4788 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 9, SEPTEMBER 2013

Transcription

1 4788 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 9, SEPTEMBER 213 Opportunitic Wirele Energy Harveting in Cognitive Radio Network Seungyun Lee, Rui Zang, Member, IEEE, and Kaibin Huang, Member, IEEE Abtract Wirele network can be elf-utaining by arveting energy from ambient radio-frequency (RF) ignal. Recently, reearcer ave made progre on deigning efficient circuit and device for RF energy arveting uitable for low-power wirele application. Motivated by ti and building upon te claic cognitive radio (CR) network model, ti paper propoe a novel metod for wirele network coexiting were low-power mobile in a econdary network, called econdary tranmitter (ST), arvet ambient RF energy from tranmiion by nearby active tranmitter in a primary network, called primary tranmitter (PT), wile opportunitically acceing te pectrum licened to te primary network. We conider a tocatic-geometry model in wic PT and ST are ditributed a independent omogeneou Poion point procee (HPPP) and communicate wit teir intended receiver at fixed ditance. Eac PT i aociated wit a guard zone to protect it intended receiver from ST interference, and at te ame time deliver RF energy to ST located in it arveting zone. Baed on te propoed model, we analyze te tranmiion probability of ST and te reulting patial trougput of te econdary network. Te optimal tranmiion power and denity of ST are derived for maximizing te econdary network trougput under te given outage-probability contraint in te two coexiting network, wic reveal key inigt to te optimal network deign. Finally, we ow tat our analytical reult can be generally applied to a non-cr etup, were ditributed wirele power carger are deployed to power coexiting wirele tranmitter in a enor network. Index Term Cognitive radio, energy arveting, opportunitic pectrum acce, wirele power tranfer, tocatic geometry. I. INTRODUCTION POWERING mobile device by arveting energy from ambient ource uc a olar, wind, and kinetic activitie make wirele network not only environmentally friendly but alo elf-utaining. Particularly, it a been reported in te recent literature tat arveting energy from ambient radio-frequency (RF) ignal can power a network of lowpower device uc a wirele enor [1] [6]. In teory, te Manucript received February 19, 213; revied May 25, 213; accepted July 8, 213. Te aociate editor coordinating te review of ti paper and approving it for publication wa N. Kato. Ti work a been preented in part at te IEEE International Conference on Communication Sytem (ICCS), November 21-23, 212, Singapore, and wa upported in part by te National Univerity of Singapore under te reearc grant R S. Lee and R. Zang are wit te Department of Electrical and Computer Engineering, National Univerity of Singapore, Singapore ( {.lee, elezang}@nu.edu.g). R. Zang i alo wit te Intitute for Infocomm Reearc, A*STAR, Singapore. K. Huang i wit te Department of Applied Matematic, Hong Kong Polytecnic Univerity, Hong Kong ( uangkb@ieee.org). Digital Object Identifier 1.119/TWC /13$31. c 213 IEEE maximum power available for RF energy arveting at a freepace ditance of 4 meter i known to be 7uW and 1uW for 2.4GHz and 9MHz frequency, repectively [2]. Mot recently, Zungeru et al. ave acieved arveted power of 3.5mW at a ditance of.6 meter and 1uW at a ditance of 11 meter uing Powercat RF energy-arveter operating at 915MHz [2]. It i expected tat more advanced tecnologie for RF energy arveting will be available in te near future due to e.g. te rapid advancement in deigning igly efficient rectifying antenna [3]. In ti work, we invetigate te impact of RF energy arveting on te newly emerging cognitive radio (CR) type of network. To ti end, we propoe a novel metod for wirele network coexiting were tranmitter from a econdary network, called econdary tranmitter (ST), eiter opportunitically arvet RF energy from tranmiion by nearby tranmitter from a primary network, or tranmit ignal if tee primary tranmitter (PT) are ufficiently far away. ST tore arveted energy in recargeable batterie wit finite capacity and apply te available energy for ubequent tranmiion wen batterie are fully carged. Te trougput of te econdary network i analyzed baed on a tocatic-geometry model, were te PT and ST are ditributed according to independent omogeneou Poion point procee (HPPP). In ti model, eac PT i aumed to randomly acce te pectrum wit a given probability and eac active (tranmitting) PT i centered at a guard zone a well a a arveting zone tat i inide te guard zone. A a reult, eac ST arvet energy if it lie in te arveting zone of any active PT, or tranmit if it i outide te guard zone of all active PT, or i idle oterwie. Ti model i applied to maximize te patial trougput of te econdary network by optimizing key parameter including te ST tranmit power and denity ubject to given PT tranmit power and denity, guard/arveting zone radiu, and outageprobability contraint in bot te primary and econdary network. Our work i motivated by a joint invetigation of te propoed conventional opportunitic pectrum acce and te newly introduced opportunitic energy arveting in CR network, i.e., during te idle time of ST due to te preence of nearby active PT, tey can take uc an opportunity to arvet ignificant RF energy from primary tranmiion. Specifically, a own in Fig. 1, eac ST can be in one of te following tree mode at any given time: arveting mode if it i inide te arveting zone of an active PT and not fully carged; tranmitting mode if it i fully carged and outide te guard zone of all active PT; and idle mode if it i fully

2 LEE et al.: OPPORTUNISTIC WIRELESS ENERGY HARVESTING IN COGNITIVE RADIO NETWORKS 4789 r g r PT: Tranmitting PT: Idle ST: Harveting ST: Tranmitting ST: Idle (fully carged) ST: Idle (not fully carged) Harveting zone Guard zone Fig. 1. A wirele energy arveting CR network in wic PT and ST are ditributed a independent HPPP. Eac PT/ST a it intended information receiver at fixed ditance (not own in te figure for brevity). ST arvet energy from a nearby PT if it i inide it arveting zone. To protect te primary tranmiion, ST inide a guard zone i proibited from tranmiion. carged but inide any of te guard zone, or neiter fully carged nor inide any of te arveting zone. te receiver opportunitically arvet RF energy or decode information ubject to time-varying co-cannel interference [16]. More recently, Huang and Lau ave propoed a new cellular network arcitecture coniting of power beacon deployed to deliver wirele energy to mobile terminal and caracterized te trade-off between te power-beacon denity and cellular network patial trougput [17]. In anoter track, te emerging CR tecnology enable efficient pectrum uage by allowing a econdary network to are te pectrum licened to a primary network witout ignificantly degrading it performance [18]. Beide active development of algoritm for opportunitic tranmiion by econdary uer (ee e.g. [19], [2] and reference terein), notable reearc a been purued on caracterizing te trougput of coexiting wirele network baed on te tool of tocatic geometry. For example, te capacity trade-off between two or more coexiting network aring a common pectrum ave been tudied in [21] [23]. Moreover, te outage probability of a Poion-ditributed CR network wit guard zone a been analyzed by Lee and Haenggi [24], were te econdary uer opportunitically acce te primary uer cannel only wen tey are not inide any of te guard zone. A. Related Work Recently, wirele communication powered by energy arveting a emerged to be a new and active reearc area. However, due to energy arveting, exiting tranmiion algoritm for conventional wirele ytem wit contant power upplie (e.g., batterie) need to be redeigned to account for te new callenge uc a random energy arrival. For point-to-point wirele ytem powered by energy arveting, te optimal power-allocation algoritm ave been deigned and own to follow modified water-filling by Ho and Zang [7] and Ozel et al. [8]. From a network perpective, Huang invetigated te trougput