NOMA mmWave cellular network with D2Dcommunications are investigated The effects of differentparameters on the probability of outage and ergodic capacityare analyzed such as the base station transmission power thenumber of base station antennas the power ratio of NOMAuser and the distance between D2D users In order to verifythe performance of the system the traditional TDMA themeis adopted as the comparison between the two users of eachbeam In particular the time slot is equally divided by the twousers Hence the capacity of this theme is 119877119879119863119872119860 which isdenoted as
A simplified cellular network system is discussed for theperformance analyzed here The carrier frequency is 28GHzwhich is commonly used for wireless broadband serviceThere are 16 antennas in the base station whose coverageradius is 100m There is single antenna with D2D user Andthe distance between D2D users is 30m Meanwhile thetransmission power of base station and D2D users is 5 dbmIn addition there are 8 NOMA users and 4 D2D usersin the cellular network The path loss exponent is set as3 Furthermore the small scale fading is denoted as 119867 sim119866119886119898119898119886(2 1) which is simplified for the simulation
41 Outage Probability In this section we consider theoutage probability of the NOMA far user and near user
Figure 2 depicts the outage probability in the differentbase station transmission power with 1198771 = 5 bitsHz and1198772 = 332 bitsHz As the base station transmission powerincreases it can be seen that the outage probability of theNOMA users decreases with the exponential form Further-more the performance of each userrsquos outage probability inthe NOMA scheme is significantly better than the TDMAand the closed-form solution obtained is consistent with theMonte Carlo simulation results
In Figure 3 the impact of antenna number in the basestation on the outage probability (1198771 = 564 bitsHz and 1198772
= 4 bitsHz) is presented The simulation results effectivelyverify that the number of antennas of the base stationcan decrease the usersrsquo outage probability in the MIMO-NOMA mmWave cellular network thereby improving thethroughput of the system under the limited time-frequencyresources As can be seen from Figure 3 the number ofantennas has a greater impact on user 2 than user 1When thenumber of antennas is 36 the outage probability of the systemis satisfied which can balance the number of RF chains andthe system performance Then the NOMA scheme performsbetter than the traditional TDMA in the mmWave MIMOcellular network with D2D communications
In Figure 4 we discuss the influence of the power ratiocoefficient in the cellular network between the NOMA usersIt can be seen that the outage probability (1198771 = 4 bitsHz and1198772 = 3 bitsHz) of the two users in NOMA is balanced whenthe power ratio coefficient is approximately 02
Analysis result User 1Numerical result User 1TDMA User 1Analysis result User 2Numerical result User 2TDMA User 2
10minus2
10minus1
100
Out
age p
roba
bilit
y
10 15 20 255Transmission Power (dbm)
Figure 2 Impact of transmission power on outage probability
Analysis result User 1Numerical result User 1TDMA User 1Analysis result User 2Numerical result User 2TDMA User 2
10minus2
10minus1
100
Out
age p
roba
bilit
y
10 15 20 25 30 355Antenna Number
Figure 3 Impact of antenna number on outage probability
In Figure 5 the effect of the distance between D2D usersis consideredThe figure indicates that the outage probability(1198771 = 5 bitsHz and1198772 = 332 bitsHz) of the NOMAusers isreduced in the formof an exponent when the distance ofD2Duser is linear growth Since the distance betweenD2Dusers isincreasing the interference from the D2D transmitter to theNOMA user is weak Hence the throughput of the NOMAusers is improved while the outage probability is dropping
8 Wireless Communications and Mobile Computing
Analysis result User 1Numerical result User 1Analysis result User 2Numerical result User 2
01 015 02 025 03 035 04 045005Power ratio coefficient
10minus3
10minus2
10minus1
100
Out
age p
roba
bilit
y
Figure 4 Impact of power ratio coefficient on outage probability
Analysis result User 1Numerical result User 1Analysis result User 2Numerical result User 2
30 40 50 60 70 8020D2D Distance (m)
10minus2
10minus1
100
Out
age p
roba
bilit
y
Figure 5 Impact of D2D distance on outage probability
42 Ergodic Capacity In this section the total ergodiccapacity is considered in the MIMO-NOMA mmWave cel-lular network with D2D communications It can be seenthat the numerical results are consistent with the closed-form solution which is better than the traditional TDMAMeanwhile the transmission power and the number of basestation antennas have a greater impact and the power ratiocoefficient and the distance between D2D users have lesseffect
In Figure 6 the impact of the transmission power of basestation on the ergodic capacity is considered in the MIMO-NOMA mmWave cellular network with D2D communica-tions It is shown that the ergodic capacity is growing linearly
Analysis resultNumerical resultTDMA
10 15 20 255Transmission Power (dbm)
8
10
12
14
16
18
Syste
m C
apac
ityFigure 6 Impact of transmission power on ergodic capacity
with the increase of transmission power In addition theergodic capacity of the systemwe proposed is higher than thetraditional TDMA Hence in order to improve the ergodiccapacity of the system we can increase the base stationtransmission power as much as possible without affectingothers
As the number of the base station antennas is increasingit is indicated that the ergodic capacity can be improvedbetter than the traditional TDMA in Figure 7 Benefitingfrom the length of mmWave more and more antennas canbe equipped for the base station At the same time we needto balance the improvement in ergodic capacity brought bythe increasing of the number of antennas and the powerconsumption and hardware requirements of the increase inRF chains to determine the final number of antennas
In Figure 8 the ergodic capacity is affected by thechange of the power ratio coefficient of the NOMA usersin the MIMO-NOMA mmWave cellular network with D2Dcommunications It can be seen that the total ergodic capacitychanges slowly with the increase of power ratio
In Figure 9 since the interference from the D2D users isdecreasing the total ergodic capacity is improved with theincrease of the distance between theD2Dusers in theMIMO-NOMA mmWave cellular network It can also be seen thatthe ergodic capacity in the MIMO-NOMAmmWave cellularnetwork is always better than the traditional TDMA
5 Conclusion
In this paper the outage probability and the ergodic capacityof the NOMA in the MIMO-NOMA mmWave cellularnetwork with D2D communications are studied The closed-form solutions of the outage probability and the ergodiccapacity are obtained which are consistent with the numeri-cal results Meanwhile the performance of NOMA is shown
Wireless Communications and Mobile Computing 9
Analysis resultNumerical resultTDMA
4
6
8
10
12
14
16
Syste
m C
apac
ity
10 15 20 25 30 355Antenna Number
Figure 7 Impact of antenna number on ergodic capacity
Analysis resultNumerical resultTDMA
01 015 02 025 03 035 04 045005Power Ratio Coefficient
6
7
8
9
10
11
12
Syste
m C
apac
ity
Figure 8 Impact of power ratio coefficient on ergodic capacity
to be better than traditional TDMA in the MIMO mmWavecellular network with D2D communications Furthermorethe higher transmission power of base station and the largerantenna array can also improve system performance
Data Availability
No data were used to support this study
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Analysis resultNumerical resultTDMA
6
7
8
9
10
11
12
13
Syste
m C
apac
ity
30 40 50 60 70 8020D2D Distance (m)
Figure 9 Impact of D2D distance on ergodic capacity
Acknowledgments
This work was supported by Advance Research Projects of13th Five-Year Plan of Civil Aerospace Technology (B0105)and the National Natural Science Foundation of China(61771051)
References
[1] M Tehrani M Uysal and H Yanikomeroglu ldquoDevice-to-device communication in 5G cellular networks challengessolutions and future directionsrdquo IEEE Communications Mag-azine vol 52 no 5 pp 86ndash92 2014
[2] S-Y Lien C-C Chien G S-T Liu H-L Tsai R Li and YJ Wang ldquoEnhanced LTE device-to-device proximity servicesrdquoIEEE Communications Magazine vol 54 no 12 pp 174ndash1822016
[3] L Lei ZD ZhongC Lin andXM Shen ldquoOperator controlleddevice-to-device communications in LTE-advanced networksrdquoIEEEWireless Communications Magazine vol 19 no 3 pp 96ndash104 2012
[4] A Asadi and V Mancuso ldquoNetwork-assisted outband D2D-clustering in 5G cellular networks theory and practicerdquo IEEETransactions onMobile Computing vol 16 no 8 pp 2246ndash22592017
[5] J HuW Heng Y Zhu GWang X Li and JWu ldquoOverlappingcoalition formation games for joint interference managementand resource allocation in D2D communicationsrdquo IEEE Accessvol 6 pp 6341ndash6349 2018
[6] H Min J Lee S Park and D Hong ldquoCapacity enhancementusing an interference limited area for device-to-device uplinkunderlaying cellular networksrdquo IEEE Transactions on WirelessCommunications vol 10 no 12 pp 3995ndash4000 2011
[7] Z Uykan and R Jantti ldquoTransmission-order optimization forbidirectional device-to-device (D2D) communications under-laying cellular TDD networksmdasha graph theoretic approachrdquoIEEE Journal on Selected Areas in Communications vol 34 no1 pp 1ndash14 2016
10 Wireless Communications and Mobile Computing
[8] L L Wei R Q Hu T He and Y Qian ldquoDevice-to-device(d2d)communications underlaying MU-MIMO cellular networksrdquoin Proceedings of the IEEE Global Communications Conference(GLOBECOM rsquo13) pp 4902ndash4907 IEEE Atlanta Ga USADecember 2013
[9] X Li W Zhang H Zhang andW Li ldquoA combining call admis-sion control and power control scheme for D2D communica-tions underlaying cellular networksrdquo China Communicationsvol 13 no 10 pp 137ndash145 2016
[10] H Sun Y Xu and R Q Hu ldquoA NOMA and MU-MIMOsupported cellular network with underlaid D2D communica-tionsrdquo in Proceedings of the 2016 IEEE 83rd Vehicular TechnologyConference (VTC Spring) pp 1ndash5 Nanjing China May 2016
[11] Z Ding X Lei G K Karagiannidis R Schober J Yuan andV K Bhargava ldquoA survey on non-orthogonal multiple accessfor 5G networks research challenges and future trendsrdquo IEEEJournal on Selected Areas in Communications vol 35 no 10 pp2181ndash2195 2017
[12] N Ye X Li H Yu AWangW Liu andXHou ldquoDeep learningaided grant-free noma towards reliable low-latency access intactile internet of thingsrdquo IEEE Transactions on IndustrialInformatics vol 15 no 5 pp 2995ndash3005 2019
