IRS-Assisted Wireless Powered NOMA: Do We Really Need Different Phase Shifts in DL and UL?
11 IRS-Assisted Wireless Powered NOMA: IsDynamic Passive Beamforming Really Needed?
Qingqing Wu,
Member, IEEE , Xiaobo Zhou, and Robert Schober,
Fellow, IEEE
Abstract —Intelligent reflecting surface (IRS) is a promisingtechnology to improve the performance of wireless poweredcommunication networks (WPCNs) due to its capability toreconfigure signal propagation environments via smart reflection.In particular, the high passive beamforming gain promised byIRS can significantly enhance the efficiency of both downlinkwireless power transfer (DL WPT) and uplink wireless infor-mation transmission (UL WIT) in WPCNs. Although adoptingdifferent IRS phase shifts for DL WPT and UL WIT, i.e., dynamicIRS beamforming , is in principle possible but incurs additionalsignaling overhead and computational complexity, it is an openproblem whether it is actually beneficial. To answer this question,we consider an IRS-assisted WPCN where multiple devicesemploy a hybrid access point (HAP) to first harvest energy andthen transmit information using non-orthogonal multiple access(NOMA). Specifically, we aim to maximize the sum throughputof all devices by jointly optimizing the IRS phase shifts and theresource allocation. To this end, we first prove that dynamic IRSbeamforming is not needed for the considered system, which helpsreduce the number of IRS phase shifts to be optimized. Then, wepropose both joint and alternating optimization based algorithmsto solve the resulting problem. Simulation results demonstrate theeffectiveness of our proposed designs over benchmark schemesand also provide useful insights into the importance of IRS forrealizing spectrally and energy efficient WPCNs.
Index Terms —IRS, wireless powered networks, NOMA, dy-namic beamforming, time allocation. I. INTRODUCTION
Intelligent reflecting surface (IRS) has been recently pro-posed as a cost-effective technology to improve the spectralefficiency and energy efficiency of future wireless networks[1]. Specifically, by smartly adjusting the phase shifts ofa large number of reflecting elements, IRS can reconfigurethe wireless propagation environment to achieve differentdesign objectives, such as signal focusing and interferencesuppression. In particular, the fundamental squared power gain of IRS was firstly unveiled in [1], which thus has motivatedan upsurge of interest in investigating joint active and passivebeamforming for various system setups e.g., physical layersecurity and spectrum sharing/cognitive radio [2]–[7].While the above works focused on applying IRS for improv-ing wireless information transmission (WIT), there is a grow-ing interest in exploiting the high beamforming gain of IRSto enhance the efficiency of wireless power transfer (WPT) toInternet-of-Things (IoT) devices. One line of research targetsIRS passive beamforming for simultaneous wireless infor-mation and power transfer (SWIPT), where information andenergy receivers are concurrently served [8]–[13]. The other
Q. Wu is with the State Key Laboratory of Internet of Things for SmartCity, University of Macau, China 999078 (email: [email protected]).
HAP Wireless Powered Devices Downlink Wireless Power TransferUplink Wireless Information TransmissionIRS
Fig. 1. An IRS-assisted WPCN employing NOMA for UL WIT. line of research focuses on IRS-assisted wireless poweredcommunication networks (WPCNs), where self-sustainabledevices first harvest energy in the downlink (DL) and thentransmit information signals in the uplink (UL) [14]–[16],based on the well-known “harvest and then transmit” protocolillustrated in Fig. 1. The WPCN sum throughput maximizationproblem was studied in [14] for UL WIT with time-divisionmultiple access (TDMA). To improve the WIT efficiency, thecommon throughput maximization problem of an IRS-assistedWPCN was studied in [15] with user cooperation in the UL.However, this study was limited to a WPCN with two users.In [16], the extension to the multiuser case was presented,where space-division multiple access (SDMA) was employedfor UL WIT by jointly optimizing the IRS phase shifts andthe transmit powers.Non-orthogonal multiple access (NOMA) is