of a mobile ad-oc network (MANET) powered by energy arveting were te network patial trougput i maximized by optimizing te tranmit power level under an outage contraint [9]. Furtermore, te performance of olar-powered wirele enor/me network a been analyzed in [1], in wic variou leep and wakeup trategie are conidered. Among oter energy cavenging ource uc a olar and wind, background RF ignal can be a viable new ource for wirele energy arveting [11]. A new reearc trend on wirele power tranfer i to integrate ti tecnology wit wirele communication. In [12] and [13], imultaneou wirele power and information tranfer a been invetigated, aiming at maximizing information rate and tranferred power over ingle-antenna additive wite Gauian noie (AWGN) cannel. For broadcat cannel, Zang and Ho ave tudied multi-antenna tranmiion for imultaneou wirele information and power tranfer wit practical receiver deign uc a time witcing and power plitting [14]. Moreover, Zou et al. ave propoed a new receiver deign for enabling wirele information and power tranmiion at te ame time, by judiciouly integrating conventional information and energy receiver [15]. For point-to-point wirele ytem, Liu et al. ave tudied opportunitic RF energy arveting were B. Summary and Organization In ti paper, we conider a CR network wit time lotted tranmiion and PT/ST location modeled by independent HPPP. Te ST tranmiion power i aumed to be ufficiently mall to meet te low-power requirement wit RF energy arveting. Under ti etup, te main reult of ti paper are ummarized a follow: 1) We propoe a new CR network arcitecture were ST are powered by arveting RF energy from active primary tranmiion. We tudy te ST tranmiion probability a a function of ST tranmit power in te preence of bot guard zone and arveting zone baed on a Markov cain model. For te cae of ingle-lot and double-lot carging, we obtain te expreion of te exact ST tranmiion probability, wile for te general cae of multi-lot carging wit more tan two lot, we obtain te upper and lower bound on te ST tranmiion probability. 2) Wit te reult of ST tranmiion probability, we derive te outage probabilitie of coexiting primary and econdary network ubject to teir mutual interference, baed on tocatic geometry and a implified aumption on te HPPP of tranmitting ST wit an effective denity equal to te product of te ST tranmiion probability and te ST denity. Furtermore, we maximize te patial trougput of te econdary network under given outage contraint for te coexiting network by jointly optimizing te ST tranmiion power and denity, and obtain imple cloed-form expreion of te optimal olution. 3) Furtermore, we ow tat our analytical reult can be generally applied to even non-cr etup, were ditributed wirele power carger (WPC) are deployed to power coexiting wirele information tranmitter (WIT) in a enor network, a own in Fig. 2. Practically, WPC can be implemented a e.g. wirele carging veicle [25], or fixed power beacon [17] randomly deployed in a wirele enor network.

3 479 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 9, SEPTEMBER 213 r WPC: Tranmitting WIT: Harveting WIT: Tranmitting WIT: Idle (not fully carged) Harveting zone Fig. 2. A wirele powered enor network in wic WPC and WIT are ditributed a independent HPPP. Eac WIT a an intended receiver at a fixed ditance (not own in te figure for brevity). WIT arvet energy from a nearby WPC if inide it arveting zone. Unlike te CR etup in Fig. 1, te guard zone i not applicable in ti cae, and tu a fully carged WIT can tranmit at any time. Baed on our reult for te CR network etup, we derive te maximum network trougput of uc wirele powered enor network in term of te optimal denity and tranmit power of WIT. Te remainder of ti paper i organized a follow. Section II decribe te ytem model and performance metric. Section III analyze te tranmiion probability of energyarveting ST. Section IV tudie te outage probabilitie in te primary and econdary network. Section V invetigate te maximization of te econdary network trougput ubject to te