[13] J An K Yang J Wu N Ye S Guo and Z Liao ldquoAchievingsustainable ultra-dense heterogeneous networks for 5Grdquo IEEECommunications Magazine vol 55 no 12 pp 84ndash90 2017
[14] N Ye AWang X Li H Yu A Li andH Jiang ldquoA randomnon-orthogonal multiple access scheme for mmtcrdquo in Proceedingsof the 2017 IEEE 85th Vehicular Technology Conference (VTCSpring) pp 1ndash6 June 2017
[15] K Yang N Yang N Ye M Jia Z Gao and R Fan ldquoNon-orthogonal multiple access achieving sustainable future radioaccessrdquo IEEE Communications Magazine vol 57 no 2 pp 116ndash121 2019
[16] S M R Islam N Avazov O A Dobre and K-S KwakldquoPower-domain non-orthogonal multiple access (NOMA) in5G systems potentials and challengesrdquo IEEE CommunicationsSurveys amp Tutorials vol 19 no 2 pp 721ndash742 2017
[17] N Ye AWang X Li W Liu X Hou and H Yu ldquoOn constella-tion rotation of noma with sic receiverrdquo IEEE CommunicationsLetters vol 22 no 3 pp 514ndash517 2018
[18] MHojeij C A Nour J Farah and C Douillard ldquoJoint resourceand power allocation technique for downlink power-domainnon-orthogonalmultiple accessrdquo inProceedings of the 2018 IEEEConference on Antenna Measurements amp Applications (CAMA)pp 1ndash4 September 2018
[19] F A Rabee K Davaslioglu and R Gitlin ldquoThe optimumreceived power levels of uplink non-orthogonal multiple access(NOMA) signalsrdquo in Proceedings of the 18th IEEE Wireless andMicrowave Technology Conference WAMICON 2017 pp 1ndash4USA April 2017
[20] Y Li andG A A Baduge ldquoNoma-aided cell-freemassivemimosystemsrdquo IEEEWireless Communications Letters vol 7 pp 950ndash953 2018
[21] N Ye A Wang X Li et al ldquoRate-adaptive multiple access foruplink grant-free transmissionrdquo Wireless Communications andMobile Computing vol 2018 Article ID 8978207 21 pages 2018
[22] N Ye H Han L Zhao and A-H Wang ldquoUplink nonorthogo-nal multiple access technologies toward 5G a surveyrdquo WirelessCommunications and Mobile Computing vol 2018 Article ID6187580 26 pages 2018
[23] Y LiuW-J Lu S Shi et al ldquoPerformance analysis of a downlinkcooperative noma network over nakagami-m fading channelsrdquoIEEE Access vol 6 pp 53034ndash53043 2018
[24] X Wang J Wang L He and J Song ldquoOutage analysis fordownlink noma with statistical channel state informationrdquoIEEEWireless Communications Letters vol 7 no 2 pp 142ndash1452018
[25] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAnoverview ofMIMOcommunicationsmdasha key to gigabit wirelessrdquoProceedings of the IEEE vol 92 no 2 pp 198ndash217 2004
[26] W Cai C Chen L Bai Y Jin and J Choi ldquoUser selectionand power allocation schemes for downlink NOMA systemswith imperfect CSIrdquo in Proceedings of the 2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp 1ndash5 MontrealQC Canada September 2016
[27] Z Ding and H V Poor ldquoDesign of massive-MIMO-NOMAwith limited feedbackrdquo IEEE Signal Processing Letters vol 23no 5 pp 629ndash633 2016
[28] Z Ding F Adachi andHV Poor ldquoThe application ofMIMO tonon-orthogonal multiple accessrdquo IEEE Transactions onWirelessCommunications vol 15 no 1 pp 537ndash552 2016
[29] Q Sun SHan I Chin-Lin andZ Pan ldquoOn the ergodic capacityof MIMO NOMA systemsrdquo IEEE Wireless CommunicationsLetters vol 4 no 4 pp 405ndash408 2015
[30] J Ding J Cai and C Yi ldquoAn improved coalition game approachfor MIMO-NOMA clustering integrating beamforming andpower allocationrdquo IEEE Transactions on Vehicular Technologyvol 68 no 2 pp 1672ndash1687 2019
[31] J-B Kim I-H Lee and J Lee ldquoCapacity scaling for D2D aidedcooperative relaying systems using NOMArdquo IEEE WirelessCommunications Letters vol 7 no 1 pp 42ndash45 2018
[32] S Papaioannou G Kalfas C Vagionas et al ldquo5G mm WaveNetworks Leveraging Enhanced Fiber-Wireless Convergencefor High-Density Environments The 5G-PHOS Approachrdquoin Proceedings of the 2018 IEEE International Symposium onBroadband Multimedia Systems and Broadcasting (BMSB) pp1ndash5 Valencia Spain June 2018
[33] SANaqvi and SAHassan ldquoCombiningNOMAandmmWavetechnology for cellular communicationrdquo in Proceedings of the2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp1ndash5 Montreal QC Canada September 2016
[34] F Rusek D Persson B K Lau et al ldquoScaling up MIMOopportunities and challenges with very large arraysrdquo IEEESignal Processing Magazine vol 30 no 1 pp 40ndash60 2013
[35] T Bai A Alkhateeb and R W Heath ldquoCoverage and capacityof millimeter-wave cellular networksrdquo IEEE CommunicationsMagazine vol 52 no 9 pp 70ndash77 2014
[36] X Gao L Dai S Han I Chih-Lin and R W Heath ldquoEnergy-efficient hybrid analog and digital precoding for MmWaveMIMO systems with large antenna arraysrdquo IEEE Journal onSelected Areas in Communications vol 34 no 4 pp 998ndash10092016
[37] X Gao L Dai Z Chen Z Wang and Z Zhang ldquoNear-optimal beam selection for beamspace mmwave massive mimosystemsrdquo IEEE Communications Letters vol 20 no 5 pp 1054ndash1057 2016
[38] Z Wang M Li Q Liu and A L Swindlehurst ldquoHybrid pre-coder and combiner design with low-resolution phase shiftersin mmWave MIMO systemsrdquo IEEE Journal of Selected Topics inSignal Processing vol 12 no 2 pp 256ndash269 2018
Wireless Communications and Mobile Computing 11
[39] Y Sun Z Ding and X Dai ldquoOn the performance of downlinkNOMA in multi-cell mmWave networksrdquo IEEE Communica-tions Letters vol 22 no 11 pp 2366ndash2369 2018
[40] NDeng andMHaenggi ldquoAfine-grained analysis ofmillimeter-wave device-to-device networksrdquo IEEE Transactions on Com-munications vol 65 no 11 pp 4940ndash4954 2017
[41] D Zhang Z Zhou C Xu Y Zhang J Rodriguez and T SatoldquoCapacity analysis of NOMA with mmWave massive MIMOsystemsrdquo IEEE Journal on Selected Areas in Communicationsvol 35 no 7 pp 1606ndash1618 2017
[42] S Singh M N Kulkarni A Ghosh and J G AndrewsldquoTractable model for rate in self-backhauled millimeter wavecellular networksrdquo IEEE Journal on Selected Areas in Commu-nications vol 33 no 10 pp 2191ndash2211 2015
[43] X Yan H Xiao C-X Wang and K An ldquoOn the ergodiccapacity of NOMA-based cognitive hybrid satellite terrestrialnetworksrdquo in Proceedings of the 2017 IEEECIC InternationalConference on Communications in China ICCC 2017 pp 1ndash5China October 2017
[44] Y Huang F Al-Qahtani C Zhong Q Wu J Wang and HAlnuweiri ldquoPerformance analysis ofmultiusermultiple antennarelaying networks with co-channel interference and feedbackdelayrdquo IEEE Transactions on Communications vol 62 no 1 pp59ndash73 2014
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
Table 1 Parameters of the outage probability
a b c d1198651205741997888rarr2 (119898) 120582119906(1198991)119875119899 1003817100381710038171003817119866(1198991)10038171003817100381710038172 120582119906(1198992)119875119899 1003817100381710038171003817119866(1198992)
In order to compute (34) we first compute the first itemofthe formula As we set before 119886 = 120582119906(1198991)119875119899119866(1198991)2 119889 = 119875119863119888 = 1205902119899 1198671 = ℎ119906(1198991)2 sim 119866119886119898119898119886(120596 120595) 1198672 = ℎ119901119906(1198991)2 sim119866119886119898119898119886(120578 120579) we can get
Similarly we can set a b c d as different parametersto obtain the other items of the formula (34) and then pulleverything together The asymptotic result for the ergodiccapacity of the consider system can be obtained
Wireless Communications and Mobile Computing 7
4 Numerical Results
In this section the outage probability and the ergodic capacityof MIMO-NOMA mmWave cellular network with D2Dcommunications are investigated The effects of differentparameters on the probability of outage and ergodic capacityare analyzed such as the base station transmission power thenumber of base station antennas the power ratio of NOMAuser and the distance between D2D users In order to verifythe performance of the system the traditional TDMA themeis adopted as the comparison between the two users of eachbeam In particular the time slot is equally divided by the twousers Hence the capacity of this theme is 119877119879119863119872119860 which isdenoted as
A simplified cellular network system is discussed for theperformance analyzed here The carrier frequency is 28GHzwhich is commonly used for wireless broadband serviceThere are 16 antennas in the base station whose coverageradius is 100m There is single antenna with D2D user Andthe distance between D2D users is 30m Meanwhile thetransmission power of base station and D2D users is 5 dbmIn addition there are 8 NOMA users and 4 D2D usersin the cellular network The path loss exponent is set as3 Furthermore the small scale fading is denoted as 119867 sim119866119886119898119898119886(2 1) which is simplified for the simulation
41 Outage Probability In this section we consider theoutage probability of the NOMA far user and near user
Figure 2 depicts the outage probability in the differentbase station transmission power with 1198771 = 5 bitsHz and1198772 = 332 bitsHz As the base station transmission powerincreases it can be seen that the outage probability of theNOMA users decreases with the exponential form Further-more the performance of each userrsquos outage probability inthe NOMA scheme is significantly better than the TDMAand the closed-form solution obtained is consistent with theMonte Carlo simulation results
In Figure 3 the impact of antenna number in the basestation on the outage probability (1198771 = 564 bitsHz and 1198772
= 4 bitsHz) is presented The simulation results effectivelyverify that the number of antennas of the base stationcan decrease the usersrsquo outage probability in the MIMO-NOMA mmWave cellular network thereby improving thethroughput of the system under the limited time-frequencyresources As can be seen from Figure 3 the number ofantennas has a greater impact on user 2 than user 1When thenumber of antennas is 36 the outage probability of the systemis satisfied which can balance the number of RF chains andthe system performance Then the NOMA scheme performsbetter than the traditional TDMA in the mmWave MIMOcellular network with D2D communications
In Figure 4 we discuss the influence of the power ratiocoefficient in the cellular network between the NOMA usersIt can be seen that the outage probability (1198771 = 4 bitsHz and1198772 = 3 bitsHz) of the two users in NOMA is balanced whenthe power ratio coefficient is approximately 02
Analysis result User 1Numerical result User 1TDMA User 1Analysis result User 2Numerical result User 2TDMA User 2
10minus2
10minus1
100
Out
age p
roba
bilit
y
10 15 20 255Transmission Power (dbm)
Figure 2 Impact of transmission power on outage probability