practically ap-pealing for UL WIT in WPCNs due to its capability to improvespectrum efficiency and user fairness by allowing multipleusers to simultaneously access the same spectrum. To thebest of the authors’ knowledge, optimization of IRS-assistedWPCNs employing NOMA for UL WIT has not been studiedin the literature yet. Furthermore, since DL WPT and UL WIToccur in different time slots and have different objectives, itis usually believed that exploiting different IRS phase-shiftvectors in the two phases, which is referred to as dynamicIRS beamforming , may improve system performance. Assuch, all existing works on IRS-assisted WPCNs (e.g., [14]–[16]) naturally assume dynamic passive beamforming in theirproblem formulations. However, it remains an open problemwhether dynamic IRS beamforming is actually beneficial formaximizing the throughput of wireless powered IoT networksemploying NOMA.Motivated by the above considerations, we study an IRS-assisted WPCN where an IRS is deployed to assist the DLWPT and UL WIT between a hybrid access point (HAP) and a r X i v : . [ c s . I T ] F e b multiple devices. For this setup, we aim to maximize the sumthroughput of all devices by jointly optimizing the resource al-location and IRS phase shifts (i.e., passive beamforming). Forthe first time, we unveil that adopting different IRS phase shiftsfor DL WPT and UL WIT, i.e., dynamic IRS beamforming, isnot beneficial for the considered system. Since the algorithmiccomputations are typically executed at the HAP, which thensends the optimized phase shifts to the IRS controller, this re-sult not only reduces the number of optimization variables, butalso lowers the feedback signalling overhead, especially whenthe IRS is practically large. Exploiting the insight gained, wefurther propose both joint and alternating optimization basedalgorithms to solve the resulting problem. Numerical resultsdemonstrate the significant performance gains achieved by theproposed algorithms compared to benchmark schemes andreveal that integrating IRS into WPCNs not only improvesthe system throughput but also reduces the system energyconsumption. Notations:
For a vector x , [ x ] n denotes its n -th entry and x T and x H denote its transpose and Hermitian transpose,respectively. O ( · ) denotes the computational complexity order. Re {·} denotes the real part of a complex number. tr( S ) denotes the trace of matrix S . arg( x ) denotes the phase vectorof x .II. S YSTEM M ODEL AND P ROBLEM F ORMULATION
A. System Model
As shown in Fig. 1, we consider an IRS-aided WPCN,which comprises an HAP, an IRS, and K wireless-powereddevices. The HAP and the devices are all equipped with asingle antenna and the IRS consists of N reflecting elements.To ease practical implementation, the HAP and all devicesare assumed to operate over the same frequency band, withthe total available transmission time denoted by T max . Inaddition, the quasi-static flat-fading channel model is adoptedwhich means that the channel coefficients remain constantduring T max . As such, UL/DL channel reciprocity holds forall channels, which allows channel state information (CSI)acquisition for the DL based on UL training. The WPCNadopts the typical “harvest and then transmit” protocol [15]where the devices first harvest energy from the DL signalemitted by the HAP and then use the available energy totransmit information to the HAP in the UL. To be ableto characterize the maximum achievable performance, it isassumed that the CSI of all channels is perfectly known atthe HAP (see [17] for practical channel acquisition methods).The equivalent baseband channels from the HAP to the IRS,from the IRS to device k , and from the HAP to device k are denoted by g ∈ C N × , h Hr,k ∈ C × N , and h Hd,k ∈ C ,respectively, where k = 1 , · · · , K .During DL WPT, the HAP broadcasts an energy signalwith constant transmit power P A during time τ . The energyharvested from the noise is assumed to be negligible as in[18], since the noise power is much smaller than the powerreceived from the HAP. Let Θ = diag ( e jθ , · · · , e jθ N ) denotethe reflection phase-shift matrix of the IRS for DL WPT where θ n ∈ [0 , π ) , ∀ n . Thus, the amount of harvested energy