primary and econdary outage probability contraint. Section VI extend te reult to te wirele powered enor network etup. Finally, Section VII conclude te paper. II. SYSTEM MODEL A. Network Model A own in Fig. 1, we conider a CR network in wic PT and ST are ditributed a independent HPPP 1 wit denity λ p and λ, repectively, wit λ p λ. It i aumed tat time i lotted and eac PT independently accee te pectrum wit probability p at eac time lot. Tu, te point proce of active PT form anoter HPPP wit denity λ p = pλ p, according to te Coloring Teorem [28], wic varie independently over different lot. For convenience, we refer to active PT imply a PT in te ret of ti paper. We denote te point procee of PT and ST a Φ p = {X} and Φ = {Y }, repectively, were X, Y R 2 denote te coordinate of te PT and ST, repectively. In addition, it i aumed tat eac PT/ST tranmit wit fixed power to it intended primary/econdary receiver (PR/SR) at ditance d p and d, repectively, in random direction. We denote te fixed tranmiion power level of PT and ST a P p and P, 1 In general, tranmitter location in cognitive radio network may ave non-omogeneou or even non-poion patial ditribution, wic are difficult to caracterize and not amenable to analyi. In ti paper, we aume HPPP for tranmitter location to obtain tractable analyi for te network performance. repectively. We aume P p P in ti paper for energy arveting application of practical interet. ST acce te pectrum of te primary network and tu teir tranmiion potentially interfere wit PR. To protect te primary tranmiion, ST are prevented from tranmitting wen tey lie in any of te guard zone, modeled a dik wit a fixed radiu centered at eac PT. Specifically, let b(t,x) R 2 repreent a dik of radiu x centered at T R 2 ;tenb(x, r g ) denote te guard zone wit radiu r g for protecting PT X Φ p.defineg = X Φ p b(x, r g ) a te union of all PT guard zone; accordingly, an ST Y Φ cannot tranmit if Y G. Note tat in practice te guard zone i uually centered at a PR rater tan a PT a we ave aumed, wile our aumption i made to implify our analyi, imilarly a in [19]. We furter aume d p r g to guarantee tat guard zone centered at PT (rater tan PR) will protect te primary tranmiion properly. Under te above aumption, te probability p g tat a typical ST, denoted by Y, doe not lie in G i equal to te probability tat tere i no PT inide te dik centered at Y wit radiu r g, i.e., b(y,r g ). Note tat te number of PT inide b(y,r g ), denoted by N, i a Poion random variable wit mean πrg 2λ p; tu, it probability ma function (PMF) i given by Pr{N = n} = e (πr2 πr2 g λp g λ p) n, n! n =, 1, 2,... (1) Conequently, p g can be obtained a p g =Pr{Y / G} (2) =Pr{N =} (3) = e πr2 g λp. (4) We aume flat-fading cannel wit pat-lo and Rayleig fading; ence, te cannel gain are modeled a exponential random variable. A a reult, in a particular time lot, te ignal tranmitted from a PT/ST are received at te origin wit power g X P p X and g Y P Y, repectively, were {g X } X Φp and {g Y } Y Φ are independent and identically ditributed (i.i.d.) exponential random variable wit unit mean, >2 i te pat-lo exponent, and X, Y denote te ditance from node X, Y to te origin, repectively. B. Energy-Harveting Model To make ue of te RF energy a an energy-arveting ource, eac RF energy arveter in an ST mut be equipped wit a power converion circuit tat can extract DC power from te received electromagnetic wave [1]. Suc circuit in practice ave certain enitivity requirement, i.e., te input power need to be larger tan a predeigned treold for te circuit to arvet RF energy efficiently. Ti fact tu motivate u to define te arveting zone, wic i a dik wit radiu r centered at eac PT X Φ p wit r r g. Te radiu r i determined by te energy arveting circuit enitivity for a given P p, uc tat only ST inide a arveting zone can receive power larger tan te energy arveting treold, wic i given by P p r. Te power received by an ST outide any arveting zone i too mall to activate te energy arveting circuit, and tu i aumed to be negligible in ti paper.

