SIMULTANEOUS INFORMATION-AND-POWER TRANSFER FOR BROADBAND DOWNLINK SYTEMS

This is the Pre-Published Versio. SIMULTANEOUS INFORMATION-AND-POWER TRANSFER FOR BROADBAND DOWNLINK SYTEMS Kaibi Huag Hog Kog Polytechic Uiversity, Hog Kog Email: huagkb@ieee.org Erik G. Larsso Liko pig Uiversity, Swede Email: erik.larsso@isy.liu.se Abstract Far-field wireless rechargig based o microwave power trasfer (MPT) will free mobile devices from iterruptio due to fiite battery lives. Itegratig MPT with wireless commuicatios to support simultaeous iformatio-ad-power trasfer (SIPT) allows the same spectrum to be used for dual purposes without compromisig the quality of service. I this paper, we propose the ovel approach of realizig SIPT i a broadbad dowlik system where users are assiged orthogoal frequecy sub-chaels ad a base statio trasfers iformatio ad eergy to users over spatially separated chaels called the data ad MPT chaels. Optimizig the power cotrol for such a system results i a ew class of multiuser power-cotrol problems featurig the circuit-power costraits, amely that the wirelessly trasferred power must be sufficietly large for operatig receiver circuits. Solvig these problems gives a set of power-cotrol algorithms that exploit chael diversity i frequecy for simultaeously ehacig the throughput ad MPT efficiecy. For the sigle-user SIPT system, the optimal power allocatio is show to perform water fillig i frequecy with water levels for differet users depedig o the correspodig MPT sub-chael gais. Next, a efficiet power-cotrol algorithm is proposed for the multiuser SIPT system based o sequetial schedulig of mobiles by comparig their data rates ad circuitpower costraits. This algorithm is proved to be optimal for the practical sceario of highly correlated data ad MPT chaels. Idex Terms Power trasmissio, cellular etworks, power cotrol, eergy harvestig, mobile commuicatio. I. INTRODUCTION Microwave power trasfer (MPT) for far-field wireless rechargig will elimiate the cables tetherig mobiles to the electric grid [1]. The itegratio betwee MPT ad wireless commuicatio, called simultaeous iformatio-ad-power trasfer (SIPT), allows a same spectrum to be used for dual purposes, which is the theme of this paper [2]. MPT research i past decades have focused o developig microwave devices for large-scale ad log-distace power trasfer either terrestrially [1], from solar satellites to the earth [3], or for powerig small airplaes [4]. These devices such as rectifyig ateas are essetial for implemetig SIPT trasceivers. However, a complete SIPT solutio is much more complex ad requires sophisticated algorithms for resource allocatio, adaptive trasmissio ad sigal processig targetig SIPT, which is a area largely ope. This motivates the curret work that proposes ovel power-cotrol algorithms for eablig SIPT i broadbad systems e.g., 3GPP LTE or WiFi. Researchers have studied SIPT from the iformatiotheoretic perspective [5] [7]. I [5], the capacity of a sigle- The work of K. Huag was partially supp was supported i part by the Hog Kog Polytechic Uiversity Iteral Grat (No. 1-ZVAF) ad that of E. G. Larsso by the Swedish Foudatio for Strategic Research, ad ELLIIT. user chael is derived uder the costrait that the received power must exceed a threshold represetig fixed circuitpower cosumptio, referred to as the circuit-power costrait. For SIPT over a iductive-couplig circuit, maximizig the iformatio capacity uder the metioed costrait yields a tradeoff betwee the iformatio-ad-eergy trasfer-rates [6]. Similar tradeoffs have bee formulated ad optimized for various types of SIPT systems icludig two-user MIMO broadcast chaels [7], [8], two-way commuicatio liks [9], multiple-access chaels ad poit-to-poit liks assisted by passive relays [10]. SIPT has bee also ivestigated from the etwork perspective usig stochastic geometry ad the optimal desity tradeoffs have bee derived betwee base statios for data access ad those for MPT [11]. I additio, a efficiet receiver desig for implemetig SIPT was reported i [12]. I cotrast with most prior work assumig arrow-bad chaels, we cosider SIPT for broadbad dowlik systems based o the orthogoal frequecy-divisio multiple-access (OFDMA) ad optimize power allocatio over frequecy subchaels. To this ed, a ovel class of power-cotrol problems are formulated by itroducig multiuser-circuit-power costraits. Each receiver is assumed to comprise a iformatio processor (for demodulatig ad decodig data) ad a eergy harvester, which are attached to separate sigle ateas. Give a multi-atea base statio ad trasmit beamformig, this receiver architecture creates two effective sigle-iputsigle-output (SISO) broadbad chaels