Analysis result User 1Numerical result User 1TDMA User 1Analysis result User 2Numerical result User 2TDMA User 2
10minus2
10minus1
100
Out
age p
roba
bilit
y
10 15 20 25 30 355Antenna Number
Figure 3 Impact of antenna number on outage probability
In Figure 5 the effect of the distance between D2D usersis consideredThe figure indicates that the outage probability(1198771 = 5 bitsHz and1198772 = 332 bitsHz) of the NOMAusers isreduced in the formof an exponent when the distance ofD2Duser is linear growth Since the distance betweenD2Dusers isincreasing the interference from the D2D transmitter to theNOMA user is weak Hence the throughput of the NOMAusers is improved while the outage probability is dropping
8 Wireless Communications and Mobile Computing
Analysis result User 1Numerical result User 1Analysis result User 2Numerical result User 2
01 015 02 025 03 035 04 045005Power ratio coefficient
10minus3
10minus2
10minus1
100
Out
age p
roba
bilit
y
Figure 4 Impact of power ratio coefficient on outage probability
Analysis result User 1Numerical result User 1Analysis result User 2Numerical result User 2
30 40 50 60 70 8020D2D Distance (m)
10minus2
10minus1
100
Out
age p
roba
bilit
y
Figure 5 Impact of D2D distance on outage probability
42 Ergodic Capacity In this section the total ergodiccapacity is considered in the MIMO-NOMA mmWave cel-lular network with D2D communications It can be seenthat the numerical results are consistent with the closed-form solution which is better than the traditional TDMAMeanwhile the transmission power and the number of basestation antennas have a greater impact and the power ratiocoefficient and the distance between D2D users have lesseffect
In Figure 6 the impact of the transmission power of basestation on the ergodic capacity is considered in the MIMO-NOMA mmWave cellular network with D2D communica-tions It is shown that the ergodic capacity is growing linearly
Analysis resultNumerical resultTDMA
10 15 20 255Transmission Power (dbm)
8
10
12
14
16
18
Syste
m C
apac
ityFigure 6 Impact of transmission power on ergodic capacity
with the increase of transmission power In addition theergodic capacity of the systemwe proposed is higher than thetraditional TDMA Hence in order to improve the ergodiccapacity of the system we can increase the base stationtransmission power as much as possible without affectingothers
As the number of the base station antennas is increasingit is indicated that the ergodic capacity can be improvedbetter than the traditional TDMA in Figure 7 Benefitingfrom the length of mmWave more and more antennas canbe equipped for the base station At the same time we needto balance the improvement in ergodic capacity brought bythe increasing of the number of antennas and the powerconsumption and hardware requirements of the increase inRF chains to determine the final number of antennas
In Figure 8 the ergodic capacity is affected by thechange of the power ratio coefficient of the NOMA usersin the MIMO-NOMA mmWave cellular network with D2Dcommunications It can be seen that the total ergodic capacitychanges slowly with the increase of power ratio
In Figure 9 since the interference from the D2D users isdecreasing the total ergodic capacity is improved with theincrease of the distance between theD2Dusers in theMIMO-NOMA mmWave cellular network It can also be seen thatthe ergodic capacity in the MIMO-NOMAmmWave cellularnetwork is always better than the traditional TDMA
5 Conclusion
In this paper the outage probability and the ergodic capacityof the NOMA in the MIMO-NOMA mmWave cellularnetwork with D2D communications are studied The closed-form solutions of the outage probability and the ergodiccapacity are obtained which are consistent with the numeri-cal results Meanwhile the performance of NOMA is shown
Wireless Communications and Mobile Computing 9
Analysis resultNumerical resultTDMA
4
6
8
10
12
14
16
Syste
m C
apac
ity
10 15 20 25 30 355Antenna Number
Figure 7 Impact of antenna number on ergodic capacity
Analysis resultNumerical resultTDMA
01 015 02 025 03 035 04 045005Power Ratio Coefficient
6
7
8
9
10
11
12
Syste
m C
apac
ity
Figure 8 Impact of power ratio coefficient on ergodic capacity
to be better than traditional TDMA in the MIMO mmWavecellular network with D2D communications Furthermorethe higher transmission power of base station and the largerantenna array can also improve system performance
Data Availability
No data were used to support this study
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Analysis resultNumerical resultTDMA
6
7
8
9
10
11
12
13
Syste
m C
apac
ity
30 40 50 60 70 8020D2D Distance (m)
Figure 9 Impact of D2D distance on ergodic capacity
Acknowledgments
This work was supported by Advance Research Projects of13th Five-Year Plan of Civil Aerospace Technology (B0105)and the National Natural Science Foundation of China(61771051)
References
[1] M Tehrani M Uysal and H Yanikomeroglu ldquoDevice-to-device communication in 5G cellular networks challengessolutions and future directionsrdquo IEEE Communications Mag-azine vol 52 no 5 pp 86ndash92 2014
[2] S-Y Lien C-C Chien G S-T Liu H-L Tsai R Li and YJ Wang ldquoEnhanced LTE device-to-device proximity servicesrdquoIEEE Communications Magazine vol 54 no 12 pp 174ndash1822016
[3] L Lei ZD ZhongC Lin andXM Shen ldquoOperator controlleddevice-to-device communications in LTE-advanced networksrdquoIEEEWireless Communications Magazine vol 19 no 3 pp 96ndash104 2012
[4] A Asadi and V Mancuso ldquoNetwork-assisted outband D2D-clustering in 5G cellular networks theory and practicerdquo IEEETransactions onMobile Computing vol 16 no 8 pp 2246ndash22592017
[5] J HuW Heng Y Zhu GWang X Li and JWu ldquoOverlappingcoalition formation games for joint interference managementand resource allocation in D2D communicationsrdquo IEEE Accessvol 6 pp 6341ndash6349 2018
[6] H Min J Lee S Park and D Hong ldquoCapacity enhancementusing an interference limited area for device-to-device uplinkunderlaying cellular networksrdquo IEEE Transactions on WirelessCommunications vol 10 no 12 pp 3995ndash4000 2011
[7] Z Uykan and R Jantti ldquoTransmission-order optimization forbidirectional device-to-device (D2D) communications under-laying cellular TDD networksmdasha graph theoretic approachrdquoIEEE Journal on Selected Areas in Communications vol 34 no1 pp 1ndash14 2016
10 Wireless Communications and Mobile Computing
[8] L L Wei R Q Hu T He and Y Qian ldquoDevice-to-device(d2d)communications underlaying MU-MIMO cellular networksrdquoin Proceedings of the IEEE Global Communications Conference(GLOBECOM rsquo13) pp 4902ndash4907 IEEE Atlanta Ga USADecember 2013
[9] X Li W Zhang H Zhang andW Li ldquoA combining call admis-sion control and power control scheme for D2D communica-tions underlaying cellular networksrdquo China Communicationsvol 13 no 10 pp 137ndash145 2016
[10] H Sun Y Xu and R Q Hu ldquoA NOMA and MU-MIMOsupported cellular network with underlaid D2D communica-tionsrdquo in Proceedings of the 2016 IEEE 83rd Vehicular TechnologyConference (VTC Spring) pp 1ndash5 Nanjing China May 2016
[11] Z Ding X Lei G K Karagiannidis R Schober J Yuan andV K Bhargava ldquoA survey on non-orthogonal multiple accessfor 5G networks research challenges and future trendsrdquo IEEEJournal on Selected Areas in Communications vol 35 no 10 pp2181ndash2195 2017
[12] N Ye X Li H Yu AWangW Liu andXHou ldquoDeep learningaided grant-free noma towards reliable low-latency access intactile internet of thingsrdquo IEEE Transactions on IndustrialInformatics vol 15 no 5 pp 2995ndash3005 2019
[13] J An K Yang J Wu N Ye S Guo and Z Liao ldquoAchievingsustainable ultra-dense heterogeneous networks for 5Grdquo IEEECommunications Magazine vol 55 no 12 pp 84ndash90 2017
[14] N Ye AWang X Li H Yu A Li andH Jiang ldquoA randomnon-orthogonal multiple access scheme for mmtcrdquo in Proceedingsof the 2017 IEEE 85th Vehicular Technology Conference (VTCSpring) pp 1ndash6 June 2017
[15] K Yang N Yang N Ye M Jia Z Gao and R Fan ldquoNon-orthogonal multiple access achieving sustainable future radioaccessrdquo IEEE Communications Magazine vol 57 no 2 pp 116ndash121 2019
[16] S M R Islam N Avazov O A Dobre and K-S KwakldquoPower-domain non-orthogonal multiple access (NOMA) in5G systems potentials and challengesrdquo IEEE CommunicationsSurveys amp Tutorials vol 19 no 2 pp 721ndash742 2017
[17] N Ye AWang X Li W Liu X Hou and H Yu ldquoOn constella-tion rotation of noma with sic receiverrdquo IEEE CommunicationsLetters vol 22 no 3 pp 514ndash517 2018
[18] MHojeij C A Nour J Farah and C Douillard ldquoJoint resourceand power allocation technique for downlink power-domainnon-orthogonalmultiple accessrdquo inProceedings of the 2018 IEEEConference on Antenna Measurements amp Applications (CAMA)pp 1ndash4 September 2018
[19] F A Rabee K Davaslioglu and R Gitlin ldquoThe optimumreceived power levels of uplink non-orthogonal multiple access(NOMA) signalsrdquo in Proceedings of the 18th IEEE Wireless andMicrowave Technology Conference WAMICON 2017 pp 1ndash4USA April 2017
[20] Y Li andG A A Baduge ldquoNoma-aided cell-freemassivemimosystemsrdquo IEEEWireless Communications Letters vol 7 pp 950ndash953 2018
[21] N Ye A Wang X Li et al ldquoRate-adaptive multiple access foruplink grant-free transmissionrdquo Wireless Communications andMobile Computing vol 2018 Article ID 8978207 21 pages 2018
[22] N Ye H Han L Zhao and A-H Wang ldquoUplink nonorthogo-nal multiple access technologies toward 5G a surveyrdquo WirelessCommunications and Mobile Computing vol 2018 Article ID6187580 26 pages 2018
[23] Y LiuW-J Lu S Shi et al ldquoPerformance analysis of a downlinkcooperative noma network over nakagami-m fading channelsrdquoIEEE Access vol 6 pp 53034ndash53043 2018
[24] X Wang J Wang L He and J Song ldquoOutage analysis fordownlink noma with statistical channel state informationrdquoIEEEWireless Communications Letters vol 7 no 2 pp 142ndash1452018
[25] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAnoverview ofMIMOcommunicationsmdasha key to gigabit wirelessrdquoProceedings of the IEEE vol 92 no 2 pp 198ndash217 2004
[26] W Cai C Chen L Bai Y Jin and J Choi ldquoUser selectionand power allocation schemes for downlink NOMA systemswith imperfect CSIrdquo in Proceedings of the 2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp 1ndash5 MontrealQC Canada September 2016
[27] Z Ding and H V Poor ldquoDesign of massive-MIMO-NOMAwith limited feedbackrdquo IEEE Signal Processing Letters vol 23no 5 pp 629ndash633 2016
[28] Z Ding F Adachi andHV Poor ldquoThe application ofMIMO tonon-orthogonal multiple accessrdquo IEEE Transactions onWirelessCommunications vol 15 no 1 pp 537ndash552 2016