atdevice k can be expressed as E hk = η k P A | h Hd,k + h Hr,k Θ g | τ (1) = η k P A | h Hd,k + q Hk v | τ , where η k ∈ (0 , is the energy conversion efficiency ofdevice k , q k = h Hr,k diag ( g ) , and v = [ e jθ , · · · , e jθ N ] T .For UL WIT, NOMA is adopted where all devices transmittheir respective information signals to the HAP simultaneouslyfor a duration of τ with transmit powers p k , k = 1 , · · · , K .The HAP applies successive interference cancellation (SIC) toeliminate multiuser interference. Specifically, for detecting themessage of the k -th device, the HAP first decodes the messageof the i -th device, ∀ i < k , and then removes this messagefrom the received signal, in the order of i = 1 , , ..., k − .The signal received from the i -th user, ∀ i > k , is treated asnoise. Hence, the achievable throughput of device k in bits/Hzcan be expressed as r k = τ log (cid:32) p k | h Hd,k + q Hk v | (cid:80) Ki = k +1 p i | h Hd,i + q Hi v | + σ (cid:33) , (2)where σ is the additive white Gaussian noise power at theHAP and v = [ e jϕ , · · · , e jϕ N ] T denotes the IRS phase shiftvector for UL WIT. Then, the sum throughput is given by R sum = K (cid:88) k =1 r k = τ log (cid:32) K (cid:88) k =1 p k | h Hd,k + q Hk v | σ (cid:33) . (3) B. Problem Formulation
Our objective is to maximize the sum throughput of theconsidered system by jointly optimizing the IRS phase shifts,the time allocation, and the transmit powers. This leads to thefollowing optimization problem(P1) : max τ ,τ , { pk } , v , v τ log (cid:32) K (cid:88) k =1 p k | h Hd,k + q Hk v | σ (cid:33) (4a) s . t . p k τ ≤ η k P A | h Hd,k + q Hk v | τ , ∀ k, (4b) τ + τ ≤ T max , (4c) τ ≥ , τ ≥ , p k ≥ , ∀ k, (4d) | [ v ] n | = 1 , n = 1 , · · · , N, (4e) | [ v ] n | = 1 , n = 1 , · · · , N. (4f)In (P1), (4b) and (4c) represent the energy causality andtotal time constraints, respectively, (4d) are non-negativityconstraints, and (4e) and (4f) are unit-modulus constraints forthe phase shifts employed for DL WPT and UL WIT, respec-tively. Intuitively, since the DL and UL transmissions havedifferent objectives, i.e., WPT and WIT, adopting differentphase-shift vectors, i.e., v and v , is expected to be beneficialfor maximizing the system sum throughput. However, usingdifferent IRS phase-shift vectors also increases the feedbacksignalling overhead to the IRS and the computational com-plexity at the HAP due to the large number of optimizationvariables. Furthermore, (P1) is a non-convex optimizationproblem and difficult to solve optimally in general due tocoupled optimization variables in (4a) and (4b) as well as thenon-convex unit-nodulus constraints in (4e) and (4f). III. P
ROPOSED S OLUTION
In this section, we first answer the question whether theoptimal solution of (P1) requires dynamic IRS beamforming.Then, we propose two efficient algorithms to solve the result-ing optimization problem.
A. Is Dynamic Passive Beamforming Needed?
Proposition 1.
For (P1), v (cid:63) = v (cid:63) holds, where v (cid:63) and v (cid:63) are the optimal phase-shift vectors for DL WPT and UL WIT,respectively.Proof. First, it can be easily shown that constraint (4b) ismet with equality for the optimal solution since otherwise p k can be always increased to improve the objective value until(4b) becomes active. Then, substituting (4b) into the objectivefunction eliminates { p k } . As such, for any given τ and τ ,(P1) is equivalent to max v , v K (cid:88) k =1 α k | h Hd,k + q Hk v | | h Hd,k + q Hk v | (5a) s . t . (4e), (4f), (5b)where α k = τ P A η k τ σ . Denote by w the vector maximizing (cid:80) Kk =1 α k | h Hd,k + q Hk v | subject to constraints | [ v ] n | = 1 , ∀ n .For the objective function in (5a), we can establish thefollowing inequalities K (cid:88) k =1 (cid:0) √ α k | h Hd,k + q Hk v | (cid:1) (cid:0) √ α k | h Hd,k + q Hk v | (cid:1) (6) ( a ) ≤ (cid:118)(cid:117)(cid:117)(cid:116)(cid:32) K (cid:88) k =1 α k | h Hd,k + q Hk v | (cid:33) (cid:32) K (cid:88) k =1 α k | h Hd,k + q Hk v | (cid:33) ( b ) ≤ (cid:118)(cid:117)(cid:117)(cid:116)(cid:32) K (cid:88) k =1 α k | h Hd,k + q Hk w | (cid:33) = K (cid:88) k =1 α k | h Hd,k + q Hk w | , (7)where ( a ) is due to the Cauchy-Schwarz inequality