Abstract— In this paper, we consider cognitive radio net-works in which energy constrained secondary users (SUs) canharvest energy from the randomly deployed power beacons.A new frame structure is proposed for the considered networks.In the considered network, a wireless power transfer model isproposed, and the closed-form expressions for the power outageprobability are derived. In addition, in order to reduce the energyconsumption at SUs, sub-Nyquist sampling are performed atSUs. Subsequently, compressive sensing and matrix completiontechniques are invoked to recover the original signals at thefusion center by utilizing the sparsity property of spectralsignals. Throughput optimizations of the secondary networksare formulated into two linear constrained problems, whichaim to maximize the throughput of a single SU and the wholecooperative network, respectively. Three methods are providedto obtain the maximal throughput of secondary networks byoptimizing the time slots allocation and the transmit power.Simulation results show that the maximum throughput can beimproved by implementing compressive spectrum sensing in theproposed frame structure design.
Index Terms— Compressive sensing, matrix completion,spectrum sensing, sub-Nyquist sampling, wireless power transfer.
I. INTRODUCTION
ENERGY efficiency and spectrum efficiency are two crit-ical issues in designing wireless networks. Recent devel-
opments in energy harvesting provides a promising techniqueto improve the energy efficiency in wireless networks. Dif-ferent from harvesting energy from traditional energy sources(e.g., solar, wind, water, and other physical phenomena) [1],the emerging wireless power transfer (WPT) further under-pins the trend of green communications by harvesting en-ergy from radio frequency (RF) signals [2]. Inspiring by thegreat convenience offering by WPT, several works have beenstudied to investigate the performance of different kinds ofenergy constraint networks [3]–[7]. Two practical receiverarchitectures, namely a time switching receiver and a power
Manuscript received May 7, 2016; revised August 18, 2016 andOctober 10, 2016; accepted October 24, 2016. Date of publication Novem-ber 2, 2016; date of current version April 14, 2017.This work was presentedat the IEEE GLOBECOM Conference, San Diego, CA, USA, 2015. Theassociate editor coordinating the review of this paper and approving it forpublication was Y. Li.
A. Nallanathan is with King’s College London, London WC2R 2LS, U.K.(e-mail: [email protected]).
Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TCOMM.2016.2623606
splitting receiver [8], were proposed in a multi-input and multi-output (MIMO) system in [3], which laid a foundation inthe recent research of WPT. In [4], a new hybrid networkarchitecture is designed to enable charging mobiles wirelesslyin cellular networks. In [5], three wireless power transferschemes were proposed for secure device-to-device (D2D)communication scenarios. For cooperative systems, new powerallocation strategies are proposed in a cooperative networkswhere multiple sources and destinations are communicated byan energy harvesting relay in [6]. For non-orthogonal multipleaccess (NOMA) networks, a new cooperative simultaneouslywireless information and power transfer NOMA protocol isproposed with considering the scenario where all users arerandomly deployed in [7].
Along with improving energy efficiency through energy har-vesting, wideband cognitive radio (CR) technique can improvethe spectrum efficiency and capacity of wireless networksthrough dynamic spectrum access [9]. More particularly, thesecondary users (SUs) in CR networks (CRNs) are normallyenergy constrained and powered by battery. Therefore, SUsare normally critical to energy consumption in order to in-crease the battery life of SUs. In order to design networkswith high spectrum efficiency and energy efficiency, it isnecessary for the SUs in CRNs to be equipped with theenergy harvesting capability. However, for the SUs poweredby energy harvested from wireless RF, high sampling rate isdifficult to be achieved in wideband CRNs. To overcome thisissue, compressive sensing (CS), which was initially proposedin [10], is introduced to wideband spectrum sensing in [11]to reduce the power consumption at SUs. As the spectrumof interest is normally underutilized in reality [12], [13],it exhibits a sparsity property in frequency domain, whichmakes sub-Nyquist sampling possible by implementing theCS technique at SUs [37]. In addition, when dealing withmatrices containing limited available entries, low-rank matrixcompletion (MC) [14] was proposed to recover the completematrix. As the sparsity property of received signals can betransformed into low-rank property of the matrix constructedin the cooperative networks, the authors in [15] proposed toapply joint sparsity recovery and low-rank MC to reduce therequirements on sensing and transmission without degradingthe sensing performance in CRNs. In order to improve robust-ness against channel noise, a denoised algorithm was proposedin [16] for compressive spectrum sensing at single SU andlow-rank MC based spectrum sensing at multiple SUs.
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A. Related Work
Some throughput optimization work has been recently de-veloped in wireless powered communication networks. The au-thors in [17] considered the throughput maximization problemfor both battery-free and battery-deployed cases by optimizingthe time slots for energy harvesting and data transmission.In addition, recent work [18]–[20] on the CRNs powered byenergy harvesting mainly focuses on the spatial throughputoptimization under various constraints. The authors in [18]considered CRNs with an energy-harvesting SU with infinitebattery capacity. The goal is to design an optimal spectrumsensing policy that maximizes the expected throughput subjectto an energy causality constraint and a collision constraint.In order to improve both energy efficiency and spectral effi-ciency, the authors in [19] considered a similar network modeland the stochastic optimization problem is formulated intoa constrained partially observable Markov decision process.At the beginning of each time slot, a SU needs to determinewhether to remain idle so as to conserve energy, or to executespectrum sensing to acquire knowledge of the current spectrumoccupancy state. The throughput is maximized by optimizingthe spectrum sensing policy and the detection threshold. Theauthors in [20] consider an energy constraint RF-poweredCRN by optimizing the pair of the sensing duration and thesensing threshold to maximize the average throughput of thesecondary network. More practically, the authors in [21] pro-posed to optimize the throughput of energy harvesting sensornetworks by further considering the constraint on hardwarememory. Furthermore, the implementation of the proposedscheme has been realized, which motives us to bring thewireless powered networks from theory to practice.
B. Motivations and Contributions
The aforementioned work has played a vital role and laidsolid foundation for developing new strategies for frame struc-ture design. However, in [17], spectrum sensing is not consid-ered in the frame structure design. In addition, in [18]–[20], theproposed frame structure designs mainly aim to maximize thethroughput by optimizing the threshold and time slots. Whenconsidering the energy efficiency and spectrum efficiency, itis meaningful to introduce sub-Nyquist sampling to reducethe energy consumption at SUs in wireless powered CRNs.Difficult from [22], in this paper, a new frame structure isproposed for the SUs in wireless powered CRNs with differentbehaviours (active and inactive which are to be introducedlater in Section II). With invoking CS and MC techniques,throughput is optimized at the level of an individual SU andthe whole cooperative network, respectively.
The summarized contributions of this paper are illustratedas follows:
• We propose a new frame structure for the wireless pow-ered CRNs, in which a new WPT model and the sub-Nyquist sampling are considered.
• In the WPT model, we adopt a bounded WPT schemewhere each SU selects a beacon (PB) nearby with thestrongest channel to harvest energy. The closed-formexpressions for the power outage probability is derived.
With the sub-Nqyust sampling performed at each SU, CSand low-rank MC techniques are utilized at the remote FCto recovery the original signals.