4 LEE et al.: OPPORTUNISTIC WIRELESS ENERGY HARVESTING IN COGNITIVE RADIO NETWORKS 4791 Let b(x, r ) repreent te arveting zone centered at PT X Φ p uc tat an ST Y can arvet energy from one or more PT if Y H,wereH = X Φ p b(x, r ) denote te union of te arveting zone of all PT. Te probability p tat a typical ST Y lie in H i equal to te probability tat tere i at leat one PT inide te dik b(y,r ). Similar to (1), te number of PT inide b(y,r ), denoted by K, ia Poion random variable wit mean πr 2λ p and PMF given by Pr{K = k} = e πr2 λp (πr2 λ p) k, k =, 1, 2,... (5) k! Accordingly, p i given by p =Pr{Y H} (6) =Pr{K 1} (7) = e πr2 λp (πr2 λ p) k k! k=1 (8) =1 e πr2 λp. (9) Since λ p and r are bot practically mall, we can aume πr 2 λ p 1. Tu, p given in (8) can be approximated a Pr{K =1} by ignoring te iger-order term wit k>1. Terefore, wen Y H, Y i inide te arveting zone of one ingle PT mot probably, wic equivalently mean tat te arveting zone of different PT do not overlap at mot time. A a reult, te amount of average power arveted by Y Hin a time lot can be lower-bounded by ηp p R were R r denote te ditance between Y and it nearet PT, and <η<1 denote te arveting efficiency. Note tat te arveted power a been averaged over te cannel ortterm fading witin a lot. C. ST Tranmiion Model We aume tat eac ST a a battery of finite capacity equal to te minimum energy required for one-lot tranmiion wit power P for implicity. Upon te battery being fully carged, an ST will tranmit wit all tored energy in te next lot if it i outide all te guard zone. We denote te probability tat Y a been fully carged at te beginning of a time lot a p f and te probability tat it will be able to tranmit in ti lot a p t. A mentioned above, te point proce of PT Φ p varie independently over different lot, and tu te event tat an ST a been fully carged in one lot and tat it i outide all te guard zone in te next lot are independent. Conequently, p t can imply be obtained a p t = p f p g, (1) were p g i given in (4), and p f will be derived in Section III. D. Performance Metric For bot PR and SR, te received ignal-to-interferenceplu-noie ratio (SINR) i required to exceed a given target for reliable tranmiion. Let θ p and θ be te target SINR for te PR and SR, repectively. Te outage probability i ten defined a P (p) out =Pr{SINR (p) <θ p } for te primary network and P () out = Pr{SINR () < θ } for te econdary network. Te outage-probability contraint are applied uc tat P (p) out ɛ p and P () out ɛ wit given <ɛ p,ɛ < 1. Note tat te tranmitting ST in general do not form an HPPP due to te preence of guard zone and energy arveting zone, but teir average denity over te network i given by p t λ. Accordingly, given fixed PT denity λ p and tranmiion power P p, te performance metric of te econdary network i te patial trougput C (bp/hz/unit-area) given by C = p t λ log 2 (1 + θ ), (11) under te given primary/econdary outage probability contraint ɛ p and ɛ. III. TRANSMISSION PROBABILITY OF SECONDARY TRANSMITTERS In ti ection, te tranmiion probability of a typical ST p t given in (1) i analyzed uing te Markov cain model. For convenience, we define M a te maximum number of energyarveting time lot required to fully carge te battery of an ST. Since te minimum power arveted by an ST in one lot i ηp p r, wic occur wen te ST i at te edge of a arveting zone, it follow tat M =,were P ηp pr x denote te mallet integer larger tan or equal to x. Note tat M =1correpond to te cae were te battery i fully carged witin one lot time; tu ti cae i referred to a ingle-lot carging. Similarly, te cae of M =2i referred to a double-lot carging. It will be own in ti ection tat if