and ( b ) holds since w maximizes (cid:80) Kk =1 α k | h Hd,k + q Hk v | and theequality holds when v (cid:63) = v (cid:63) = w .Proposition 1 explicitly shows that dynamic IRS beam-forming is not needed for UL WPT and DL WIT and usingconstant passive beamforming is sufficient to maximize thesum throughput of the considered system. As such, if the HAPis in charge of computing the IRS phase shifts, it only needs tofeed back N phase-shift values (i.e., v ) to the IRS, rather than N (i.e., v and v ), which reduces the signalling overheadand the associated delay, especially for practically large N .Furthermore, exploiting Proposition 1, we only need to solvethe following problem, which involves a smaller number ofoptimization variables (i.e., IRS phase shifts) max τ ,τ , v τ log (cid:32) K (cid:88) k =1 τ P A η k | h Hd,k + q Hk v | τ σ (cid:33) (8a) s . t . τ + τ ≤ T max , (8b) τ ≥ , τ ≥ , (8c) | [ v ] n | = 1 , n = 1 , · · · , N. (8d) Although simpler, problem (8) is still a non-convex optimiza-tion problem. B. Proposed Joint Optimization Algorithm
To deal with the non-convex objective function (8a), weintroduce a slack variable S and reformulate problem (8) asfollows max τ ,τ , v τ log (cid:18) Sτ (cid:19) (9a) s . t . S ≤ K (cid:88) k =1 τ P A η k | h Hd,k + q Hk v | σ , (9b) τ + τ ≤ T max , (9c) τ ≥ , τ ≥ , (9d) | [ v ] n | = 1 , n = 1 , · · · , N. (9e)It can be verified that for the optimal solution of problem(9), constraint (9b) is met with equality, since otherwise wecan always increase the objective value by increasing S . Let | h Hd,k + q Hk v | = | ¯ q Hk ¯ v | , where ¯ v = [ v H H and ¯ q Hk =[ q Hk h Hd,k ] . Define Q k = ¯ q k ¯ q Hk and V = ¯ v ¯ v H which needsto satisfy V (cid:23) and rank( V ) = 1 . Then, (9b) can beexpressed as S ≤ K (cid:88) k =1 η k P A τ [Tr( V Q k )] σ . (10)The key observation is that although τ [Tr( V Q k )] =[Tr( V Q k )] / τ in (10) is not jointly convex with respect to V and τ , it is jointly convex with respect to Tr( V Q k ) and τ . Recall that any convex function is globally lower-boundedby its first-order Taylor expansion at any point. This thusmotivates us to apply the successive convex approximation(SCA) technique for solving problem (9). Therefore, withgiven local point ˆ V and ˆ τ , we obtain the following lowerbound [Tr( V Q k )] /τ ≥ [Tr( ˆ V Q k )] / ˆ τ − [Tr( ˆ V Q k )] / ˆ τ (cid:18) τ − τ (cid:19) + 2Tr( ˆ V Q k )1 / ˆ τ (cid:16) Tr( V Q k ) − Tr( ˆ V Q k ) (cid:17) (cid:44) G ( V , τ ) . (11)With the lower bound in (11), problem (9) is approximated asthe following problem max τ ,τ , V ,S τ log (cid:18) Sτ (cid:19) (12a) s . t . S ≤ K (cid:88) k =1 P A η k σ G ( V , τ ) , (12b) τ + τ ≤ T max , (12c) τ ≥ , τ ≥ , (12d) [ V ] n,n = 1 , n = 1 , · · · , N + 1 , (12e) rank( V ) = 1 , V (cid:23) . (12f)Note that by relaxing the rank-one constraint in (12f), problem(12) becomes a convex semidefinite program (SDP) and we can successively solve it by using standard convex optimiza-tion solvers such as CVX, until convergence is achieved.After convergence, Gaussian randomization can be appliedto obtain a high-quality solution. Alternatively, instead ofrelaxing the rank-one constraint, we can further transform itinto an equivalent constraint based on the largest singular value(see Section IV-A for details) and then solve the resultingproblem using the penalty method [9]. The computationalcomplexity of this algorithm lies in solving the SDP andis given by O ( I JO N . ) where I JO denotes the number ofiterations required for convergence. Since all optimizationvariables are optimized simultaneously, the joint optimizationalgorithm serves as a benchmark scheme for other schemeshaving lower complexities. C. Proposed Alternating Optimization Algorithm