of differet fuctios for each lik, referred to as the data chael ad the MPT chael. Note that trasmit beamformig is particularly suitable for cellular systems where feedback methods have bee implemeted for acquirig trasmit CSI [13]. For a sigle-user system, the optimal power-cotrol over frequecy is proved to follow waterig fillig with the water level for each user beig a mootoe icreasig fuctio of the correspodig MPT sub-chael gai. Next, for multiuser dowlik, a efficiet sub-optimal algorithm is proposed for multiuser power cotrol. This algorithm combies the classic water fillig ad sequetial schedulig of users by comparig the gais of their data ad MPT sub-chaels, achievig closeto-optimal performace. Furthermore, the proposed algorithm is proved to be optimal for the practical sceario that the data ad MPT chaels are highly correlated. II. SYSTEM MODEL Cosider the multiuser system as illustrated i Fig. 1 where a multi-atea base-statio serves K mobiles. The spectrum is partitioed ito K sub-chaels ad each is assiged to oe

Sub-cha. 1 Sub-cha. 2 Sub-cha. K Base Statio Sigal Spectrum Passive Receivers User 1 User 2 User K Receiver Architecture Iformatio Processor Power Eergy Harvester Fig. 1. Simultaeous iformatio-ad-power trasfer i a broadbad multiuser system where K users share the chael by OFDMA. user. Note that the problem formulatio for the case of oe user assiged multiple sub-chaels differs from the curret oe i havig more complex circuit-power costraits but the solutio methods are similar. Ideally, the sub-chael assigmets should be joitly optimized with power cotrol over the states of both the data ad MPT chaels uder the multiuser-circuitpower costraits but the optimal desig seems itractable. For tractability, we assume give sub-chael assigmets ad focus o power cotrol. The passive receiver used by each user comprises a iformatio processor ad a eergy harvester as illustrated i Fig. 1. The eergy harvester coverts iput sigals ito DC power for supplyig the receiver s fixed circuit power cosumptio deoted as p c. Let the vectors h ad h represet particular realizatios of the -th multiple-iput-sigle-output (MISO) data ad MPT sub-chaels, respectively. Moreover, the trasmit-beamformig vector for user is deoted as f. This implies that the same beamformig vector is used for both iformatio ad data trasfers ad this assumptio is viable sice the typical eviromet for efficiet MPT has liesof-sight. A beamformig vector for this case steers a beam towards the iteded user ad ca be computed by estimatig the user s directio of arrival. However, i the presece of rich scatterig, the beamformig vectors for the two purposes should be differet, givig rise to the issue of power splittig for data ad iformatio trasfers as addressed i [7]. The beamformig vectors {f } are assumed give ad their desigs are outside the scope of this paper. The the effective SISOchael gais resultig from beamformig ca be writte as h = f h 2 for the data chael ad h = f h 2 for the MPT chael. It follows that the sum throughput is C = log 2 (1 + P h ) (1) Data where uit oise variace is assumed to simplify otatio ad the trasmissio powers {P } satisfy both the trasmissiopower costrait P p t with p t beig the total available power, ad the circuit-power costrait, amely P h p c for all. The sigle-user system is also cosidered where the user is assiged all K sub-chaels. The correspodig throughput is give by C i (1) uder the same trasmissiopower costrait but a differet sigle circuit-power costrait P h p c sice the harvested power is P h. III. SIPT FOR SINGLE-USER SYSTEMS Usig (1), the problem of the optimal power cotrol for a sigle-user system ca be formulated as: maximize: log (1 + P h ) (P1) P 0, P p t, P h p c where the last iequality is the circuit-power costrait. P1 is observed to be a covex optimizatio problem. Note that P1 with {h } replaced by {h } is equivalet to the problem formulated i [6] where iformatio ad power propagate through the same chael. For the remaiig part of this sectio, we ivestigate the structure of the optimal power-cotrol policy by solvig P1. First, it is ecessary to test the feasibility of powerig the receiver give trasmissio power p t. This requires computig the limit of the harvested power p max by solvig the followig optimizatio problem: maximize: P h (P1.1) P 0 P p t. By ispectig P1.1, it is obtaied that p max = p t max h. It follows that SIPT is feasible if ad oly if p t max h. (2) Next, give the coditio i (2), we check if the circuitpower costrait i P1 is active. Assumig it is iactive, P1 reduces to the followig problem for the classic multi-chael power-cotrol: maximize: log (1 + P h ) (P1.2) p c P 0 P = p t.