[29] Q Sun SHan I Chin-Lin andZ Pan ldquoOn the ergodic capacityof MIMO NOMA systemsrdquo IEEE Wireless CommunicationsLetters vol 4 no 4 pp 405ndash408 2015
[30] J Ding J Cai and C Yi ldquoAn improved coalition game approachfor MIMO-NOMA clustering integrating beamforming andpower allocationrdquo IEEE Transactions on Vehicular Technologyvol 68 no 2 pp 1672ndash1687 2019
[31] J-B Kim I-H Lee and J Lee ldquoCapacity scaling for D2D aidedcooperative relaying systems using NOMArdquo IEEE WirelessCommunications Letters vol 7 no 1 pp 42ndash45 2018
[32] S Papaioannou G Kalfas C Vagionas et al ldquo5G mm WaveNetworks Leveraging Enhanced Fiber-Wireless Convergencefor High-Density Environments The 5G-PHOS Approachrdquoin Proceedings of the 2018 IEEE International Symposium onBroadband Multimedia Systems and Broadcasting (BMSB) pp1ndash5 Valencia Spain June 2018
[33] SANaqvi and SAHassan ldquoCombiningNOMAandmmWavetechnology for cellular communicationrdquo in Proceedings of the2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp1ndash5 Montreal QC Canada September 2016
[34] F Rusek D Persson B K Lau et al ldquoScaling up MIMOopportunities and challenges with very large arraysrdquo IEEESignal Processing Magazine vol 30 no 1 pp 40ndash60 2013
[35] T Bai A Alkhateeb and R W Heath ldquoCoverage and capacityof millimeter-wave cellular networksrdquo IEEE CommunicationsMagazine vol 52 no 9 pp 70ndash77 2014
[36] X Gao L Dai S Han I Chih-Lin and R W Heath ldquoEnergy-efficient hybrid analog and digital precoding for MmWaveMIMO systems with large antenna arraysrdquo IEEE Journal onSelected Areas in Communications vol 34 no 4 pp 998ndash10092016
[37] X Gao L Dai Z Chen Z Wang and Z Zhang ldquoNear-optimal beam selection for beamspace mmwave massive mimosystemsrdquo IEEE Communications Letters vol 20 no 5 pp 1054ndash1057 2016
[38] Z Wang M Li Q Liu and A L Swindlehurst ldquoHybrid pre-coder and combiner design with low-resolution phase shiftersin mmWave MIMO systemsrdquo IEEE Journal of Selected Topics inSignal Processing vol 12 no 2 pp 256ndash269 2018
Wireless Communications and Mobile Computing 11
[39] Y Sun Z Ding and X Dai ldquoOn the performance of downlinkNOMA in multi-cell mmWave networksrdquo IEEE Communica-tions Letters vol 22 no 11 pp 2366ndash2369 2018
[40] NDeng andMHaenggi ldquoAfine-grained analysis ofmillimeter-wave device-to-device networksrdquo IEEE Transactions on Com-munications vol 65 no 11 pp 4940ndash4954 2017
[41] D Zhang Z Zhou C Xu Y Zhang J Rodriguez and T SatoldquoCapacity analysis of NOMA with mmWave massive MIMOsystemsrdquo IEEE Journal on Selected Areas in Communicationsvol 35 no 7 pp 1606ndash1618 2017
[42] S Singh M N Kulkarni A Ghosh and J G AndrewsldquoTractable model for rate in self-backhauled millimeter wavecellular networksrdquo IEEE Journal on Selected Areas in Commu-nications vol 33 no 10 pp 2191ndash2211 2015
[43] X Yan H Xiao C-X Wang and K An ldquoOn the ergodiccapacity of NOMA-based cognitive hybrid satellite terrestrialnetworksrdquo in Proceedings of the 2017 IEEECIC InternationalConference on Communications in China ICCC 2017 pp 1ndash5China October 2017
[44] Y Huang F Al-Qahtani C Zhong Q Wu J Wang and HAlnuweiri ldquoPerformance analysis ofmultiusermultiple antennarelaying networks with co-channel interference and feedbackdelayrdquo IEEE Transactions on Communications vol 62 no 1 pp59ndash73 2014
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
4 Numerical Results
In this section the outage probability and the ergodic capacityof MIMO-NOMA mmWave cellular network with D2Dcommunications are investigated The effects of differentparameters on the probability of outage and ergodic capacityare analyzed such as the base station transmission power thenumber of base station antennas the power ratio of NOMAuser and the distance between D2D users In order to verifythe performance of the system the traditional TDMA themeis adopted as the comparison between the two users of eachbeam In particular the time slot is equally divided by the twousers Hence the capacity of this theme is 119877119879119863119872119860 which isdenoted as
A simplified cellular network system is discussed for theperformance analyzed here The carrier frequency is 28GHzwhich is commonly used for wireless broadband serviceThere are 16 antennas in the base station whose coverageradius is 100m There is single antenna with D2D user Andthe distance between D2D users is 30m Meanwhile thetransmission power of base station and D2D users is 5 dbmIn addition there are 8 NOMA users and 4 D2D usersin the cellular network The path loss exponent is set as3 Furthermore the small scale fading is denoted as 119867 sim119866119886119898119898119886(2 1) which is simplified for the simulation
41 Outage Probability In this section we consider theoutage probability of the NOMA far user and near user
Figure 2 depicts the outage probability in the differentbase station transmission power with 1198771 = 5 bitsHz and1198772 = 332 bitsHz As the base station transmission powerincreases it can be seen that the outage probability of theNOMA users decreases with the exponential form Further-more the performance of each userrsquos outage probability inthe NOMA scheme is significantly better than the TDMAand the closed-form solution obtained is consistent with theMonte Carlo simulation results
In Figure 3 the impact of antenna number in the basestation on the outage probability (1198771 = 564 bitsHz and 1198772
= 4 bitsHz) is presented The simulation results effectivelyverify that the number of antennas of the base stationcan decrease the usersrsquo outage probability in the MIMO-NOMA mmWave cellular network thereby improving thethroughput of the system under the limited time-frequencyresources As can be seen from Figure 3 the number ofantennas has a greater impact on user 2 than user 1When thenumber of antennas is 36 the outage probability of the systemis satisfied which can balance the number of RF chains andthe system performance Then the NOMA scheme performsbetter than the traditional TDMA in the mmWave MIMOcellular network with D2D communications
In Figure 4 we discuss the influence of the power ratiocoefficient in the cellular network between the NOMA usersIt can be seen that the outage probability (1198771 = 4 bitsHz and1198772 = 3 bitsHz) of the two users in NOMA is balanced whenthe power ratio coefficient is approximately 02
Analysis result User 1Numerical result User 1TDMA User 1Analysis result User 2Numerical result User 2TDMA User 2
10minus2
10minus1
100
Out
age p
roba
bilit
y
10 15 20 255Transmission Power (dbm)
Figure 2 Impact of transmission power on outage probability
Analysis result User 1Numerical result User 1TDMA User 1Analysis result User 2Numerical result User 2TDMA User 2
10minus2
10minus1
100
Out
age p
roba
bilit
y
10 15 20 25 30 355Antenna Number
Figure 3 Impact of antenna number on outage probability
In Figure 5 the effect of the distance between D2D usersis consideredThe figure indicates that the outage probability(1198771 = 5 bitsHz and1198772 = 332 bitsHz) of the NOMAusers isreduced in the formof an exponent when the distance ofD2Duser is linear growth Since the distance betweenD2Dusers isincreasing the interference from the D2D transmitter to theNOMA user is weak Hence the throughput of the NOMAusers is improved while the outage probability is dropping
8 Wireless Communications and Mobile Computing
Analysis result User 1Numerical result User 1Analysis result User 2Numerical result User 2
01 015 02 025 03 035 04 045005Power ratio coefficient
10minus3
10minus2
10minus1
100
Out
age p
roba
bilit
y
Figure 4 Impact of power ratio coefficient on outage probability
Analysis result User 1Numerical result User 1Analysis result User 2Numerical result User 2
30 40 50 60 70 8020D2D Distance (m)
10minus2
10minus1
100
Out
age p
roba
bilit
y
Figure 5 Impact of D2D distance on outage probability
42 Ergodic Capacity In this section the total ergodiccapacity is considered in the MIMO-NOMA mmWave cel-lular network with D2D communications It can be seenthat the numerical results are consistent with the closed-form solution which is better than the traditional TDMAMeanwhile the transmission power and the number of basestation antennas have a greater impact and the power ratiocoefficient and the distance between D2D users have lesseffect
In Figure 6 the impact of the transmission power of basestation on the ergodic capacity is considered in the MIMO-NOMA mmWave cellular network with D2D communica-tions It is shown that the ergodic capacity is growing linearly
Analysis resultNumerical resultTDMA
10 15 20 255Transmission Power (dbm)
8
10
12
14
16
18
Syste
m C
apac
ityFigure 6 Impact of transmission power on ergodic capacity
with the increase of transmission power In addition theergodic capacity of the systemwe proposed is higher than thetraditional TDMA Hence in order to improve the ergodiccapacity of the system we can increase the base stationtransmission power as much as possible without affectingothers
As the number of the base station antennas is increasingit is indicated that the ergodic capacity can be improvedbetter than the traditional TDMA in Figure 7 Benefitingfrom the length of mmWave more and more antennas canbe equipped for the base station At the same time we needto balance the improvement in ergodic capacity brought bythe increasing of the number of antennas and the powerconsumption and hardware requirements of the increase inRF chains to determine the final number of antennas
In Figure 8 the ergodic capacity is affected by thechange of the power ratio coefficient of the NOMA usersin the MIMO-NOMA mmWave cellular network with D2Dcommunications It can be seen that the total ergodic capacitychanges slowly with the increase of power ratio
In Figure 9 since the interference from the D2D users isdecreasing the total ergodic capacity is improved with theincrease of the distance between theD2Dusers in theMIMO-NOMA mmWave cellular network It can also be seen thatthe ergodic capacity in the MIMO-NOMAmmWave cellularnetwork is always better than the traditional TDMA
5 Conclusion
In this paper the outage probability and the ergodic capacityof the NOMA in the MIMO-NOMA mmWave cellularnetwork with D2D communications are studied The closed-form solutions of the outage probability and the ergodiccapacity are obtained which are consistent with the numeri-cal results Meanwhile the performance of NOMA is shown
Wireless Communications and Mobile Computing 9
Analysis resultNumerical resultTDMA
4
6
8
10
12
14
16
Syste
m C
apac
ity
10 15 20 25 30 355Antenna Number
Figure 7 Impact of antenna number on ergodic capacity
Analysis resultNumerical resultTDMA