• Throughput optimisation of the proposed frame structuresare formulated into two linear constrained problems withthe purpose of maximising the throughput of a singleSU and the whole cooperative networks, respectively. Theformulated problems are solved by using three differentmethods to obtain the maximal achievable throughput,respectively.
• We show that the proposed frame structure design out-performs the traditional one in terms of throughput. It isnoted that the multiple SUs scenario can achieve betteroutage performance than the single SU scenario.
C. Organisations
The rest of this paper is organised as follows. Section IIdescribes the considered WPT model and spectrum sensingmodel based on the proposed frame structure. Section IIIpresents the throughput optimization for the single SU withapplying CS technique. Section IV provides the throughputoptimization at the cooperative network level with adoptingMC technique. Section V shows the numerical analyses ofthe considered network model with the purpose of optimizingthroughput of single SU and the whole cooperative network,respectively. Section VI concludes this paper.
II. NETWORK MODEL
A. Network Description
We consider a CRN, where SUs are energy constrained. Thewhole spectrum of interest can be divided into I channels.A channel is either occupied by a primary user (PU) orunoccupied. Meanwhile, there is no overlap between differentchannels. The number of occupied channels is assumed tobe K , where K ≤ I . Each SU performs sensing on the wholespectrum. It is assumed that all SUs keep quiet as forcedby protocols, e.g., at the media access control layer duringspectrum sensing period. Thus the received signals from activePUs with channel noise. As shown in Fig. 1, for each SU,it is assumed that the sensing and transmission can only bescheduled by utilising energy harvested from PBs. The spatialtopology of all PBs are modelled using homogeneous poissonpoint process (PPP) �p with density λp . Without loss ofgenerality, we consider that a typical SU is located at theorigin in a two-dimensional plane. Each SU is equipped witha single antenna and has a corresponding receiver with fixeddistance. Each PB is furnished with M antennas and maximalratio transmission (MRT) is employed at PBs to perform WPTto the energy constrained SU. Once the spectrum holes areidentified, each SU is assigned a spectrum hole by the FCto start data transmission. Here, we assume that there areenough number of spectrum holes to be allocated to SUs in aCSS network as the wideband spectrum sensing is performedat each SU. Additionally, it is assumed that the time ofeach frame is T . The proposed framework structure for theconsidered network with J (J ≥ 1) SUs is shown in Fig. 1.The J spatially distributed SUs can be divided into two sets:active SUs and inactive SUs. Active SUs refer to SUs that
1466 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 65, NO. 4, APRIL 2017
Fig. 1. Proposed frame structure design with energy harvesting, spectrum sensing and data transmission.
can complete the spectrum sensing task with harvested energy.Inactive SUs refer to SUs without enough energy to conductspectrum sensing. The frame structures for active SUs andinactive SUs are as follows:
1) Active SUs: As outlined by the blue oval in Fig. 1,the frame period for an active SU includes four timeslots: 1) energy harvesting time slot, in which each SUharvests the energy from PBs during the α1T period,with α1 being the fraction of energy harvesting in oneframe period; 2) spectrum sensing time slot, in whicheach SU performs sub-Nyquist sampling by applying CStechniques. The compressed measurements are then sentto a remote powerful FC during the βT period by usingthe harvested energy during the α1T period; 3) energyharvesting time slot for data transmission, in whicheach SU harvests the energy from PBs during the α2Tperiod, with α2 being the fraction of energy harvestingin one frame period. During this time slot, the originalsignals are recovered and the spectrum occupancies aredetermined by adopting energy detection at the FC. Sub-sequently, the obtained sensing decisions are sent backto corresponding SUs; and 4) data transmission slot, inwhich each SU performs data transmission during the(1 − α1 − β − α2) T period. By moving the burden ofspectrum recovery and decision making from energy-constrained SUs to a powerful FC, energy consumptionat the SU can be reduced significantly. Additionally,SUs have a higher opportunity to performing energyharvesting;
2) Inactive SUs: Before performing spectrum sensing, eachparticipating SU compares energy harvested during thefirst time slot EH1 with ES , where ES is the energy con-sumption for spectrum sensing at the second time slot.
If EH1 is greater than ES , the SU is determined asactive and would continue performing spectrum sensing.If EH1 is less than ES , the SU would switch to energyharvesting model again and wait for the decision onspectrum occupancies from the FC before starting datatransmission. Therefore, as outlined by the red oval inFig. 1, the frame structure of inactive SUs only includestwo time slots: (α1 + β + α2) T for energy harvestingand the rest for data transmission. In the case of CSS,only measurements from active SUs are collected atthe FC. The signals received by SUs exhibit a sparsityproperty that yields a matrix with low-rank propertyat the FC. Therefore, the full information of spectrumoccupancies can be obtained by adopting the low-rankMC technique. Once the complete matrix is recoveredat the FC, the final decisions on spectrum occupanciescan be determined. Subsequently, the FC sends back thebinary decision with the allocated spectrum hole to eachSU in the CSS network.
B. Wireless Power Transfer Model
Different from the previous research works [5], [23], weconsider a bounded power transfer model by assuming aminimum allowed distance d0 between the selected PB andpowered SU, which is used to avoid the singularity caused byproximity between PBs and SUs [24], [25]. If PBs are reallyclose to the SU, the harvested energy would mathematicallygo to infinity [4]. It is assumed that there is no batterystorage energy for future use. Therefore, all the harvestedenergy during energy harvesting time slots is used to performspectrum sensing and data transmission in the current frameperiod [4], [6], [26]. It is also assumed that all required energyof SUs are harvested from PBs. Additionally, all PBs are
QIN et al.: WIRELESS POWERED CR NETWORKS WITH COMPRESSIVE SENSING AND MATRIX COMPLETION 1467
assumed to operate in the same specific frequency band forsimplicity. The operation band of PBs is assumed to be isolatedfrom that of the spectrum sensing and data transmission.
In this work, we adopt a power transfer scheme where eachSU only selects one PB with the strongest channel1 The energyharvesting channels are assumed to be quasi-static Rayleighfading channels, where the channel coefficients are constantfor each transmission block but vary independently betweendifferent blocks. At each SU, the energy harvested from theselected PB in the first and the third time slots can be obtainedas follows:
EH1 = maxp∈�p,‖dp‖≥d0
{∥∥hp∥∥2
L(dp
)}ηPpγ T, (1)
where γ is the ratio of the time used for energy harvestingto the total time of a frame, η is the power conversionefficiency at the SU, Pp is the transmit power of PBs. Here,due to the WPT channels are modeled as Rayleigh fadingwith zero mean and unit variance, the entries of hp ∈ C M×1
are independent complex Gaussian distributed with zero meanand unit variance employed to capture the effects of small-scale fading between PBs and the SU, which is because of theMRT enabled power transmission from PB with M antennas.L(dp
) = Ad−ξp is the power-law path-loss exponent. The
path-loss function depends on the distance dp , a frequencydependent constant A, and an environment/terrain dependentpath-loss exponent ξ > 2.