Next, we propose an efficient alternating optimization algo-rithm where the phase shifts and time allocation are alternatelyoptimized until convergence is achieved. The key advantage ofthe algorithm is that it admits a (semi) closed-form solution ineach iteration, which thus avoids the computational complexityincurred by using SDP solvers.First, for any fixed v , it can be shown that problem (8)is simplified to a convex optimization problem where theoptimal time allocation can be obtained by using the Lagrangeduality method as in [18] where the details are omitted herefor brevity. Second, for any fixed τ and τ , problem (8) isreduced to max v K (cid:88) k =1 α k | h Hd,k + q Hk v | = K (cid:88) k =1 α k (¯ v H Q k ¯ v ) (13a) s . t . | [ v ] n | = 1 , n = 1 , · · · , N, (13b)where α k = τ P A η k τ σ as in (5). Although maximizing a convexfunction does not lead to a convex optimization problem, theconvexity of (13a) allows us to apply the SCA technique forsolving problem (13). Specifically, for a given local point ˆ v ,the first-order Taylor expansion based lower bound for the k -thterm in (13a) can be expressed as (¯ v H Q k ¯ v ) ≥ v H Q k ˆ v (cid:0) { ˆ v H Q k ¯ v } − v H Q k ˆ v (cid:1) + (ˆ v H Q k ˆ v ) = 4Re { C k ˆ v H Q k ¯ v } − C k , (14)where C k = ˆ v H Q k ˆ v . Based on (14), a lower bound for (13a)is given by (cid:40)(cid:32) K (cid:88) k =1 α k C k ˆ v H Q k (cid:33) ¯ v (cid:41) − K (cid:88) k =1 α k C k . (15)Based on (15), it is not difficult to show that the optimalsolution satisfying (13b) is given by ¯ v = e j arg( β ) where β = ( (cid:80) Kk =1 α k C k ˆ v H Q k ) H .Note that the objective value of problem (8) is non-decreasing by alternately optimizing the time allocation andphase shifts, and also upper-bounded by a finite value. Thus,the proposed algorithm is guaranteed to converge. The com-plexity of this algorithm mainly lies in the calculation of thephase shifts for problem (13) and thus is given by O ( I AO N ) , z xHAP (0,0,0) IRS (10,0,3) r Fig. 2. Simulation setup. where I AO is the number of iterations required for conver-gence. IV. N UMERICAL R ESULTS
This section presents simulation results to demonstrate theeffectiveness of the proposed solutions and to provide usefulinsights for IRS-aided WPCN design. The HAP and IRSare respectively located at (0 , , meter (m) and (10 , , m, as shown in Fig. 2. The user devices are randomly anduniformly distributed within a radius of . m centered at (10 , , m. The pathloss exponents of both the HAP-IRS andIRS-device channels are set to . , while those of the HAP-device channels are set to . . Furthermore, Rayleigh fadingis adopted as small-scale fading for all channels. The signalattenuation at a reference distance of m is set as dB. Theremaining system parameters are set as follows: η k = 0 . , ∀ k , σ = − dBm, T max = 1 s, and P A = 40 dBm. A. Performance Comparison
In Fig. 3(a), we plot the sum throughput versus the numberof IRS elements for K = 5 and K = 10 . For comparison,we consider the following schemes: 1) “Proposed JO withSDR” where problem (12) with rank( V ) = 1 in (12f)relaxed is solved successively, and thus, this scheme servesas a performance upper bound; 2) “Proposed JO with GR”where Gaussian randomization is applied to recover a rank-one V based on the solution of the scheme in 1); 3) “Pro-posed JO with Penalty” where we replace rank( V ) = 1 by Tr( V ) − λ max ( V ) ≤ with λ max ( V ) denoting the largesteigenvalue of V and then solve the resulting problem usingthe penalty method [9]; 4) “Proposed AO” in Section III-C;5) Fixed time allocation with optimized IRS phase shifts, i.e., τ = 0 . T max ; 6) Fixed IRS phase shifts with optimized timeallocation, i.e., θ n = 0 , ∀ n ; and 7) Without IRS.It is observed from Fig. 3(a) that the sum throughput gainachieved by our proposed JO/AO designs over the bench-mark schemes increases as N increases for both K = 5 and K = 10 . In particular, the proposed AO algorithmachieves almost the same performance as the proposed JOwith SDR/GR/Penalty and is thereby a practically appealingsolution considering its low complexity, especially for large N . Besides, the performance of the scheme with fixed phaseshifts is less sensitive to increasing N and only achievesa marginal gain over the system without IRS, whereas thescheme with fixed time allocation performs even worse thanthe system without IRS for small N , but outperforms the
10 20 30 40 50 60 70 80 90
Number of reflecting elements N S u m t h r oughpu t ( b i t s / H z ) Proposed JO with SDRProposed JO with GRProposed JO with PenaltyProposed AOFixed time allocationFixed IRS phase shiftsWithout IRS
K=5K=10 (a) Performance comparison.