01 015 02 025 03 035 04 045005Power Ratio Coefficient
6
7
8
9
10
11
12
Syste
m C
apac
ity
Figure 8 Impact of power ratio coefficient on ergodic capacity
to be better than traditional TDMA in the MIMO mmWavecellular network with D2D communications Furthermorethe higher transmission power of base station and the largerantenna array can also improve system performance
Data Availability
No data were used to support this study
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Analysis resultNumerical resultTDMA
6
7
8
9
10
11
12
13
Syste
m C
apac
ity
30 40 50 60 70 8020D2D Distance (m)
Figure 9 Impact of D2D distance on ergodic capacity
Acknowledgments
This work was supported by Advance Research Projects of13th Five-Year Plan of Civil Aerospace Technology (B0105)and the National Natural Science Foundation of China(61771051)
References
[1] M Tehrani M Uysal and H Yanikomeroglu ldquoDevice-to-device communication in 5G cellular networks challengessolutions and future directionsrdquo IEEE Communications Mag-azine vol 52 no 5 pp 86ndash92 2014
[2] S-Y Lien C-C Chien G S-T Liu H-L Tsai R Li and YJ Wang ldquoEnhanced LTE device-to-device proximity servicesrdquoIEEE Communications Magazine vol 54 no 12 pp 174ndash1822016
[3] L Lei ZD ZhongC Lin andXM Shen ldquoOperator controlleddevice-to-device communications in LTE-advanced networksrdquoIEEEWireless Communications Magazine vol 19 no 3 pp 96ndash104 2012
[4] A Asadi and V Mancuso ldquoNetwork-assisted outband D2D-clustering in 5G cellular networks theory and practicerdquo IEEETransactions onMobile Computing vol 16 no 8 pp 2246ndash22592017
[5] J HuW Heng Y Zhu GWang X Li and JWu ldquoOverlappingcoalition formation games for joint interference managementand resource allocation in D2D communicationsrdquo IEEE Accessvol 6 pp 6341ndash6349 2018
[6] H Min J Lee S Park and D Hong ldquoCapacity enhancementusing an interference limited area for device-to-device uplinkunderlaying cellular networksrdquo IEEE Transactions on WirelessCommunications vol 10 no 12 pp 3995ndash4000 2011
[7] Z Uykan and R Jantti ldquoTransmission-order optimization forbidirectional device-to-device (D2D) communications under-laying cellular TDD networksmdasha graph theoretic approachrdquoIEEE Journal on Selected Areas in Communications vol 34 no1 pp 1ndash14 2016
10 Wireless Communications and Mobile Computing
[8] L L Wei R Q Hu T He and Y Qian ldquoDevice-to-device(d2d)communications underlaying MU-MIMO cellular networksrdquoin Proceedings of the IEEE Global Communications Conference(GLOBECOM rsquo13) pp 4902ndash4907 IEEE Atlanta Ga USADecember 2013
[9] X Li W Zhang H Zhang andW Li ldquoA combining call admis-sion control and power control scheme for D2D communica-tions underlaying cellular networksrdquo China Communicationsvol 13 no 10 pp 137ndash145 2016
[10] H Sun Y Xu and R Q Hu ldquoA NOMA and MU-MIMOsupported cellular network with underlaid D2D communica-tionsrdquo in Proceedings of the 2016 IEEE 83rd Vehicular TechnologyConference (VTC Spring) pp 1ndash5 Nanjing China May 2016
[11] Z Ding X Lei G K Karagiannidis R Schober J Yuan andV K Bhargava ldquoA survey on non-orthogonal multiple accessfor 5G networks research challenges and future trendsrdquo IEEEJournal on Selected Areas in Communications vol 35 no 10 pp2181ndash2195 2017
[12] N Ye X Li H Yu AWangW Liu andXHou ldquoDeep learningaided grant-free noma towards reliable low-latency access intactile internet of thingsrdquo IEEE Transactions on IndustrialInformatics vol 15 no 5 pp 2995ndash3005 2019
[13] J An K Yang J Wu N Ye S Guo and Z Liao ldquoAchievingsustainable ultra-dense heterogeneous networks for 5Grdquo IEEECommunications Magazine vol 55 no 12 pp 84ndash90 2017
[14] N Ye AWang X Li H Yu A Li andH Jiang ldquoA randomnon-orthogonal multiple access scheme for mmtcrdquo in Proceedingsof the 2017 IEEE 85th Vehicular Technology Conference (VTCSpring) pp 1ndash6 June 2017
[15] K Yang N Yang N Ye M Jia Z Gao and R Fan ldquoNon-orthogonal multiple access achieving sustainable future radioaccessrdquo IEEE Communications Magazine vol 57 no 2 pp 116ndash121 2019
[16] S M R Islam N Avazov O A Dobre and K-S KwakldquoPower-domain non-orthogonal multiple access (NOMA) in5G systems potentials and challengesrdquo IEEE CommunicationsSurveys amp Tutorials vol 19 no 2 pp 721ndash742 2017
[17] N Ye AWang X Li W Liu X Hou and H Yu ldquoOn constella-tion rotation of noma with sic receiverrdquo IEEE CommunicationsLetters vol 22 no 3 pp 514ndash517 2018
[18] MHojeij C A Nour J Farah and C Douillard ldquoJoint resourceand power allocation technique for downlink power-domainnon-orthogonalmultiple accessrdquo inProceedings of the 2018 IEEEConference on Antenna Measurements amp Applications (CAMA)pp 1ndash4 September 2018
[19] F A Rabee K Davaslioglu and R Gitlin ldquoThe optimumreceived power levels of uplink non-orthogonal multiple access(NOMA) signalsrdquo in Proceedings of the 18th IEEE Wireless andMicrowave Technology Conference WAMICON 2017 pp 1ndash4USA April 2017
[20] Y Li andG A A Baduge ldquoNoma-aided cell-freemassivemimosystemsrdquo IEEEWireless Communications Letters vol 7 pp 950ndash953 2018
[21] N Ye A Wang X Li et al ldquoRate-adaptive multiple access foruplink grant-free transmissionrdquo Wireless Communications andMobile Computing vol 2018 Article ID 8978207 21 pages 2018
[22] N Ye H Han L Zhao and A-H Wang ldquoUplink nonorthogo-nal multiple access technologies toward 5G a surveyrdquo WirelessCommunications and Mobile Computing vol 2018 Article ID6187580 26 pages 2018
[23] Y LiuW-J Lu S Shi et al ldquoPerformance analysis of a downlinkcooperative noma network over nakagami-m fading channelsrdquoIEEE Access vol 6 pp 53034ndash53043 2018
[24] X Wang J Wang L He and J Song ldquoOutage analysis fordownlink noma with statistical channel state informationrdquoIEEEWireless Communications Letters vol 7 no 2 pp 142ndash1452018
[25] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAnoverview ofMIMOcommunicationsmdasha key to gigabit wirelessrdquoProceedings of the IEEE vol 92 no 2 pp 198ndash217 2004
[26] W Cai C Chen L Bai Y Jin and J Choi ldquoUser selectionand power allocation schemes for downlink NOMA systemswith imperfect CSIrdquo in Proceedings of the 2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp 1ndash5 MontrealQC Canada September 2016
[27] Z Ding and H V Poor ldquoDesign of massive-MIMO-NOMAwith limited feedbackrdquo IEEE Signal Processing Letters vol 23no 5 pp 629ndash633 2016
[28] Z Ding F Adachi andHV Poor ldquoThe application ofMIMO tonon-orthogonal multiple accessrdquo IEEE Transactions onWirelessCommunications vol 15 no 1 pp 537ndash552 2016
[29] Q Sun SHan I Chin-Lin andZ Pan ldquoOn the ergodic capacityof MIMO NOMA systemsrdquo IEEE Wireless CommunicationsLetters vol 4 no 4 pp 405ndash408 2015
[30] J Ding J Cai and C Yi ldquoAn improved coalition game approachfor MIMO-NOMA clustering integrating beamforming andpower allocationrdquo IEEE Transactions on Vehicular Technologyvol 68 no 2 pp 1672ndash1687 2019
[31] J-B Kim I-H Lee and J Lee ldquoCapacity scaling for D2D aidedcooperative relaying systems using NOMArdquo IEEE WirelessCommunications Letters vol 7 no 1 pp 42ndash45 2018
[32] S Papaioannou G Kalfas C Vagionas et al ldquo5G mm WaveNetworks Leveraging Enhanced Fiber-Wireless Convergencefor High-Density Environments The 5G-PHOS Approachrdquoin Proceedings of the 2018 IEEE International Symposium onBroadband Multimedia Systems and Broadcasting (BMSB) pp1ndash5 Valencia Spain June 2018
[33] SANaqvi and SAHassan ldquoCombiningNOMAandmmWavetechnology for cellular communicationrdquo in Proceedings of the2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp1ndash5 Montreal QC Canada September 2016
[34] F Rusek D Persson B K Lau et al ldquoScaling up MIMOopportunities and challenges with very large arraysrdquo IEEESignal Processing Magazine vol 30 no 1 pp 40ndash60 2013
[35] T Bai A Alkhateeb and R W Heath ldquoCoverage and capacityof millimeter-wave cellular networksrdquo IEEE CommunicationsMagazine vol 52 no 9 pp 70ndash77 2014
[36] X Gao L Dai S Han I Chih-Lin and R W Heath ldquoEnergy-efficient hybrid analog and digital precoding for MmWaveMIMO systems with large antenna arraysrdquo IEEE Journal onSelected Areas in Communications vol 34 no 4 pp 998ndash10092016
[37] X Gao L Dai Z Chen Z Wang and Z Zhang ldquoNear-optimal beam selection for beamspace mmwave massive mimosystemsrdquo IEEE Communications Letters vol 20 no 5 pp 1054ndash1057 2016
[38] Z Wang M Li Q Liu and A L Swindlehurst ldquoHybrid pre-coder and combiner design with low-resolution phase shiftersin mmWave MIMO systemsrdquo IEEE Journal of Selected Topics inSignal Processing vol 12 no 2 pp 256ndash269 2018
Wireless Communications and Mobile Computing 11
[39] Y Sun Z Ding and X Dai ldquoOn the performance of downlinkNOMA in multi-cell mmWave networksrdquo IEEE Communica-tions Letters vol 22 no 11 pp 2366ndash2369 2018
[40] NDeng andMHaenggi ldquoAfine-grained analysis ofmillimeter-wave device-to-device networksrdquo IEEE Transactions on Com-munications vol 65 no 11 pp 4940ndash4954 2017
[41] D Zhang Z Zhou C Xu Y Zhang J Rodriguez and T SatoldquoCapacity analysis of NOMA with mmWave massive MIMOsystemsrdquo IEEE Journal on Selected Areas in Communicationsvol 35 no 7 pp 1606ndash1618 2017
[42] S Singh M N Kulkarni A Ghosh and J G AndrewsldquoTractable model for rate in self-backhauled millimeter wavecellular networksrdquo IEEE Journal on Selected Areas in Commu-nications vol 33 no 10 pp 2191ndash2211 2015
[43] X Yan H Xiao C-X Wang and K An ldquoOn the ergodiccapacity of NOMA-based cognitive hybrid satellite terrestrialnetworksrdquo in Proceedings of the 2017 IEEECIC InternationalConference on Communications in China ICCC 2017 pp 1ndash5China October 2017
[44] Y Huang F Al-Qahtani C Zhong Q Wu J Wang and HAlnuweiri ldquoPerformance analysis ofmultiusermultiple antennarelaying networks with co-channel interference and feedbackdelayrdquo IEEE Transactions on Communications vol 62 no 1 pp59ndash73 2014
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 result User 1Numerical result User 1Analysis result User 2Numerical result User 2
01 015 02 025 03 035 04 045005Power ratio coefficient
10minus3
10minus2
10minus1
100
Out
age p
roba
bilit
y
Figure 4 Impact of power ratio coefficient on outage probability
Analysis result User 1Numerical result User 1Analysis result User 2Numerical result User 2
30 40 50 60 70 8020D2D Distance (m)
10minus2
10minus1
100
Out
age p
roba
bilit
y
Figure 5 Impact of D2D distance on outage probability