For the active SUs, based on (1), the maximum harvestedpower PH1 which can be utilized for sensing at the SU is givenby
PH1 = EH1
βT= max
p∈�p,‖dp‖≥d0
{∥∥hp∥∥2
L(dp
)} ηPpα1
β, (2)
where EH1 refers to the energy harvested in the first time slot.As energy can only be stored in the current frame, the
total energy for data transmission is the sum of the remainingenergy in the second slot and the energy harvested in the thirdtime slot, which is given by
ET2 = (EH1 − ES
) + EH2, (3)
where ES = PsβT with Ps being the power consumption ofspectrum sensing.
Based on (1) and (3), the corresponding power for datatransmission is given by
PT2 =max
p∈�p,‖dp‖≥d0
{∥∥hp∥∥2
L(dp
)}ηPp (α1 + α2)− Psβ
1 − α1 − β − α2.
(4)
For the inactive SUs, the harvested energy can be given by
EH3 = maxp∈�p,‖dp‖≥d0
{∥∥hp∥∥2
L(dp
)}ηPp(α1 + β + α2)T .
(5)
1Note that the strongest PB is not necessarily to be the nearest one,because of the instantaneous effect of small-scale fading is also taken intoconsiderations. to harvest energy. The other PBs would turn to sleep mode tosave the energy waste. The motivation behind using this scheme is that it iscapable of achieving more energy efficient power transfer compared to otherpossible schemes (e.g., use all of PBs for power transfer).
Based on (5), the maximum transmit power at the inactiveSU can be expressed as
PH3 = EH3
(1 − α1 − β − α2) T. (6)
C. Spectrum Sensing Model With Sub-Nyquist Sampling
At the j th SU (SU j ) in the considered network, the receivedsignals can be expressed as:
rj = hj ∗ s + nj, (7)
where s ∈ C n×1 refers to the transmitted primary signals intime domain, and hj ∈ C n×1 is the channel gain betweenthe transmitter and receiver, and nj ∼ CN (0, σ 2In) refers toAdditive White Gaussian Noise (AWGN) with zero mean andvariance σ 2.
Based on the Nyquist sampling theory, the sampling rateis required to be no less than twice of the signal bandwidth.However, for wideband spectrum sensing, high sampling rateis difficult to achieve and also leads to high energy consump-tion which is challenging for energy-constrained SUs. It isnoticed that the transmitted signal s exhibits a sparsity prop-erty in frequency domain as a large percentage of spectrumis normally underutilized in practice. This sparsity propertyenables sub-Nyquist sampling at SUs without loss any signalinformation. The compressed measurements collected at SU j
can be given by
xj = �jrj = �jF −1j rfj = j
(hfjsf + nfj
), (8)
where �j ∈ C�×n (� < n) is the measurement matrix utilizedto collect the compressed measurements xj ∈ C�×1, and sf ,hfj and nfj refer to the frequency representations of transmitprimary signals, channel coefficients, and the AWGN receivedat SU j . Additionally, j = �jF j
−1, where F j−1 is inverse
discrete Fourier transform (IDFT) matrix. The compressionratio is defined as κ = �
n , (0 ≤ κ ≤ 1).After the compressed measurements are collected, SUs send
them to a remote FC to perform signal recovery by an error-free reporting channel. By adopting such a powerful FC,energy-constrained SUs can get rid of signal recovery processand continue harvesting more energy from PSs. At the FC, thecompressed measurements X can be expressed as
X = vec (Rf) = (vec (Hf Sf)+ Nf ) , (9)
where Rf = [rf1, rf2, . . . , rfJ
]which is in size of n × J ,
and vec (Rf ) =[r T
f 1, . . . , rTf J
]T ∈ C (n J)×1. Sf ∈ C n×J ,
Hf ∈ C n×n and Nf ∈ C n×J refer to the matrix constructedby transmit primary signals, channel coefficients and AWGNin frequency domain. In addition, the measurement matrix is adiagonal matrix = diag (1,2, . . . ,J) in size of × Nwith = � × J and N = n × J . After the compressedmeasurements are collected at the FC, signal recovery can beformulated as a convex optimization problem. The considerednetwork becomes a single node case when J = 1. Thenthe existing algorithm for CS can be utilized to recover theoriginal signals. In the cooperative networks (J > 1), existingalgorithms for low-rank MC can be implemented to complete
1468 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 65, NO. 4, APRIL 2017
the matrix. It has been proved that exact signal recovery canbe guaranteed if the number of available measurements areno less than a minimum bound. With enough number ofmeasurements, exact signals are obtained at the FC. Subse-quently, energy detection is adopted to determine spectrumoccupancies, in which the decisions are made by comparingthe energy of recovered signal with a threshold [27] defined as
λ =(σ 2
s + σ 2)(
1 + Q−1(P̄d
)√
n/2
). (10)
Once the sensing decisions are determined at the FC, theywould be sent back to the participating SUs in the CSSnetwork by the reporting channel to start the data transmissionperiod.
III. THROUGHPUT OPTIMIZATION OF
A SINGLE SECONDARY USER
In this section, the closed form expressions are derivedfor the power outage probability of spectrum sensing anddata transmission, respectively. With the CS technique imple-mented, performance analysis with the target of maximizingthroughput of each individual active SU locally is provided.
A. Power Outage Probability Analysis
We assume there exists a threshold transmit power, be-low which the spectrum sensing in the second slot or thedata transmission in the fourth slot cannot be scheduled.We introduce power outage probability, i.e., probability thatthe harvested energy is not sufficient to perform spectrumsensing or carry out the data transmission at a certain de-sired quality-of-service (QoS) level. In practical scenarios, weexpect a constant power for the data transmission. There-fore, we also denote the power threshold Ps as the sensingpower in the second slot and Pt as the transmit power ofthe SU, respectively. The following theorem provides theexact analysis for the power outage probability at the singleSU scenario.
Theorem 1: The power outage probability of spectrum sens-ing Pout
s in the second time slot and the power outageprobability of data transmission Pout
t in the fourth time slotcan be expressed in closed-form as follows:
Poutζ = exp
⎡⎣−πλpδ
μδζ
M−1∑m=0
�(
m + δ, μζ dξ0
)
m!
⎤⎦, (11)
where ζ ∈ (s, t), μs = βPsηPp Aα1
, μt = Pt (1−α1−β−α2)+PsβηPp A(α1+α2)
,δ = 2/ξ , and �(·, ·) is the upper incomplete Gamma function.Proof: See Appendix A.
Remark 1: The derived results in Theorem 1 indicates thatthe power outage probability is a strictly monotonic increasingfunction of λp.
B. Compressive Spectrum Sensing
In the scenario of CS based spectrum sensing, the originalsignal sf of each individual SU can be obtained respectivelyby solving the l1 norm optimization problem as follows:
min ‖sf‖1 s.t.∥∥j · hfjsf − xj
∥∥22 ≤ εj, (12)
where ε j is the error bound related to the noise level. This opti-mization problem can be solved by many existing algorithmsfor CS, such as by adopting many existing algorithms suchas CoSaMP [28], SpaRCS [29], etc. The computational com-plexity of solving the optimization problem in (12) is O
(n3
),
which is mainly determined by the size of signals (n) to berecovered. However, this process is proposed to be performedat a powerful FC rather than the energy-constrained SUs. Bydoing so, energy consumption at SUs can be significantlyreduced.