10 20 30 40 50 60 70 80 90
Number of reflecting elements N
Proposed AOWithout IRS
K=5K=10 (b) Impact of N on DL WPT duration.
10 20 30 40 50 60 70 80 90
Number of reflecting elements N H a r v e s t ed ene r g y a t ea c h de v i c e ( J ou l e ) -6 Proposed AO, D1Proposed AO, D2Without IRS, D1Without IRS, D2 (c) Impact of N on user harvested energy.Fig. 3. Simulation results. scheme with fixed phase shifts for large N . This is expectedsince as N increases, the passive beamforming gain achievedby phase-shift optimization helps compensate the performanceloss incurred by fixed time allocation. Nevertheless, Fig. 3(a)highlights the importance of the joint design of the IRS phaseshifts and the time allocation. B. Impact of IRS on WPCNs
We note that the significant throughput improvement shownin Fig. 3(a) is due to the deployment of the IRS and not dueto an increase in the total energy consumption at the HAP,which is given by E HAP = P A τ . To illustrate this explicitly,we plot in Fig. 3(b) the optimized DL WPT duration τ versus N obtained with the proposed AO algorithm and without IRS.It is observed that for IRS-assisted WPCNs, the optimizedDL WPT duration decreases as N increases and thus thetotal system energy consumed at the HAP E HAP is actuallyreduced. This also leaves devices more transmission time forUL WIT, which benefits the sum throughput since R sum ismonotonically increasing in τ . This suggests that integratingIRS into WPCNs introduces a desirable “double-gain” as itnot only improves the system throughput but also reduces theenergy consumption, thus rendering this architecture spectrallyand energy efficient.Furthermore, although the DL WPT duration τ decreasesdue to the deployment of the IRS, it is not at the cost ofreducing the energy harvested at the devices. In Fig. 3(c), weplot the harvested energy of two randomly selected devices(e.g., D1 and D2), i.e., E hk = η k P A | h Hd,k + q Hk v | τ , versus N when K = 5 . One can observe that the harvested energymonotonically increases with N for both devices. Consideringthe decrease of τ shown in Fig. 3(b), it is not difficult toconclude that the increase of E hk is solely due to the improvedeffective channel power gain | h Hd,k + q Hk v | , which furtherdemonstrates the effectiveness of IRS for WPCNs.V. C ONCLUSIONS
This paper studied IRS-assisted WPCNs employing NOMAfor UL WIT. Specifically, the IRS phase shifts and timeallocation for DL WPT and UL WIT were jointly optimized tomaximize the system sum throughput. We first unveiled thatdynamic IRS beamforming cannot improve the performanceof the considered system, which simplifies the problem andreduces the signalling overhead. Based on this result, weproposed both joint and alternating optimization algorithmsfor system throughput maximization where the latter admitsclosed-form expressions and is practically appealing. Nu-merical results showed that our proposed designs are ableto drastically improve the system performance compared toseveral baseline schemes and also shed light on how theIRS improves the throughput of WPCNs while decreasing theenergy consumption as the number of IRS elements increases.In future work, it is worth investigating the effectiveness ofdynamic IRS beamforming for WPCNs with imperfect CSI,minimum user throughput requirements, etc. R EFERENCES[1] Q. Wu and R. Zhang, “Intelligent reflecting surface enhanced wirelessnetwork via joint active and passive beamforming,”
IEEE Trans. WirelessCommun. , vol. 18, no. 11, pp. 5394–5409, Nov. 2019.[2] N. Rajatheva et al. , “White paper on broadband connectivity in 6G,” arXivpreprint arXiv:2004.14247 , 2020.[3] M. Cui, G. Zhang, and R. Zhang, “Secure wireless communication viaintelligent reflecting surface,”
IEEE Wireless Commun. Lett. , vol. 8, no. 5,pp. 1410–1414, Oct. 2019.[4] X. Guan, Q. Wu, and R. Zhang, “Intelligent reflecting surface assistedsecrecy communication: Is artificial noise helpful or not?”