42 Ergodic Capacity In this section the total ergodiccapacity is considered in the MIMO-NOMA mmWave cel-lular network with D2D communications It can be seenthat the numerical results are consistent with the closed-form solution which is better than the traditional TDMAMeanwhile the transmission power and the number of basestation antennas have a greater impact and the power ratiocoefficient and the distance between D2D users have lesseffect
In Figure 6 the impact of the transmission power of basestation on the ergodic capacity is considered in the MIMO-NOMA mmWave cellular network with D2D communica-tions It is shown that the ergodic capacity is growing linearly
Analysis resultNumerical resultTDMA
10 15 20 255Transmission Power (dbm)
8
10
12
14
16
18
Syste
m C
apac
ityFigure 6 Impact of transmission power on ergodic capacity
with the increase of transmission power In addition theergodic capacity of the systemwe proposed is higher than thetraditional TDMA Hence in order to improve the ergodiccapacity of the system we can increase the base stationtransmission power as much as possible without affectingothers
As the number of the base station antennas is increasingit is indicated that the ergodic capacity can be improvedbetter than the traditional TDMA in Figure 7 Benefitingfrom the length of mmWave more and more antennas canbe equipped for the base station At the same time we needto balance the improvement in ergodic capacity brought bythe increasing of the number of antennas and the powerconsumption and hardware requirements of the increase inRF chains to determine the final number of antennas
In Figure 8 the ergodic capacity is affected by thechange of the power ratio coefficient of the NOMA usersin the MIMO-NOMA mmWave cellular network with D2Dcommunications It can be seen that the total ergodic capacitychanges slowly with the increase of power ratio
In Figure 9 since the interference from the D2D users isdecreasing the total ergodic capacity is improved with theincrease of the distance between theD2Dusers in theMIMO-NOMA mmWave cellular network It can also be seen thatthe ergodic capacity in the MIMO-NOMAmmWave cellularnetwork is always better than the traditional TDMA
5 Conclusion
In this paper the outage probability and the ergodic capacityof the NOMA in the MIMO-NOMA mmWave cellularnetwork with D2D communications are studied The closed-form solutions of the outage probability and the ergodiccapacity are obtained which are consistent with the numeri-cal results Meanwhile the performance of NOMA is shown
Wireless Communications and Mobile Computing 9
Analysis resultNumerical resultTDMA
4
6
8
10
12
14
16
Syste
m C
apac
ity
10 15 20 25 30 355Antenna Number
Figure 7 Impact of antenna number on ergodic capacity
Analysis resultNumerical resultTDMA
01 015 02 025 03 035 04 045005Power Ratio Coefficient
6
7
8
9
10
11
12
Syste
m C
apac
ity
Figure 8 Impact of power ratio coefficient on ergodic capacity
to be better than traditional TDMA in the MIMO mmWavecellular network with D2D communications Furthermorethe higher transmission power of base station and the largerantenna array can also improve system performance
Data Availability
No data were used to support this study
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Analysis resultNumerical resultTDMA
6
7
8
9
10
11
12
13
Syste
m C
apac
ity
30 40 50 60 70 8020D2D Distance (m)
Figure 9 Impact of D2D distance on ergodic capacity
Acknowledgments
This work was supported by Advance Research Projects of13th Five-Year Plan of Civil Aerospace Technology (B0105)and the National Natural Science Foundation of China(61771051)
References
[1] M Tehrani M Uysal and H Yanikomeroglu ldquoDevice-to-device communication in 5G cellular networks challengessolutions and future directionsrdquo IEEE Communications Mag-azine vol 52 no 5 pp 86ndash92 2014
[2] S-Y Lien C-C Chien G S-T Liu H-L Tsai R Li and YJ Wang ldquoEnhanced LTE device-to-device proximity servicesrdquoIEEE Communications Magazine vol 54 no 12 pp 174ndash1822016
[3] L Lei ZD ZhongC Lin andXM Shen ldquoOperator controlleddevice-to-device communications in LTE-advanced networksrdquoIEEEWireless Communications Magazine vol 19 no 3 pp 96ndash104 2012
[4] A Asadi and V Mancuso ldquoNetwork-assisted outband D2D-clustering in 5G cellular networks theory and practicerdquo IEEETransactions onMobile Computing vol 16 no 8 pp 2246ndash22592017
[5] J HuW Heng Y Zhu GWang X Li and JWu ldquoOverlappingcoalition formation games for joint interference managementand resource allocation in D2D communicationsrdquo IEEE Accessvol 6 pp 6341ndash6349 2018
[6] H Min J Lee S Park and D Hong ldquoCapacity enhancementusing an interference limited area for device-to-device uplinkunderlaying cellular networksrdquo IEEE Transactions on WirelessCommunications vol 10 no 12 pp 3995ndash4000 2011
[7] Z Uykan and R Jantti ldquoTransmission-order optimization forbidirectional device-to-device (D2D) communications under-laying cellular TDD networksmdasha graph theoretic approachrdquoIEEE Journal on Selected Areas in Communications vol 34 no1 pp 1ndash14 2016
10 Wireless Communications and Mobile Computing
[8] L L Wei R Q Hu T He and Y Qian ldquoDevice-to-device(d2d)communications underlaying MU-MIMO cellular networksrdquoin Proceedings of the IEEE Global Communications Conference(GLOBECOM rsquo13) pp 4902ndash4907 IEEE Atlanta Ga USADecember 2013
[9] X Li W Zhang H Zhang andW Li ldquoA combining call admis-sion control and power control scheme for D2D communica-tions underlaying cellular networksrdquo China Communicationsvol 13 no 10 pp 137ndash145 2016
[10] H Sun Y Xu and R Q Hu ldquoA NOMA and MU-MIMOsupported cellular network with underlaid D2D communica-tionsrdquo in Proceedings of the 2016 IEEE 83rd Vehicular TechnologyConference (VTC Spring) pp 1ndash5 Nanjing China May 2016
[11] Z Ding X Lei G K Karagiannidis R Schober J Yuan andV K Bhargava ldquoA survey on non-orthogonal multiple accessfor 5G networks research challenges and future trendsrdquo IEEEJournal on Selected Areas in Communications vol 35 no 10 pp2181ndash2195 2017
[12] N Ye X Li H Yu AWangW Liu andXHou ldquoDeep learningaided grant-free noma towards reliable low-latency access intactile internet of thingsrdquo IEEE Transactions on IndustrialInformatics vol 15 no 5 pp 2995ndash3005 2019
[13] J An K Yang J Wu N Ye S Guo and Z Liao ldquoAchievingsustainable ultra-dense heterogeneous networks for 5Grdquo IEEECommunications Magazine vol 55 no 12 pp 84ndash90 2017
[14] N Ye AWang X Li H Yu A Li andH Jiang ldquoA randomnon-orthogonal multiple access scheme for mmtcrdquo in Proceedingsof the 2017 IEEE 85th Vehicular Technology Conference (VTCSpring) pp 1ndash6 June 2017
[15] K Yang N Yang N Ye M Jia Z Gao and R Fan ldquoNon-orthogonal multiple access achieving sustainable future radioaccessrdquo IEEE Communications Magazine vol 57 no 2 pp 116ndash121 2019
[16] S M R Islam N Avazov O A Dobre and K-S KwakldquoPower-domain non-orthogonal multiple access (NOMA) in5G systems potentials and challengesrdquo IEEE CommunicationsSurveys amp Tutorials vol 19 no 2 pp 721ndash742 2017
[17] N Ye AWang X Li W Liu X Hou and H Yu ldquoOn constella-tion rotation of noma with sic receiverrdquo IEEE CommunicationsLetters vol 22 no 3 pp 514ndash517 2018
[18] MHojeij C A Nour J Farah and C Douillard ldquoJoint resourceand power allocation technique for downlink power-domainnon-orthogonalmultiple accessrdquo inProceedings of the 2018 IEEEConference on Antenna Measurements amp Applications (CAMA)pp 1ndash4 September 2018
[19] F A Rabee K Davaslioglu and R Gitlin ldquoThe optimumreceived power levels of uplink non-orthogonal multiple access(NOMA) signalsrdquo in Proceedings of the 18th IEEE Wireless andMicrowave Technology Conference WAMICON 2017 pp 1ndash4USA April 2017
[20] Y Li andG A A Baduge ldquoNoma-aided cell-freemassivemimosystemsrdquo IEEEWireless Communications Letters vol 7 pp 950ndash953 2018
[21] N Ye A Wang X Li et al ldquoRate-adaptive multiple access foruplink grant-free transmissionrdquo Wireless Communications andMobile Computing vol 2018 Article ID 8978207 21 pages 2018
[22] N Ye H Han L Zhao and A-H Wang ldquoUplink nonorthogo-nal multiple access technologies toward 5G a surveyrdquo WirelessCommunications and Mobile Computing vol 2018 Article ID6187580 26 pages 2018
[23] Y LiuW-J Lu S Shi et al ldquoPerformance analysis of a downlinkcooperative noma network over nakagami-m fading channelsrdquoIEEE Access vol 6 pp 53034ndash53043 2018
[24] X Wang J Wang L He and J Song ldquoOutage analysis fordownlink noma with statistical channel state informationrdquoIEEEWireless Communications Letters vol 7 no 2 pp 142ndash1452018
[25] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAnoverview ofMIMOcommunicationsmdasha key to gigabit wirelessrdquoProceedings of the IEEE vol 92 no 2 pp 198ndash217 2004
[26] W Cai C Chen L Bai Y Jin and J Choi ldquoUser selectionand power allocation schemes for downlink NOMA systemswith imperfect CSIrdquo in Proceedings of the 2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp 1ndash5 MontrealQC Canada September 2016
[27] Z Ding and H V Poor ldquoDesign of massive-MIMO-NOMAwith limited feedbackrdquo IEEE Signal Processing Letters vol 23no 5 pp 629ndash633 2016
[28] Z Ding F Adachi andHV Poor ldquoThe application ofMIMO tonon-orthogonal multiple accessrdquo IEEE Transactions onWirelessCommunications vol 15 no 1 pp 537ndash552 2016
[29] Q Sun SHan I Chin-Lin andZ Pan ldquoOn the ergodic capacityof MIMO NOMA systemsrdquo IEEE Wireless CommunicationsLetters vol 4 no 4 pp 405ndash408 2015
[30] J Ding J Cai and C Yi ldquoAn improved coalition game approachfor MIMO-NOMA clustering integrating beamforming andpower allocationrdquo IEEE Transactions on Vehicular Technologyvol 68 no 2 pp 1672ndash1687 2019
[31] J-B Kim I-H Lee and J Lee ldquoCapacity scaling for D2D aidedcooperative relaying systems using NOMArdquo IEEE WirelessCommunications Letters vol 7 no 1 pp 42ndash45 2018
[32] S Papaioannou G Kalfas C Vagionas et al ldquo5G mm WaveNetworks Leveraging Enhanced Fiber-Wireless Convergencefor High-Density Environments The 5G-PHOS Approachrdquoin Proceedings of the 2018 IEEE International Symposium onBroadband Multimedia Systems and Broadcasting (BMSB) pp1ndash5 Valencia Spain June 2018
[33] SANaqvi and SAHassan ldquoCombiningNOMAandmmWavetechnology for cellular communicationrdquo in Proceedings of the2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp1ndash5 Montreal QC Canada September 2016
[34] F Rusek D Persson B K Lau et al ldquoScaling up MIMOopportunities and challenges with very large arraysrdquo IEEESignal Processing Magazine vol 30 no 1 pp 40ndash60 2013
[35] T Bai A Alkhateeb and R W Heath ldquoCoverage and capacityof millimeter-wave cellular networksrdquo IEEE CommunicationsMagazine vol 52 no 9 pp 70ndash77 2014