The performance metric of spectrum sensing can be mea-sured by the probability of detection Pd and probability offalse alarm Pf . For a target probability of detection, P̄d , withwhich the PUs are sufficiently protected, the threshold can bedetermined by (10) accordingly if the number of samples nis fixed. As a result, Pf for the spectrum sensing with singleSU can be derived as follows:
Pf = Q
(Q−1
(P̄d
)√ σ 2s +σ 2
σ 2 +√
n2σ 2
sσ 2
), (13)
where σ 2 and σ 2s refer to the noise power and signal power,
respectively.Assuming the energy cost per sample es in spectrum sensing
is fixed, the energy consumption of spectrum sensing isproportional to the number of collected samples as given by:
n = βT Ps
es. (14)
In fact, the number of collected samples n is determinedby the sensing time slot. In this case, the energy consumedby reporting collected measurements and receiving decisionresults between SUs to the FC is ignored. Substituting (14)into (13), we obtain
P f =(
1 − Q
(Q−1 (P̄d
) (1 + σ 2
s
σ 2
)+
√βT Ps
2es
σ 2s
σ 2
)). (15)
C. Throughput Analysis
By considering the power outage probability, the throughputof each individual SU in a CRN can be expressed as
τ = (1 − Pout
s
) × (1 − Pout
t
) × (1 − Pf
)
× (1 − α1 − β − α2) τt , (16)
where τt = log2
(1 + Pt
N0
)is the throughput for the data
transmission slot, and N0 refers to the AWGN level in the datatransmission channel. Here we simplify the data transmissionprocess by not considering the fading, which means thethroughput τt is only determined by the transmit signal-to-noise-radio (SNR).
When implementing CS technique to achieve sub-Nyquistsampling rate at an SU, it has been proven that the exactsignal recovery can be guaranteed if the number of collectedmeasurements satisfies � ≥ C · K log
(n/
K), where C is
some constant depending on each instance [30]. If the signalis recovered successfully by � samples, the achieved Pf
would be the same as that no CS technique is implementedwith n samples. Therefore, the necessary sensing time slot to
QIN et al.: WIRELESS POWERED CR NETWORKS WITH COMPRESSIVE SENSING AND MATRIX COMPLETION 1469
achieve the same P f can be reduced from βT to κβT withthe CS technique adopted, where κ is the compression ratioat SUs. Replacing Pout
s , Poutt and Pf in (16) by (11) and (15)
respectively, the full expression of the throughput withCS implemented can be expressed as follows:
τcs =∏
ζ={s,t}
⎛⎜⎝1−exp
⎛⎜⎝− πλpδ(
μcsζ
)δM−1∑m=0
�(
m + δ, μcsζ dξ0
)
m!
⎞⎟⎠
⎞⎟⎠
×(
1 − Q
(Q−1 (P̄d
) (1 + σ 2
s
σ 2
)+
√βT Ps
2es
σ 2s
σ 2
))
× (1 − α1 − κβ − α2)× log2
(1 + Pt
N0
). (17)
If there is no CS technique implemented at SUs, the timeslot fraction for spectrum sensing follows the condition that0 ≤ β ≤ 1. When the CS technique is implemented at SUs,the time slot for spectrum sensing follows the condition thatC K log
(n/
K) ≤ κβT Ps
es≤ n. By combining these two
conditions, the constraint for β becomes es (C K log(n/K ))κT Ps
≤β ≤ 1. With the implementation of CS, the β in (11) isreplaced by κβ.
Furthermore, the throughput can be maximized by solvingthe following problem:
(P0) : maxα1,β,α2,Pt
τcs
s.t. C1 : 0 ≤ α1 ≤ 1,
C2 : es(C K log
(n/
K))
κT Ps≤ β ≤ 1,
C3 : α2,min ≤ α2 ≤ 1,
C4 : 0 ≤ 1 − α1 − κβ − α2 ≤ 1,
C5 : Pt,min ≤ Pt ≤ Pt,max, (18)
where α2,min refers to the minimum time slot fraction for thethird time slot. Pt,min and Pt,max refer to the allowed minimumand maximum power levels for data transmission period.Constraint C1 bounds the time slot for energy harvesting forthe first time slot. Constraint C2 highlights the minimum timeslot for compressive spectrum sensing. The lower bound of βis used to make sure the compressed sample is sufficient toguarantee exact signal recovery. Constraint C3 ensures that thethird time slot is at least enough for signal recovery at the FCand data transmission between the SU and FC. Constraint C4guarantees that the last time slot of a frame period is utilizedfor data transmission. Finally, constraint C5 limits the transmitpower level for data transmission. It is noticed that (27) is aconstrained nonlinear optimization problem and the objectivefunction is very complex. However, the constraints are linear,which motives us to solve the optimization problem by thefollowing three methods:
1) Grid search: The grid search algorithm for solving (27)can be described in Algorithm 1. The grid search al-gorithm can find out the global optimal value if thestep size �i (i = 1, 2, 3, 4) for α1, β, α2, Pt are smallenough. However, the computational complexity wouldgreatly increase if the step is set to be small enough.
do3: while 0 ≤ 1 − α1 − κβ − α2 ≤ 1 do4: τtemp = [τtemp, τcs ] where τcs is expressed as (17).5: end while6: end for7: Return τmax = τtemp .
2) fmincon: fmincon is a toolbox in MATLAB which isefficient but it may return a local optimal value.
3) Random sampling: A set S = {v1, v2, · · · , vZ} thatsatisfies the conditions in (27) is generated randomly,where vi = (α1, β, α2, Pt ) (i ∈ {1, 2, · · · ,Z}) is a tupleof generated random samples, and Z is the number ofgenerated tuples. The accuracy of this method dependson number of tuples Z generated for calculation. Thismethod is efficient for solving (27) as it does not relyon advanced optimization techniques and the method ofgenerating (α1, β, α2, Pt ) is efficient.
IV. THROUGHPUT OPTIMIZATION OF
MULTIPLE SECONDARY USERS
In this section, the closed-form expressions for the poweroutage probability of data transmission are deprived for boththe active and inactive SUs, respectively. With the imple-mentation of MC technique, throughput of the CSS networkwith multiple SUs including the active and inactive ones isoptimized.
A. Power Outage Probability Analysis
In this subsection, we provide power outage probabilityanalysis for spectrum sensing and data transmission for bothactive and inactive SUs. In stochastic geometry networks, weusually focus on the average networks performance. As such,we first evaluate the average number of potential active users.
Corollary 1: Based on Theorem 1, we obtain the averagenumber of potential active users as follows:
J̄act = J
⎛⎝1 − exp
⎡⎣−πλpδ
μδs
M−1∑m=0
�(
m + δ, μsdξ0
)
m!
⎤⎦⎞⎠.
(19)
Proof: Note that the condition that a typical single usercan be active is that its harvested energy is capable of supportspectrum sensing. Otherwise, it has to keep silent during thesensing slot. As such, the probability to become an active useris equal to the non-outage probability for spectrum sensing.Following the similar procedure as [31], we can obtain theaverage number of active users as (19).