IEEE WirelessCommun. Lett. , vol. 9, no. 6, pp. 778–782, Jun. 2020.[5] D. Xu, X. Yu, Y. Sun, D. W. K. Ng, and R. Schober, “Resourceallocation for IRS-assisted full-duplex cognitive radio systems,”
IEEETrans. Commun. , vol. 68, no. 12, pp. 7376–7394, Dec. 2020.[6] Y. Zou, S. Gong, J. Xu, W. Cheng, D. T. Hoang, and D. Niyato,“Wireless powered intelligent reflecting surfaces for enhancing wirelesscommunications,”
IEEE Trans. Veh. Technol. , vol. 69, no. 10, pp. 12 369–12 373, Oct. 2020.[7] B. Zheng, Q. Wu, and R. Zhang, “Intelligent reflecting surface-assistedmultiple access with user pairing: NOMA or OMA?”
IEEE Commun.Lett. , vol. 24, no. 4, pp. 753–757, Apr. 2020.[8] Q. Wu and R. Zhang, “Weighted sum power maximization for intelligentreflecting surface aided SWIPT,”
IEEE Wireless Commun. Lett. , vol. 9,no. 5, pp. 586–590, May 2020.[9] Q. Wu and R. Zhang, “Joint active and passive beamforming optimizationfor intelligent reflecting surface assisted SWIPT under QoS constraints,”
IEEE J. Sel. Areas Commun. , vol. 38, no. 8, pp. 1735–1748, Aug. 2020.[10] Y. Tang, G. Ma, H. Xie, J. Xu, and X. Han, “Joint transmit and reflectivebeamforming design for IRS-assisted multiuser MISO SWIPT systems,”in
Proc. IEEE ICC , 2020, pp. 1–6.[11] J. Liu, K. Xiong, Y. Lu, D. W. K. Ng, Z. Zhong, and Z. Han, “Energyefficiency in secure IRS-aided SWIPT,”
IEEE Wireless Commun. Lett. ,vol. 9, no. 11, pp. 1884–1888, Nov. 2020.[12] Y. Zhao, B. Clerckx, and Z. Feng, “Intelligent reflecting surface-aidedSWIPT: Joint waveform, active and passive beamforming design,” arXivpreprint arXiv:2012.05646 , 2020.[13] S. Zargari, A. Khalili, and R. Zhang, “Energy efficiency maximizationvia joint active and passive beamforming design for multiuser MISO IRS-aided SWIPT,”
IEEE Wireless Commun. Lett. , Early access, 2020.[14] B. Lyu, P. Ramezani, D. T. Hoang, S. Gong, Z. Yang, and A. Jamalipour,“Optimized energy and information relaying in self-sustainable IRS-empowered WPCN,”
IEEE Trans. Commun. , vol. 69, no. 1, pp. 619–633,Jan. 2021.[15] Y. Zheng, S. Bi, Y. J. Zhang, Z. Quan, and H. Wang, “Intelligentreflecting surface enhanced user cooperation in wireless powered com-munication networks,”
IEEE Wireless Commun. Lett. , vol. 9, no. 6, pp.901–905, Jun. 2020.[16] Y. Zheng, S. Bi, Y.-J. A. Zhang, X. Lin, and H. Wang, “Joint beam-forming and power control for throughput maximization in IRS-assistedMISO WPCNs,”
IEEE Internet Things J. , Early access, 2020.[17] Q. Wu and R. Zhang, “Towards smart and reconfigurable environment:Intelligent reflecting surface aided wireless network,”
IEEE Commun.Mag. , vol. 58, no. 1, pp. 106–112, Jan. 2020.[18] H. Ju and R. Zhang, “Throughput maximization in wireless poweredcommunication networks,”