Note that the iequality i the trasmissio-power costrait i P1 is replaced with equality without loss of geerality sice the objective fuctio is a strictly mootoe icreasig fuctio of {P }. The solutio for P1.2, deoted as { P }, follows the water-fillig power cotrol [14]: 1 P = ζ 1, A h (3) 0, otherwise where A deotes the set groupig the idices of users assiged ozero powers, amely A = {1 K P > 0}, ad ζ is the matchig Lagrage multiplier give as ζ = A p t + m A 1 h m. (4) It follows that the circuit-power costrait i P1 is iactive if ad oly if P h > p c. (5) The results from the above aalysis are summarized as the followig lemma. Lemma 1. Assume that the feasibility coditio i (2) is satisfied. The optimal solutio for P1, deoted as {P }, satisfies the followig coditios. 1) If the iequality i (5) holds, P = P for 1 K. 2) Otherwise, {P } solves the followig optimizatio problem: (P1.3) maximize: log (1 + P h ) P 0, P = p t, P h = p c. Last, the costraied optimizatio problem P1.3 ca be solved usig the method of duality [15]. As a result, the optimal trasmissio powers are obtaied as 1 P = λ µ h 1, O h (6) 0, otherwise where the set O is chose to esure {P } beig oegative ad the positive scalars λ ad µ are the Lagrage multipliers solvig the dual problem, amely ucostraied miimizatio of the followig covex fuctio [15]: O log 1 λ µh + (λ + µ) 1 + λp t + µp c. O h The optimal power allocatio i (6) ca be iterpreted as water fillig i frequecy with a water level decreasig with the icreasig MPT sub-chael gai or vice versa. This agrees with the ituitio that less trasmissio power is required for turig o a receiver if the MPT loss is smaller. I cotrast, the classic water fillig i (3) has a costat water level. A. Power Cotrol IV. SIPT FOR MULTI-USER SYSTEMS The power-cotrol problem for the multiuser SIPT system is formulated as follows: (P2) maximize: log (1 + P h ) P p t [ ) pc P {0} h, where the last lie is the multiuser circuit-power costraits. To solve P2, it is useful to cosider the traditioal powercotrol problem P1.2 that is equivalet to P2 with the circuitpower costraits relaxed. Give the solutio for P1.2 i (3), defie a subset S of A as S = { A P < p c /h }. The the users whose idices belog to S fail to satisfy their circuitpower costraits. It may be uecessary to deactivate all users i S sice turig off ay of them allows the origially assiged power to be redistributed for potetially helpig others i S to meet their circuit-power costraits. Determiig the optimal subset of users from S for deactivatio requires joitly cosiderig the origially allocated powers ad additioal amouts for meetig their circuit-power costraits. This is aalytically itractable ad requires testig all subsets of S by reallocatig power for each subset, whose complexity grows expoetially with the size of S. To address this issue, a sub-optimal but efficiet algorithm is proposed for sequetially deactivatig users i S that have relatively small gais for both their data ad MPT subchaels. Note that the Lagrage multiplier ζ i (4) ca be iterpreted as the price for allocatig oe uit of power as measured agaist the data rate. Therefore, a suitable metric H ca be defied as H = log ( 1 + p ch h ) ζ p c h, S (7) for comparig the gais for satisfyig the circuit-power costraits for the users i S. The proposed algorithm uses {H } to search for the set of active users uder the circuit-power costraits ad the detailed procedure is described as follows. Algorithm 1. 1) Obtai A ad S by solvig P1.2. Compute ζ ad {H } usig (4) ad (7), respectively. 2) Deactivate the user i S that has the smallest H. I other words, modify the active user set as A = A\{m} with m = arg mi S H. 3) Give A, re-compute { P } ad ζ usig (3) ad (4), respectively. Furthermore, applyig the circuit-power