Remark 2: The derived result in Corollary 1 indicates thatthe average active number is a strictly monotonic increasingfunction of λp. As such, we can increase the value of J̄act byincreasing λp.
1470 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 65, NO. 4, APRIL 2017
1) Power Outage Probability of Spectrum Sensing: In theconsidered CSS networks, we assume that the number ofactive participating SUs is J1. In order to guarantee there areat least J1 number of active SUs to collect enough numbermeasurements for exact recovery, the constraint Jmin ≤ J1 ≤J̄act should be satisfied. Here, Jmin is defined as the minimalnumber of active SUs that can guarantee exact recovery.By considering the energy consumption for spectrum sens-ing and the minimal number of measurements required forexact recovery, the constraint on J1 can be rewritten asCμ2νK log6ν ≤ κβT Ps J1
es≤ n J̄act . As a result, the constraint
on J1 can be transformed into the constraint on β as follows:
C6 : es(Cμ2νklog6ν
)
ρT Ps J1≤ β ≤ 1, (20)
where Cμ2νklog6ν is the lower bound of the number ofobserved measurements at the FC to guarantee the exact matrixrecovery [32]. Here, ν = max (n, J ) and μ = O
(√log ν
).
With the constraint on β in (20), by considering the averagenetwork performance, the power outage probability of sensingcan be regarded as zero for simplicity. This behavior can beexplained as follows: 1) For active SUs, it is assumed that theharvested energy from the first time slot is enough for them totake measurements for spectrum sensing. Therefore, the poweroutage probability of spectrum sensing for active SUs are zero;and 2) For the inactive SUs, they will not perform spectrumsensing and only transmit data during the last time slot.
2) Power Outage Probability of Data Transmission: Forthose active SUs, the power outage probability of data trans-mission is same that of the single SU scenario in (11).For those inactive SUs, as all the time slots before datatransmission are used for energy harvesting, the power outageprobability is different from (11). The following theoremprovides exact analysis for the power outage probability ofdata transmission for both active and inactive SUs in CSSnetworks.
Theorem 2: The power outage probability of data transmis-sion at the active and inactive SUs in the fourth time slot canbe expressed in closed-form as follows:
Poutψ = exp
⎡⎣−πλpδ
μδψ
M−1∑m=0
�(
m + δ, μψdξ0
)
m!
⎤⎦ (21)
where ψ ∈ (a, i), μa = Pt (1−α1−β−α2)+PsβηPp A(α1+α2)
, and
μi = Pt (1−α1−β−α2)ηPp A(α1+β+α2)
. Proof: Based on (6), the power
outage probability of data transmission at the active SUs isthe same as Pout
t as given in (11) by replacing μa → μζ .Similarly, based on (6), the power outage probability of data
transmission at the inactive SUs can be expressed as follows:
Pouti = Pr
{PH3 < Pt
}
= Pr
{max
p∈�p,‖dp‖≥d0
{∥∥hp∥∥2
dp−ξ} < μi
}. (22)
Following the similar procedure as (A.5) and applyingμi → μs , we can obtain Pout
i in (21).The proof is completed.
B. Matrix Completion Based Cooperative Spectrum Sensing
As the spectrum is normally underutilized in practice, thetransmitted signals exhibit a sparsity property in frequencydomain, which can be transformed into a low-rank propertyof the matrix X at the FC. When only the J1 active SUssend compressed samples to the FC, the matrix with collectedmeasurements is incomplete at the FC. The exact matrix Sf canbe obtained by solving the following low-rank MC problem
where rank (·) is the rank function of a matrix whose value isequal to the number of nonzero singular values of the matrix,and ε refers to the noise level. However, the problem in (23)is NP-hard due to the combinational nature of the functionrank (·). It has been proved that the nuclear norm is the bestconvex approximation of the rank function over the unit ballof matrixes with norm no less than one [33]. Therefore, (23)can be replaced by the following convex formulation:
min ‖Sf‖∗ s.t. ‖vec (Hf Sf)− vec (X)‖22 ≤ ε. (24)
The problem in (24) can be solved by multiple existingMC solvers, such as singular value decomposition [34], nu-clear norm minimization [14], etc.
Once the exact matrix is recovered, energy detection canbe used to determine the spectrum occupancy. In the CSSnetworks, as all the participating SUs send the collectedsamples to the FC, the data fusion is considered. Supposethe channel coefficients from the PUs to each participatingSUs are known. When the channel coefficients are unknown,the weighting factor associated with the j th SU is set to beg j = 1√
J. By using the maximal ratio combining, probability
of false alarm of the CSS networks Q f becomes
Q f = Q
⎛⎝Q−1 (P̄d
)√
1 + σ 2s
Jσ 2 H +√
n
2J
σ 2s
σ 2 H
⎞⎠, (25)
where H =J∑
j=1
∣∣hj∣∣22 refers to the channel coefficients for all
the participating SUs in the considered CSS networks.
C. Throughput Analysis
By applying the MC technique at the FC, β in (21) shouldbe replaced by κβ. In addition, the throughput of consideredCSS networks with multiple SUs can be expressed as
τmc =J∏
j=1
(1 − Pout
ψ ( j))
× (1 − Q f
)
× (1 − α1 − κβ − α2) τt , (26)
where κ is defined as the compression ratio at active SUs.ψ = a refers to the J1 number of active SUs and ψ = irefers to the rest of inactive SUs in the considered networks.If no MC technique is implemented at the FC and each SU issupposed to take samples at Nyquist rate, all the participatingSUs will send samples to the FC. Then the throughput of theconsidered networks can be given by replacing Pout
ψ ( j) in (26)
QIN et al.: WIRELESS POWERED CR NETWORKS WITH COMPRESSIVE SENSING AND MATRIX COMPLETION 1471
with Pouta ( j) and κ = 1. The constraints for the multiple
nodes case are the same as that for the single node case exceptthe condition for β given in (20).
The throughput can be maximized by solving the followingproblem:
(P1) : maxα1,β,α2,Pt
τmc
s.t. C1 : 0 ≤ α1 ≤ 1,
C3 : α2,min ≤ α2 ≤ 1,
C4 : 0 ≤ 1 − α1 − κβ − α2 ≤ 1,
C5 : Pt,min ≤ Pt ≤ Pt,max,
C6 : es(Cμ2νklog6ν
)
ρT Ps J1≤ β ≤ 1. (27)
Constraints C1 and C4 bound the time slot allocated forenergy harvesting in first time slot and data transmission.Constraint C3 ensures that the third time slot is enough formatrix recovery at the FC and data transmission between theSU and FC. Constraint C5 limits the power level for datatransmission. Constraint C6 highlights the minimum time slotfor compressive spectrum sensing, in which the lower boundof β is used to make sure that the number of compressedsamples is sufficient to guarantee exact recovery at the FC.It is noticed that the structure of (P1) is similar as (P0). Thuswe can use the similar methods to obtain the near optimalthroughput for the CSS network.