[36] X Gao L Dai S Han I Chih-Lin and R W Heath ldquoEnergy-efficient hybrid analog and digital precoding for MmWaveMIMO systems with large antenna arraysrdquo IEEE Journal onSelected Areas in Communications vol 34 no 4 pp 998ndash10092016
[37] X Gao L Dai Z Chen Z Wang and Z Zhang ldquoNear-optimal beam selection for beamspace mmwave massive mimosystemsrdquo IEEE Communications Letters vol 20 no 5 pp 1054ndash1057 2016
[38] Z Wang M Li Q Liu and A L Swindlehurst ldquoHybrid pre-coder and combiner design with low-resolution phase shiftersin mmWave MIMO systemsrdquo IEEE Journal of Selected Topics inSignal Processing vol 12 no 2 pp 256ndash269 2018
Wireless Communications and Mobile Computing 11
[39] Y Sun Z Ding and X Dai ldquoOn the performance of downlinkNOMA in multi-cell mmWave networksrdquo IEEE Communica-tions Letters vol 22 no 11 pp 2366ndash2369 2018
[40] NDeng andMHaenggi ldquoAfine-grained analysis ofmillimeter-wave device-to-device networksrdquo IEEE Transactions on Com-munications vol 65 no 11 pp 4940ndash4954 2017
[41] D Zhang Z Zhou C Xu Y Zhang J Rodriguez and T SatoldquoCapacity analysis of NOMA with mmWave massive MIMOsystemsrdquo IEEE Journal on Selected Areas in Communicationsvol 35 no 7 pp 1606ndash1618 2017
[42] S Singh M N Kulkarni A Ghosh and J G AndrewsldquoTractable model for rate in self-backhauled millimeter wavecellular networksrdquo IEEE Journal on Selected Areas in Commu-nications vol 33 no 10 pp 2191ndash2211 2015
[43] X Yan H Xiao C-X Wang and K An ldquoOn the ergodiccapacity of NOMA-based cognitive hybrid satellite terrestrialnetworksrdquo in Proceedings of the 2017 IEEECIC InternationalConference on Communications in China ICCC 2017 pp 1ndash5China October 2017
[44] Y Huang F Al-Qahtani C Zhong Q Wu J Wang and HAlnuweiri ldquoPerformance analysis ofmultiusermultiple antennarelaying networks with co-channel interference and feedbackdelayrdquo IEEE Transactions on Communications vol 62 no 1 pp59ndash73 2014
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 resultNumerical resultTDMA
4
6
8
10
12
14
16
Syste
m C
apac
ity
10 15 20 25 30 355Antenna Number
Figure 7 Impact of antenna number on ergodic capacity
Analysis resultNumerical resultTDMA
01 015 02 025 03 035 04 045005Power Ratio Coefficient
6
7
8
9
10
11
12
Syste
m C
apac
ity
Figure 8 Impact of power ratio coefficient on ergodic capacity
to be better than traditional TDMA in the MIMO mmWavecellular network with D2D communications Furthermorethe higher transmission power of base station and the largerantenna array can also improve system performance
Data Availability
No data were used to support this study
Conflicts of Interest
The authors declare that there are no conflicts of interestregarding the publication of this paper
Analysis resultNumerical resultTDMA
6
7
8
9
10
11
12
13
Syste
m C
apac
ity
30 40 50 60 70 8020D2D Distance (m)
Figure 9 Impact of D2D distance on ergodic capacity
Acknowledgments
This work was supported by Advance Research Projects of13th Five-Year Plan of Civil Aerospace Technology (B0105)and the National Natural Science Foundation of China(61771051)
References
[1] M Tehrani M Uysal and H Yanikomeroglu ldquoDevice-to-device communication in 5G cellular networks challengessolutions and future directionsrdquo IEEE Communications Mag-azine vol 52 no 5 pp 86ndash92 2014
[2] S-Y Lien C-C Chien G S-T Liu H-L Tsai R Li and YJ Wang ldquoEnhanced LTE device-to-device proximity servicesrdquoIEEE Communications Magazine vol 54 no 12 pp 174ndash1822016
[3] L Lei ZD ZhongC Lin andXM Shen ldquoOperator controlleddevice-to-device communications in LTE-advanced networksrdquoIEEEWireless Communications Magazine vol 19 no 3 pp 96ndash104 2012
[4] A Asadi and V Mancuso ldquoNetwork-assisted outband D2D-clustering in 5G cellular networks theory and practicerdquo IEEETransactions onMobile Computing vol 16 no 8 pp 2246ndash22592017
[5] J HuW Heng Y Zhu GWang X Li and JWu ldquoOverlappingcoalition formation games for joint interference managementand resource allocation in D2D communicationsrdquo IEEE Accessvol 6 pp 6341ndash6349 2018
[6] H Min J Lee S Park and D Hong ldquoCapacity enhancementusing an interference limited area for device-to-device uplinkunderlaying cellular networksrdquo IEEE Transactions on WirelessCommunications vol 10 no 12 pp 3995ndash4000 2011
[7] Z Uykan and R Jantti ldquoTransmission-order optimization forbidirectional device-to-device (D2D) communications under-laying cellular TDD networksmdasha graph theoretic approachrdquoIEEE Journal on Selected Areas in Communications vol 34 no1 pp 1ndash14 2016
10 Wireless Communications and Mobile Computing
[8] L L Wei R Q Hu T He and Y Qian ldquoDevice-to-device(d2d)communications underlaying MU-MIMO cellular networksrdquoin Proceedings of the IEEE Global Communications Conference(GLOBECOM rsquo13) pp 4902ndash4907 IEEE Atlanta Ga USADecember 2013
[9] X Li W Zhang H Zhang andW Li ldquoA combining call admis-sion control and power control scheme for D2D communica-tions underlaying cellular networksrdquo China Communicationsvol 13 no 10 pp 137ndash145 2016
[10] H Sun Y Xu and R Q Hu ldquoA NOMA and MU-MIMOsupported cellular network with underlaid D2D communica-tionsrdquo in Proceedings of the 2016 IEEE 83rd Vehicular TechnologyConference (VTC Spring) pp 1ndash5 Nanjing China May 2016
[11] Z Ding X Lei G K Karagiannidis R Schober J Yuan andV K Bhargava ldquoA survey on non-orthogonal multiple accessfor 5G networks research challenges and future trendsrdquo IEEEJournal on Selected Areas in Communications vol 35 no 10 pp2181ndash2195 2017
[12] N Ye X Li H Yu AWangW Liu andXHou ldquoDeep learningaided grant-free noma towards reliable low-latency access intactile internet of thingsrdquo IEEE Transactions on IndustrialInformatics vol 15 no 5 pp 2995ndash3005 2019
[13] J An K Yang J Wu N Ye S Guo and Z Liao ldquoAchievingsustainable ultra-dense heterogeneous networks for 5Grdquo IEEECommunications Magazine vol 55 no 12 pp 84ndash90 2017
[14] N Ye AWang X Li H Yu A Li andH Jiang ldquoA randomnon-orthogonal multiple access scheme for mmtcrdquo in Proceedingsof the 2017 IEEE 85th Vehicular Technology Conference (VTCSpring) pp 1ndash6 June 2017
[15] K Yang N Yang N Ye M Jia Z Gao and R Fan ldquoNon-orthogonal multiple access achieving sustainable future radioaccessrdquo IEEE Communications Magazine vol 57 no 2 pp 116ndash121 2019
[16] S M R Islam N Avazov O A Dobre and K-S KwakldquoPower-domain non-orthogonal multiple access (NOMA) in5G systems potentials and challengesrdquo IEEE CommunicationsSurveys amp Tutorials vol 19 no 2 pp 721ndash742 2017
[17] N Ye AWang X Li W Liu X Hou and H Yu ldquoOn constella-tion rotation of noma with sic receiverrdquo IEEE CommunicationsLetters vol 22 no 3 pp 514ndash517 2018
[18] MHojeij C A Nour J Farah and C Douillard ldquoJoint resourceand power allocation technique for downlink power-domainnon-orthogonalmultiple accessrdquo inProceedings of the 2018 IEEEConference on Antenna Measurements amp Applications (CAMA)pp 1ndash4 September 2018
[19] F A Rabee K Davaslioglu and R Gitlin ldquoThe optimumreceived power levels of uplink non-orthogonal multiple access(NOMA) signalsrdquo in Proceedings of the 18th IEEE Wireless andMicrowave Technology Conference WAMICON 2017 pp 1ndash4USA April 2017
[20] Y Li andG A A Baduge ldquoNoma-aided cell-freemassivemimosystemsrdquo IEEEWireless Communications Letters vol 7 pp 950ndash953 2018
[21] N Ye A Wang X Li et al ldquoRate-adaptive multiple access foruplink grant-free transmissionrdquo Wireless Communications andMobile Computing vol 2018 Article ID 8978207 21 pages 2018
[22] N Ye H Han L Zhao and A-H Wang ldquoUplink nonorthogo-nal multiple access technologies toward 5G a surveyrdquo WirelessCommunications and Mobile Computing vol 2018 Article ID6187580 26 pages 2018
[23] Y LiuW-J Lu S Shi et al ldquoPerformance analysis of a downlinkcooperative noma network over nakagami-m fading channelsrdquoIEEE Access vol 6 pp 53034ndash53043 2018
[24] X Wang J Wang L He and J Song ldquoOutage analysis fordownlink noma with statistical channel state informationrdquoIEEEWireless Communications Letters vol 7 no 2 pp 142ndash1452018
[25] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAnoverview ofMIMOcommunicationsmdasha key to gigabit wirelessrdquoProceedings of the IEEE vol 92 no 2 pp 198ndash217 2004
[26] W Cai C Chen L Bai Y Jin and J Choi ldquoUser selectionand power allocation schemes for downlink NOMA systemswith imperfect CSIrdquo in Proceedings of the 2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp 1ndash5 MontrealQC Canada September 2016
[27] Z Ding and H V Poor ldquoDesign of massive-MIMO-NOMAwith limited feedbackrdquo IEEE Signal Processing Letters vol 23no 5 pp 629ndash633 2016
[28] Z Ding F Adachi andHV Poor ldquoThe application ofMIMO tonon-orthogonal multiple accessrdquo IEEE Transactions onWirelessCommunications vol 15 no 1 pp 537ndash552 2016
[29] Q Sun SHan I Chin-Lin andZ Pan ldquoOn the ergodic capacityof MIMO NOMA systemsrdquo IEEE Wireless CommunicationsLetters vol 4 no 4 pp 405ndash408 2015
[30] J Ding J Cai and C Yi ldquoAn improved coalition game approachfor MIMO-NOMA clustering integrating beamforming andpower allocationrdquo IEEE Transactions on Vehicular Technologyvol 68 no 2 pp 1672ndash1687 2019
[31] J-B Kim I-H Lee and J Lee ldquoCapacity scaling for D2D aidedcooperative relaying systems using NOMArdquo IEEE WirelessCommunications Letters vol 7 no 1 pp 42ndash45 2018
[32] S Papaioannou G Kalfas C Vagionas et al ldquo5G mm WaveNetworks Leveraging Enhanced Fiber-Wireless Convergencefor High-Density Environments The 5G-PHOS Approachrdquoin Proceedings of the 2018 IEEE International Symposium onBroadband Multimedia Systems and Broadcasting (BMSB) pp1ndash5 Valencia Spain June 2018
[33] SANaqvi and SAHassan ldquoCombiningNOMAandmmWavetechnology for cellular communicationrdquo in Proceedings of the2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp1ndash5 Montreal QC Canada September 2016
[34] F Rusek D Persson B K Lau et al ldquoScaling up MIMOopportunities and challenges with very large arraysrdquo IEEESignal Processing Magazine vol 30 no 1 pp 40ndash60 2013
[35] T Bai A Alkhateeb and R W Heath ldquoCoverage and capacityof millimeter-wave cellular networksrdquo IEEE CommunicationsMagazine vol 52 no 9 pp 70ndash77 2014
[36] X Gao L Dai S Han I Chih-Lin and R W Heath ldquoEnergy-efficient hybrid analog and digital precoding for MmWaveMIMO systems with large antenna arraysrdquo IEEE Journal onSelected Areas in Communications vol 34 no 4 pp 998ndash10092016