5.5 CC = 0.5 9 5 CC = 0.9 8 CC = 0.9 7 Throughput (bit/s/hz) 4 3 2 Correlatio Coefficiet (CC) = 0.1 Throughput (bit/s/hz) 6 5 4 3 Correlatio Coefficiet (CC) = 0.1 CC = 0.5 1 Total trasmissio power = 10 db 2 1 Throughput loss [CC = 0.1 (top), 0.5 (middle), 0.9 (bottom)] 0.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Fig. 2. Circuit power (db) Throughput versus circuit power for the sigle-user SIPT system. Fig. 3. Circuit power (db) Sum throughput versus circuit power for the multiuser SIPT system. costraits o { P } to obtai S. If S =, all active users i A satisfy their circuit-power costraits ad the algorithm termiates. Otherwise, compute {H } i (7) usig the updated S ad ζ ad go to Step 2. Two remarks are offered as follows. a) By the iteratio of Algorithm 1, sice the umber of active users decreases, the values of { P } icrease; the set S reduces ad evetually becomes empty. b) The feasibility coditio i (2) also applies to the multiuser system. If this coditio holds, Algorithm 1 will select at least oe active user. B. Power Cotrol for Correlated Data-ad-MPT Chaels The data ad MPT sub-chaels for the same lik are highly correlated sice they are created by two collocated receive ateas. Thus, their gais are expected to follow the same order, amely that h m h m if ad oly if h m h for all (m, ). Without loss of geerality, it is assumed i this sectio that h 1 h 2 h k ad h 1 h 2 h k. Note that the miimum trasmissio powers uder the circuitpower costraits, amely {p c /h }, follow the reverse order: p c /h 1 p c /h 2 p c /h k. Therefore, it is optimal to activate those users havig the largest data/wpt chael gais sice they achieve high iformatio rates but have relatively loose circuit-power costraits. Let l deote the largest positive iteger i the rage 1 l K such that give { P } computed usig (3) with A = {1, 2,, l}, { P 1 l} all satisfy their correspodig circuit-power costraits. The followig propositio is a direct result of the above discussio. Propositio 1. Cosider the case where h 1 h 2 h k ad h 1 h 2 h k. The solutio for P2 is give by { P } computed usig (3) with A = {1, 2,, l}. Last, Algorithm 1 i the precedig sub-sectio is show to be optimal for the curret sceario. Propositio 2. Cosider the case where h 1 h 2 h k ad h 1 h 2 h k. Algorithm 1 yields the solutio for P2 as give i Propositio 1. The proof of Propositio 2 is omitted due to the space limitatio. The key step of the proof is to show that the metrics {H } defied i (7) ad used i Algorithm 1 follow the same order as {h } [or equivaletly {h }] for the curret case by exploitig the mootoicity of the Lagragia (from solvig P2) with respect to allocated powers larger tha { P }. V. SIMULATION RESULTS The data ad MPT sub-chael gais for each lik are modeled as the absolute values of a pair of complex CN (0, 1) radom variables with the correlatio coefficiet ρ. The gais for differet liks are idepedet ad idetically distributed. The umber of sub-chaels is K = 5 ad the total trasmissio power is p t = 10 db ad 15 db for the sigle-user ad multiuser systems, respectively. Cosider a sigle-user SIPT system with the optimal power cotrol. The curves of throughput versus circuit power p c are plotted i Fig. 2 for ρ = {0.1, 0.5, 0.9}. The throughput is observed to be almost costat for p c p t but decrease rapidly as p c exceeds p t. The chages o ρ are foud to cause oly small variatios of the throughput. Low correlatio (ρ = 0.1) results i throughput loss of about 0.4 bit/s/hz i the rage of p c p t due to that the circuit-power costrait is active more frequetly for less correlated data/mpt chaels. However, moderate correlatio (ρ = 0.5) balaces the diversity ad correlatio for these two chaels so as to yield the small throughput gai i the rage of p c p t. Next, for a multiuser SIPT system with power cotrol usig Algorithm 1, Fig. 3 displays the curves of throughput versus p c for ρ = {0.1, 0.5, 0.9}. I additio, the bottom of Fig. 3 shows the throughput loss with respect to the maximum values computed by a exhaustive search. The threshold effect at p c = p t i Fig. 2 is ot observed i Fig. 3 due to the multiuserdiversity gai, amely that the presece of multiple receivers ad idepedet sub-chaels icreases the probability that at least oe receiver is active eve if p c is large. Moreover, the sum throughput is observed to icrease ad the throughput loss reduce as ρ grows.

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