V. NUMERICAL RESULTS
In the simulation, we set the frame period to be T = 1 s,the transmit power of PBs to be Pp = 43 dBm, the number ofantennas of PB to be M = 32, the carrier frequency for powertransfer to be 900 MHz, and the energy conversion efficiencyof WPT to be η = 0.8. In addition, it is assumed that thetarget probability of detection P̄d is 90%. In this paper, welet d0 ≥ 1 m to make sure the path loss of WPT is equal or
greater than one. In the following part, SNR = σ 2sσ 2 refers to the
SNR in sensing channels. Regarding the considered Rayleighfading model, the parameters are set as zero mean and unitvariance, which is corresponding to our theoretical analysis.
A. Numerical Results on OptimizingThroughput of Single User
In this subsection, simulation results of the optimizedthroughput of single SU are demonstrated after the derivedpower outage probability in (11) and Pf in (15) are verifiedby Monte Carlo simulations.
Fig. 2 plots the power outage probability of spectrumsensing versus density of PBs λp with different power thresh-old Ps . The black solid and dash curves are used to representthe analytical results with d0 = 1 m and d0 = 1.5 m,respectively, which are both obtained from (11). Monte Carlosimulations are marked as “•” to verify our derivation. Thefigure shows the precise agreement between the simulationand analytical curves. One can be observed is that as densityof PBs increases, the power outage probability dramaticallydecreases, which is also corresponding to the remark we obtainfrom Theorem 1. This is because the multiuser diversity gain
Fig. 2. Power outage probability of spectrum sensing versus density of PBswith M = 32, Pp = 43 dBm, α1 = 0.25, α2 = 0.2, and β = 0.25.
Fig. 3. Performance comparison between theoretic results for traditionalenergy detection and the compressive spectrum sensing under different SNRlevels in sensing channels and different compression ratio κ , P̄d = 90%, andsparsity level = 12.5%.
is improved with increasing number of PBs when chargingwith WPT. The figure also demonstrates that the outage occursmore frequently as the power threshold Ps and the radius ofd0 increase.
Fig. 3 plots the probability of false alarm Pf versus SNRin sensing channels with different compression ratios κ . It isobserved that P f decreases with higher SNR, which wouldimprove the throughput of secondary network. In this case,the sparsity level is set to 12.5%, which means 12.5% of thespectrum of interest is occupied by PUs. The black solid curveis used to represent the analytical result which is obtainedfrom (15) with enough protection to PUs being provided(P̄d = 90% is defined in the IEEE 802.22 standard aboutthe cognitive radio [35]). Monte Carlo simulations with com-pression ratio κ = 100% are marked as “◦” to verify ourderivation, which represents the scenario without CS techniqueimplemented. The figure shows precise agreement betweenthe simulation results with κ = 100% and analytical curves,which is a benchmark for the following comparison. When κ isreduced to 50%, it is noticed that Pf is still well matched with
1472 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 65, NO. 4, APRIL 2017
Fig. 4. Throughput of single SU τcs versus lower bound of the third timeslot α2,min, S N R = −10 dB, and κ = 100%.
the analytical result, which means the performance of spectrumsensing is not degraded when only 50% of the samples arecollected at the SU. When κ is further reduced to 25%,Pf is increased, which means the signal recovery is not exactany more. As a result, wrong decisions would be made forspectrum occupancies, which leads to a higher Pf . Throughputof the CSS network would be degraded correspondingly asthe chance to access vacant channels is reduced. Actually,the minimal compression ratio guaranteeing successful signalrecovery is dependent on the sparsity level of signals tobe recovered and the number of samples, when signals aresampled at or above Nyquist sampling rates. This is provedby Candes in [10] and out of the scope of this paper.
Fig. 4 plots the achieved throughput τcs versus the lowerbound of time allocated to the third slot α2. Here α2 is reservedfor signal recovery at the FC and data transmission betweenthe SU and the FC. In this figure, several observations aredrawn as follows: 1) The maximal throughput achieved by gridsearch method is slight higher than that of fmincon methodas fmincon relies on the initial input and may return a localoptimal value. However, the accuracy of grid search method isdependent on the step sizes; 2) The random sampling methodachieves lower throughput than grid search and fmincon meth-ods, which demonstrates the benefits of the presented gridsearch and fmincon methods. When the generated sets increasefor random sampling, the achieved throughput get closer to theoptimal but the computational complexity is much increase;3) It is seen that the optimal value of time assigned to the thirdslot α2 always equals to the lower bound α2,min. This gives asign that the throughput can be improved if the time slot for thesignal recovery at the FC and data transmission between SUsand the FC is reduced. In other words, the energy harvestingshould be done mainly in the first time slot α1 to reduce thepower outage probability in the following spectrum sensingslot if the signal recovery and data transmission between theSU and FC can be promised.
Fig. 5 presents the throughput comparison between theproposed frame structure and the traditional one that doesnot adopting compressive spectrum sensing and remote FCto perform signal recovery. Without implementing the FC,
Fig. 5. Throughput comparison between the proposed frame structureand the traditional one versus lower bound of the third time slot α2,min,S N R = −10 dB, and κ = 100%, 40% and 20%.
SUs have to perform signal recovery by themselves andcannot harvest energy again after sampling. Meanwhile, inorder to make decisions on spectrum occupancies, each SUhas to perform energy detection locally, which introducesmore energy consumption. Here, for SUs employing traditionalframe structure, the time slot consumed for decision makingis set to α2,min to simplify the comparison. The time slotrequired for conduct spectrum sensing at Nyquist rate is setto βT with β = 0.2. In Fig. 5, we can see that the achievedthroughput is improved with decreasing compression ratio κ .This benefits from that more time slot becomes available forenergy harvesting and data transmission when compressionratio κ decreases. It can be also noted that the achievedthroughput with the traditional frame is lower than that withthe proposed frame structure, even though the compressionratio κ is set to 100%. This performance degradation is causedby that the third time slot cannot be utilized for energyharvesting, as no FC is implemented for energy detection inthe traditional frame structure. In a summary, we can concludethat the proposed frame structure outperforms the traditionalone in terms of achieved throughput.
Fig. 6 plots the achieved throughput τcs versus lowerbound of the third time slot α2,min and compression ratioκ when solving the problem in (27). It shows that theachieved maximal throughput increases with decreasing κ andincreasing α2,min. This behavior can be explained as follows:as κ decreases, the number of samples � to be collectedfor spectrum sensing at an SU is reduced as the signal inoriginal size of N × 1 can be recovered from less numberof measurements by utilizing the CS technique. When thetime slot assigned for spectrum sensing is reduced, the energyconsumption for spectrum sensing is reduced. As a result, thetime which can be assigned for data transmission is increased.Therefore, the throughput of the secondary network is im-proved. By optimizing the transmission power Pt , the energyharvested in the current frame period would be fully utilizedand the maximal throughput can be achieved accordingly.It should be noted that when the compression ratio κ is set
QIN et al.: WIRELESS POWERED CR NETWORKS WITH COMPRESSIVE SENSING AND MATRIX COMPLETION 1473
Fig. 6. Optimized throughput of single SU τcs versus lower bound of thethird time slot α2,min and compression ratio κ , and S N R = −10 dB insensing channels.
to 100% and the lower bound of the third time slot α2,min
is zero, the achieved throughput can be regarded as that ofthe traditional frame structure design without considering sub-Nyquist sampling.