[37] X Gao L Dai Z Chen Z Wang and Z Zhang ldquoNear-optimal beam selection for beamspace mmwave massive mimosystemsrdquo IEEE Communications Letters vol 20 no 5 pp 1054ndash1057 2016
[38] Z Wang M Li Q Liu and A L Swindlehurst ldquoHybrid pre-coder and combiner design with low-resolution phase shiftersin mmWave MIMO systemsrdquo IEEE Journal of Selected Topics inSignal Processing vol 12 no 2 pp 256ndash269 2018
Wireless Communications and Mobile Computing 11
[39] Y Sun Z Ding and X Dai ldquoOn the performance of downlinkNOMA in multi-cell mmWave networksrdquo IEEE Communica-tions Letters vol 22 no 11 pp 2366ndash2369 2018
[40] NDeng andMHaenggi ldquoAfine-grained analysis ofmillimeter-wave device-to-device networksrdquo IEEE Transactions on Com-munications vol 65 no 11 pp 4940ndash4954 2017
[41] D Zhang Z Zhou C Xu Y Zhang J Rodriguez and T SatoldquoCapacity analysis of NOMA with mmWave massive MIMOsystemsrdquo IEEE Journal on Selected Areas in Communicationsvol 35 no 7 pp 1606ndash1618 2017
[42] S Singh M N Kulkarni A Ghosh and J G AndrewsldquoTractable model for rate in self-backhauled millimeter wavecellular networksrdquo IEEE Journal on Selected Areas in Commu-nications vol 33 no 10 pp 2191ndash2211 2015
[43] X Yan H Xiao C-X Wang and K An ldquoOn the ergodiccapacity of NOMA-based cognitive hybrid satellite terrestrialnetworksrdquo in Proceedings of the 2017 IEEECIC InternationalConference on Communications in China ICCC 2017 pp 1ndash5China October 2017
[44] Y Huang F Al-Qahtani C Zhong Q Wu J Wang and HAlnuweiri ldquoPerformance analysis ofmultiusermultiple antennarelaying networks with co-channel interference and feedbackdelayrdquo IEEE Transactions on Communications vol 62 no 1 pp59ndash73 2014
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
[8] L L Wei R Q Hu T He and Y Qian ldquoDevice-to-device(d2d)communications underlaying MU-MIMO cellular networksrdquoin Proceedings of the IEEE Global Communications Conference(GLOBECOM rsquo13) pp 4902ndash4907 IEEE Atlanta Ga USADecember 2013
[9] X Li W Zhang H Zhang andW Li ldquoA combining call admis-sion control and power control scheme for D2D communica-tions underlaying cellular networksrdquo China Communicationsvol 13 no 10 pp 137ndash145 2016
[10] H Sun Y Xu and R Q Hu ldquoA NOMA and MU-MIMOsupported cellular network with underlaid D2D communica-tionsrdquo in Proceedings of the 2016 IEEE 83rd Vehicular TechnologyConference (VTC Spring) pp 1ndash5 Nanjing China May 2016
[11] Z Ding X Lei G K Karagiannidis R Schober J Yuan andV K Bhargava ldquoA survey on non-orthogonal multiple accessfor 5G networks research challenges and future trendsrdquo IEEEJournal on Selected Areas in Communications vol 35 no 10 pp2181ndash2195 2017
[12] N Ye X Li H Yu AWangW Liu andXHou ldquoDeep learningaided grant-free noma towards reliable low-latency access intactile internet of thingsrdquo IEEE Transactions on IndustrialInformatics vol 15 no 5 pp 2995ndash3005 2019
[13] J An K Yang J Wu N Ye S Guo and Z Liao ldquoAchievingsustainable ultra-dense heterogeneous networks for 5Grdquo IEEECommunications Magazine vol 55 no 12 pp 84ndash90 2017
[14] N Ye AWang X Li H Yu A Li andH Jiang ldquoA randomnon-orthogonal multiple access scheme for mmtcrdquo in Proceedingsof the 2017 IEEE 85th Vehicular Technology Conference (VTCSpring) pp 1ndash6 June 2017
[15] K Yang N Yang N Ye M Jia Z Gao and R Fan ldquoNon-orthogonal multiple access achieving sustainable future radioaccessrdquo IEEE Communications Magazine vol 57 no 2 pp 116ndash121 2019
[16] S M R Islam N Avazov O A Dobre and K-S KwakldquoPower-domain non-orthogonal multiple access (NOMA) in5G systems potentials and challengesrdquo IEEE CommunicationsSurveys amp Tutorials vol 19 no 2 pp 721ndash742 2017
[17] N Ye AWang X Li W Liu X Hou and H Yu ldquoOn constella-tion rotation of noma with sic receiverrdquo IEEE CommunicationsLetters vol 22 no 3 pp 514ndash517 2018
[18] MHojeij C A Nour J Farah and C Douillard ldquoJoint resourceand power allocation technique for downlink power-domainnon-orthogonalmultiple accessrdquo inProceedings of the 2018 IEEEConference on Antenna Measurements amp Applications (CAMA)pp 1ndash4 September 2018
[19] F A Rabee K Davaslioglu and R Gitlin ldquoThe optimumreceived power levels of uplink non-orthogonal multiple access(NOMA) signalsrdquo in Proceedings of the 18th IEEE Wireless andMicrowave Technology Conference WAMICON 2017 pp 1ndash4USA April 2017
[20] Y Li andG A A Baduge ldquoNoma-aided cell-freemassivemimosystemsrdquo IEEEWireless Communications Letters vol 7 pp 950ndash953 2018
[21] N Ye A Wang X Li et al ldquoRate-adaptive multiple access foruplink grant-free transmissionrdquo Wireless Communications andMobile Computing vol 2018 Article ID 8978207 21 pages 2018
[22] N Ye H Han L Zhao and A-H Wang ldquoUplink nonorthogo-nal multiple access technologies toward 5G a surveyrdquo WirelessCommunications and Mobile Computing vol 2018 Article ID6187580 26 pages 2018
[23] Y LiuW-J Lu S Shi et al ldquoPerformance analysis of a downlinkcooperative noma network over nakagami-m fading channelsrdquoIEEE Access vol 6 pp 53034ndash53043 2018
[24] X Wang J Wang L He and J Song ldquoOutage analysis fordownlink noma with statistical channel state informationrdquoIEEEWireless Communications Letters vol 7 no 2 pp 142ndash1452018
[25] A J Paulraj D A Gore R U Nabar and H Bolcskei ldquoAnoverview ofMIMOcommunicationsmdasha key to gigabit wirelessrdquoProceedings of the IEEE vol 92 no 2 pp 198ndash217 2004
[26] W Cai C Chen L Bai Y Jin and J Choi ldquoUser selectionand power allocation schemes for downlink NOMA systemswith imperfect CSIrdquo in Proceedings of the 2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp 1ndash5 MontrealQC Canada September 2016
[27] Z Ding and H V Poor ldquoDesign of massive-MIMO-NOMAwith limited feedbackrdquo IEEE Signal Processing Letters vol 23no 5 pp 629ndash633 2016
[28] Z Ding F Adachi andHV Poor ldquoThe application ofMIMO tonon-orthogonal multiple accessrdquo IEEE Transactions onWirelessCommunications vol 15 no 1 pp 537ndash552 2016
[29] Q Sun SHan I Chin-Lin andZ Pan ldquoOn the ergodic capacityof MIMO NOMA systemsrdquo IEEE Wireless CommunicationsLetters vol 4 no 4 pp 405ndash408 2015
[30] J Ding J Cai and C Yi ldquoAn improved coalition game approachfor MIMO-NOMA clustering integrating beamforming andpower allocationrdquo IEEE Transactions on Vehicular Technologyvol 68 no 2 pp 1672ndash1687 2019
[31] J-B Kim I-H Lee and J Lee ldquoCapacity scaling for D2D aidedcooperative relaying systems using NOMArdquo IEEE WirelessCommunications Letters vol 7 no 1 pp 42ndash45 2018
[32] S Papaioannou G Kalfas C Vagionas et al ldquo5G mm WaveNetworks Leveraging Enhanced Fiber-Wireless Convergencefor High-Density Environments The 5G-PHOS Approachrdquoin Proceedings of the 2018 IEEE International Symposium onBroadband Multimedia Systems and Broadcasting (BMSB) pp1ndash5 Valencia Spain June 2018
[33] SANaqvi and SAHassan ldquoCombiningNOMAandmmWavetechnology for cellular communicationrdquo in Proceedings of the2016 IEEE 84thVehicular Technology Conference (VTC-Fall) pp1ndash5 Montreal QC Canada September 2016
[34] F Rusek D Persson B K Lau et al ldquoScaling up MIMOopportunities and challenges with very large arraysrdquo IEEESignal Processing Magazine vol 30 no 1 pp 40ndash60 2013
[35] T Bai A Alkhateeb and R W Heath ldquoCoverage and capacityof millimeter-wave cellular networksrdquo IEEE CommunicationsMagazine vol 52 no 9 pp 70ndash77 2014
[36] X Gao L Dai S Han I Chih-Lin and R W Heath ldquoEnergy-efficient hybrid analog and digital precoding for MmWaveMIMO systems with large antenna arraysrdquo IEEE Journal onSelected Areas in Communications vol 34 no 4 pp 998ndash10092016
[37] X Gao L Dai Z Chen Z Wang and Z Zhang ldquoNear-optimal beam selection for beamspace mmwave massive mimosystemsrdquo IEEE Communications Letters vol 20 no 5 pp 1054ndash1057 2016
[38] Z Wang M Li Q Liu and A L Swindlehurst ldquoHybrid pre-coder and combiner design with low-resolution phase shiftersin mmWave MIMO systemsrdquo IEEE Journal of Selected Topics inSignal Processing vol 12 no 2 pp 256ndash269 2018
Wireless Communications and Mobile Computing 11
[39] Y Sun Z Ding and X Dai ldquoOn the performance of downlinkNOMA in multi-cell mmWave networksrdquo IEEE Communica-tions Letters vol 22 no 11 pp 2366ndash2369 2018
[40] NDeng andMHaenggi ldquoAfine-grained analysis ofmillimeter-wave device-to-device networksrdquo IEEE Transactions on Com-munications vol 65 no 11 pp 4940ndash4954 2017
[41] D Zhang Z Zhou C Xu Y Zhang J Rodriguez and T SatoldquoCapacity analysis of NOMA with mmWave massive MIMOsystemsrdquo IEEE Journal on Selected Areas in Communicationsvol 35 no 7 pp 1606ndash1618 2017
[42] S Singh M N Kulkarni A Ghosh and J G AndrewsldquoTractable model for rate in self-backhauled millimeter wavecellular networksrdquo IEEE Journal on Selected Areas in Commu-nications vol 33 no 10 pp 2191ndash2211 2015
[43] X Yan H Xiao C-X Wang and K An ldquoOn the ergodiccapacity of NOMA-based cognitive hybrid satellite terrestrialnetworksrdquo in Proceedings of the 2017 IEEECIC InternationalConference on Communications in China ICCC 2017 pp 1ndash5China October 2017
[44] Y Huang F Al-Qahtani C Zhong Q Wu J Wang and HAlnuweiri ldquoPerformance analysis ofmultiusermultiple antennarelaying networks with co-channel interference and feedbackdelayrdquo IEEE Transactions on Communications vol 62 no 1 pp59ndash73 2014
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
[39] Y Sun Z Ding and X Dai ldquoOn the performance of downlinkNOMA in multi-cell mmWave networksrdquo IEEE Communica-tions Letters vol 22 no 11 pp 2366ndash2369 2018
[40] NDeng andMHaenggi ldquoAfine-grained analysis ofmillimeter-wave device-to-device networksrdquo IEEE Transactions on Com-munications vol 65 no 11 pp 4940ndash4954 2017
[41] D Zhang Z Zhou C Xu Y Zhang J Rodriguez and T SatoldquoCapacity analysis of NOMA with mmWave massive MIMOsystemsrdquo IEEE Journal on Selected Areas in Communicationsvol 35 no 7 pp 1606ndash1618 2017
[42] S Singh M N Kulkarni A Ghosh and J G AndrewsldquoTractable model for rate in self-backhauled millimeter wavecellular networksrdquo IEEE Journal on Selected Areas in Commu-nications vol 33 no 10 pp 2191ndash2211 2015
[43] X Yan H Xiao C-X Wang and K An ldquoOn the ergodiccapacity of NOMA-based cognitive hybrid satellite terrestrialnetworksrdquo in Proceedings of the 2017 IEEECIC InternationalConference on Communications in China ICCC 2017 pp 1ndash5China October 2017
[44] Y Huang F Al-Qahtani C Zhong Q Wu J Wang and HAlnuweiri ldquoPerformance analysis ofmultiusermultiple antennarelaying networks with co-channel interference and feedbackdelayrdquo IEEE Transactions on Communications vol 62 no 1 pp59ndash73 2014