B. Numerical Results on Optimizing Throughput ofCooperative Spectrum Sensing Networks
In the case of optimizing the throughput of the CSS net-works, the total number of participating SUs is set be toJ = 500, including both the active and inactive SUs. Com-paring the format of (P1) and (P0), we can see that both ofthem are linear constrained. Therefore, similar as (P0), the gridsearch method can be applied to obtain the optimal throughputbut with non-negligible complexity, especially for the caseof optimizing throughput of the whole cooperative network.The fmincon method can be adopted to obtain the sub-optimal throughput efficiently. In the following simulations,the fmincon method is utilized to solve the optimization prob-lem (P1). In addition, as aforementioned in the introductionpart, many algorithms have been proposed for the low-rankMC based cooperative spectrum sensing. With P̄d = 90%,the detection performance with different compression ratiosis presented in the authors’ previous work in [16], whichwould not be demonstrated here again to reduce redundancy.In the following simulations, how the achieved throughput isinfluenced by parameters, such as the number of active SUs J1,compression ratio κ and the lower bound of the third timeslot α2,min, would be demonstrated.
Fig. 7 plots the power outage probability Pout versus densityof PBs with different power threshold Ps . In this case, thepower outage probability here is for the whole system, whichcan be calculated as Pout = 1 − (
1 − Psout
) × (1 − Pt
out
).
Both the single SU scenario and multiple SUs scenario areillustrated in the figure. It can be observed that as densityof PBs increases, the power outage probability dramaticallydecreases, which is caused by that the multiuser diversity gainis improved with increasing number of PBs when chargingwith WPT. We can also observe that the Pout of multipleSUs scenario is lower than that of single SU scenario. This is
Fig. 7. Power outage probability comparison for single SU and multipleSUs with versus density of PBs, Ps = 0 dBm, α1 = 0.25, α2 = 0.20, andβ = 0.25.
Fig. 8. Optimized throughput averaged on per SU of multiple SUs τmcversus number of active SUs J1 and compression ratio κ , S N R = −10 dBin sensing channels, and α2,min = 0.05.
because the power outage probability of spectrum sensing isalways zero in multiple SUs scenario, which in turn lower thepower outage probability of the whole system. For the multipleSUs scenario, the Pout of the active SUs, inactive SUs andthe average Pout of the CSS networks are all presented in thefigure. It is noted the averaged Pout falls between the Pout ofactive SUs and inactive SUs, which as we expected.
Fig. 8 plots the throughput τmc averaged on per SU withdifferent number of active SUs J1 and different compressionratios κ at each active SU. In this case, it is assumed thatthe exact matrix completion can be guaranteed when thenumber of active SUs J1 is in the range of 50 to 500,which refers to that the compression ratio κ changes from10% to 100%. It shows that the average throughput achievesthe best performance when the number of active SUs is set tobe the minimal possible number J1 = 50 in comparison withthat of case J1 = J . This benefits from the increasing numberof inactive SUs when the number of active SUs J1 decreasesfrom 500 to 50. With increasing number of inactive SUs,energy consumption for spectrum sensing can be alleviated
1474 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 65, NO. 4, APRIL 2017
Fig. 9. Optimized throughput averaged on per SU of multiple SUs τmcversus lower bound α2,min and compression ratio κ , and S N R = −10 dB insensing channels.
and more energy can be harvested for data transmission. It isfurther noticed that the achieved throughput is increased withthe compression ratio κ decreasing from 75% to 20%.Thisbenefits from that the required time slot for sub-Nyquistsensing is reduced when the compression ratio κ is decreased.
Fig. 9 plots the achieved throughput averaged on per SUversus different compression ratio κ and lower bound forthe third time slot α2,min . In this case, the number of activeSUs is set to J1 = 300. The achieved throughput shownin Fig. 9 is based on the condition that the exact matrixrecovery can be guaranteed with the given compression ratioκ . As shown in the figure, the achieved throughput increaseswith decreasing compression ratio κ and α2,min. The minimalcompression ratio guaranteing the exact matrix recovery isnondeterministic, which is dependent on the rank order of thematrix to be recovered and the size of matrix to be recovered.If the rank of matrix is fixed, the larger network size J ,the lower minimal compression ratio which can guarantee theexact matrix recovery.
VI. CONCLUSIONS
In this paper, a wireless powered cognitive radio (CR) net-work has been considered. In the considered networks, whileprotecting the primary users, we proposed a new frame struc-ture including energy harvesting, spectrum sensing, energyharvesting and data transmission. In the considered networkwith the proposed frame structure, closed-form expressionsin terms of power outage probability was derived for theproposed wireless power transfer (WPT) scheme. Additionally,sub-Nyquist sampling was performed at secondary users (SUs)to reduce the energy consumption during spectrum sensing.The compressive sensing and matrix completion techniqueswere adopted at a remote fusion center to perform the signalrecovery for detection making on spectrum occupancy. Byoptimizing the four time slots, throughput of an individualSU and the whole cooperative networks were maximized,respectively. Simulation results showed that the throughput canbe improved by adopting the proposed new frame structuredesign. We conclude that by carefully tuning the parameters
for different time slots and transmit power, WPT can be usedalong with sub-Nyquist sampling to provide a high qualityof throughput performance for CR network, with significantlyenergy computation reduction at power-limited SUs.
APPENDIX A: PROOF OF THEOREM 1
Based on (2), the power outage probability of spectrumsensing can be expressed as
Pouts = Pr
{PH1 ≤ Ps
}
= E�p
⎧⎨⎩
∏
p∈�p,‖dp‖≥d0
Pr{∥∥hp
∥∥2 ≤ dξpμs
}⎫⎬⎭
= E�p
⎧⎨⎩
∏
p∈�p,‖dp‖≥d0
F‖hp‖2
(dξpμs
)⎫⎬⎭, (A.1)
where F‖hp‖2 is the cumulative density function (CDF) of∥∥hp∥∥2. As aforementioned in Section II, each channel element
of hp follows Rayleigh fading, which is independent complexGaussian distributed with zero mean and unit variance. As aconsequence,
∥∥hp∥∥2 follows a chi-squared distribution, which
is given by
F‖hp‖2 (x) = 1 − � (M, x)
� (M). (A.2)
Given the fact that M is an integer value, with the aid of [36,eq. (8.832.2)], (A.2) can be expressed as
F‖hp‖2 (x) = 1 − e−x
(M−1∑m=0
xm
m!
). (A.3)
Applying the moment generating function, we rewrite (A.1)as
Pouts = exp
⎡⎢⎣−λp
∫
R2
(1 − F‖hp‖2
(dξpμs
))ddp
⎤⎥⎦. (A.4)
Then changing to polar coordinates and substituting (A.3) into(A.4), we obtain
Pouts = exp
⎡⎣−2πλp
M−1∑m=0
μms
∫∞d0
dpmξ+1e−μs dξp ddp
m!
⎤⎦.
(A.5)
Applying [36, eq. (3.381.9)] to calculate the integral, weobtain (11).
Similarly, based on (4), the power outage probability of datatransmission Pout
t can be expressed as follows:
Poutt = Pr
{PT2 ≤ Pt
}
= Pr
{max
p∈�p,‖dp‖≥d0
{∥∥hp∥∥2
dp−ξ} ≤ μt
}. (A.6)
Following the similar procedure as (A.5) andapplying μt → μs , we obtain Pout
t in (11).The proof is completed.
QIN et al.: WIRELESS POWERED CR NETWORKS WITH COMPRESSIVE SENSING AND MATRIX COMPLETION 1475
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Zhijin Qin (S’13–M’16) received the B.Sc. degreesfrom the Beijing University of Posts and Telecom-munications, Beijing, China, and the Ph.D. degreein electronic engineering from the Queen Mary Uni-versity of London, London, U.K., in 2012 and 2016,respectively. She is currently a Research Associatewith the Department of Computing, Imperial CollegeLondon, London, U.K. She received the Best PaperAward at the Wireless Technology Symposium,London, U.K., in 2012.
Her research interests include low-power wideareanetwork in Internet of Things, fog networking, compressive spectrum sensing,and nonorthogonal multiple access in 5G network. She has served as a TPCMember of the IEEE conferences, such as ICC’16, VTC’15, and VTC’14.
Yuanwei Liu (S’13–M’16) received the B.S. andM.S. degrees from the Beijing University of Postsand Telecommunications in 2014 and 2011, respec-tively, and the Ph.D. degree in electrical engineeringfrom the Queen Mary University of London, U.K.,in 2016. He is currently a Post-Doctoral ResearchFellow with the Department of Informatics, King’sCollege London, U.K.
His research interests include nonorthogonal mul-tiple access, millimeter wave, massive MIMO, Het-nets, D2D communication, cognitive radio, and
physical layer security. He currently serves an Editor of the IEEE COM-MUNICATION LETTERS. He has served as a TPC Member for many IEEEconferences, such as GLOBECOM and ICC. He received the ExemplaryReviewer Certificate of the IEEE WIRELESS COMMUNICATION LETTERSin 2015.
1476 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 65, NO. 4, APRIL 2017
Yue Gao (S’03–M’07–SM’13) received the bach-elor’s degree from the Beijing University of Postsand Telecommunications, China, in 2002, and theM.Sc. and Ph.D. degrees in telecommunications andmicrowave antennas from the Queen Mary Univer-sity of London (QMUL), U.K., in 2003 and 2007,respectively. He has been an Associate Professor,a Research Assistant, and Assistant Professor withthe School of Electronic Engineering and ComputerScience, QMUL.
He is currently leading the Whitespace MachineCommunication Lab, QMUL, where he is involved in developing theoreticalresearch into practice in the interdisciplinary area among antennas, signalprocessing, and spectrum sharing for cyber-physical system, machine-to-machine communications, and Internet of Things applications. He has au-thored or co-authored over 100 peer-reviewed journal and conference papers,two best paper awards, two patents and two licensed works to companies,and one book chapter. He is a Principal Investigator for a TV white spacetestbed project funded by the Engineering and Physical Sciences ResearchCouncil, and a number of projects funded by companies. He has served asthe Signal Processing for Communications Symposium Co-Chair of the IEEEICCC 2016. He is serving as the Publicity Co-Chair of the GLOBECOM2016, the Cognitive Radio and Networks Symposia Co-Chair of the IEEEGLOBECOM 2017, and the General Co-Chair of the IEEE WoWMoM 2017.
Maged Elkashlan received the Ph.D. degree inelectrical engineering from The University of BritishColumbia, Canada, in 2006. From 2007 to 2011, hewas with the Wireless and Networking TechnologiesLaboratory, Commonwealth Scientific and IndustrialResearch Organization, Australia. He also held anadjunct appointment with the University of Technol-ogy Sydney, Australia. In 2011, he joined the Schoolof Electronic Engineering and Computer Science,Queen Mary University of London, U.K. He alsoholds visiting faculty appointments with the Beijing
University of Posts and Telecommunications, China. His research interestsfall into the broad areas of communication theory, wireless communications,and statistical signal processing for NOMA and Hetnets.
Dr. Elkashlan received the Best Paper Awards at the IEEE InternationalConference on Communications in 2014 and 2016, the International Con-ference on Communications and Networking in China in 2014, and theIEEE Vehicular Technology Conference in 2013. He currently serves asan Editor of the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS,the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, and the IEEECOMMUNICATIONS LETTERS. He also serves as a Lead Guest Editorof the Special Issue on Green Media: The Future of Wireless Multime-dia Networks of the IEEE Wireless Communications Magazine, a LeadGuest Editor of the Special Issue on Millimeter Wave Communications for5G of the IEEE Communications Magazine, a Guest Editor of the SpecialIssue on Energy Harvesting Communications of the IEEE CommunicationsMagazine, and a Guest Editor of the Special Issue on Location Awarenessfor Radios and Networks of the IEEE JOURNAL ON SELECTED AREAS IN
COMMUNICATIONS.
Arumugam Nallanathan (S’97–M’00–SM’05) wasan Assistant Professor with the Department of Elec-trical and Computer Engineering, National Univer-sity of Singapore, from 2000 to 2007. He servedas the Head of Graduate Studies with the Schoolof Natural and Mathematical Sciences, King’s Col-lege London, from 2011 to 2012. He is currentlya Professor of Wireless Communications with theDepartment of Informatics, King’s College London,University of London. His research interests include5G wireless networks, molecular communications,
energy harvesting, and cognitive radio networks. He has authored nearly300 technical papers in scientific journals and international conferences. Hewas a co-recipient of the Best Paper Award presented at the IEEE InternationalConference on Communications 2016 and the IEEE International Conferenceon Ultra-Wideband 2007. He is an IEEE Distinguished Lecturer. He has beenselected as a Thomson Reuters Highly Cited Researcher in 2016.
Dr. Nallanathan received the IEEE Communications Society SPCE outstand-ing service award 2012 and the IEEE Communications Society RCC out-standing service award 2014. He served as the Chair of the Signal Processingand Communication Electronics Technical Committee of IEEE Communi-cations Society, the Technical Program Co-Chair (MAC track) of the IEEEWCNC 2014, the Co-Chair of the IEEE GLOBECOM 2013 (CommunicationsTheory Symposium), the Co-Chair of the IEEE ICC 2012 (Signal Processingfor Communications Symposium), the Co-Chair of the IEEE GLOBECOM2011 (Signal Processing for Communications Symposium), the TechnicalProgram Co-Chair of the IEEE International Conference on UWB 2011,the Co-Chair of the IEEE ICC 2009 (Wireless Communications Sympo-sium), the Co-chair of the IEEE GLOBECOM 2008 (Signal Processing forCommunications Symposium), and the General Track Chair of the IEEEVTC 2008. He was an Editor of the IEEE TRANSACTIONS ON WIRELESS
COMMUNICATIONS from 2006 to 2011, the IEEE WIRELESS COMMUNICA-TIONS LETTERS, and the IEEE SIGNAL PROCESSING LETTERS. He is anEditor of the IEEE TRANSACTIONS ON COMMUNICATIONS and the IEEETRANSACTIONS ON VEHICULAR TECHNOLOGY.