M =1or M =2, te battery power level can be exactly modeled by a finite-tate Markov cain; ence, te tranmiion probability p t can be obtained. However, for multi-lot carging wit M>2, only upper and lower bound on p t are obtained baed on te Markov cain analyi for te cae of M =2. A. Single-Slot Carging (M =1) If <P ηp p r, te battery of an ST i fully carged witin a lot, i.e., M =1. It tu follow tat te battery power level can only be eiter or P at te beginning of eac lot. Conider te finite-tate Markov cain wit tate pace {, 1} wit tate and 1 denoting te battery level of power and P, repectively. Furtermore, let P 1 repreent te tate-tranition probability matrix tat can be obtained a [ ] 1 p p P 1 = (12) p g 1 p g wit p g and p given in (4) and (9), repectively. Ten p t can be obtained by finding te teady-tate probability of te aumed Markov cain, a given in te following propoition. Propoition 3.1: If <P ηp p r or M =1(inglelot carging), te tranmiion probability of a typical ST i given by p t = p p g (13) p + p g = (1 e πr2 λp )e πr2 g λp. (14) 1 e πr2 λp + e πr2 g λp Proof: Let te teady-tate probability of te two-tate Markov cain be denoted by π 1 =[π 1,,π 1,1 ],wereπ 1 i

5 4792 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 9, SEPTEMBER 213 State 2 P 1 p 1 r State P pg p1 p2 b(x, 1 ) a(x, 1,r ) X Fig. 3. Divided arveting zone for te cae of double-lot carging (M = 2). te left eigenvector of P 1 correponding to te unit eigenvalue uc tat π 1 P 1 = π 1. (15) From (15), te teady-tate ditribution of te battery power level at a typical ST i obtained a π 1, = p g, π 1,1 = p. (16) p + p g p + p g Note tat te probability tat an ST i fully carged at te beginning of eac lot a defined in (1) i p f = π 1,1 in ti cae. Conequently, from (1), te deired reult in (13) i obtained. It i oberved from (14) tat in te ingle-lot carging cae, p t depend only on λ p, r and r g, but i not related to P.Te reaon i tat te battery of an ST i guaranteed to be fully carged over one lot if it get into a arveting zone; ence, te probability tat an ST i fully carged p f = π 1,1 = p p +p g doe not depend on P. B. Double-Slot Carging (M =2) If ηp p r < P 2ηP p r or M = 2, an ST need at mot 2 lot of arveting to make te battery fully carged. To etabli te Markov cain model for ti cae, we divide te arveting zone b(x, r ) into two dijoint region, ( ) 1 b(x, 1 ) and a(x, 1,r ), were 1 = P ηp p < r and a(t,x,y) = b(t,y)\b(t,x) denote te annulu wit radii <x<ycentered at T R 2. It ten follow tat te region b(x, 1 ) conit of te location at wic te power arveted by a typical ST Y from PT X i greater tan or equal to P (i.e., ingle-lot carging region), wile te region a(x, 1,r ) correpond to te location at wic te power arveted by Y i greater tan or equal to 1 2 P but maller tan P (ee Fig. 3). For convenience, we define H 1 = X Φ p b(x, 1 ) and H 2 = X Φ p a(x, 1,r ).Note tat H = H 1 H 2. We reaonably aume tat H 1 and H 2 are dijoint ince te arveting zone are mot likely dijoint a mentioned in Section II-B. Conider a 3-tate Markov cain wit tate pace {, 1, 2}. Since te battery power level can only be eiter or in te range [ 1 2 P,P ] ince ηp p r 1 2 P in ti cae, we define tate a te battery level of power, tate 1 wit te power level in te range [ 1 2 P,P ),andtate2 wit te power level equal to P. Note tat in order to tranit from tate to 1, State (a) Battery power tate of ST 1 pg 2 p 1 (b) Markov cain model 1 p Fig. 4. Te battery power tate for te cae of M =2and te correponding 3-tate Markov cain model, were (a) ow an example of te ST being in tate 1 of te Markov model in (b), i.e., te current battery power level i in te range [ 1 2 P,P). to 2, and1 to 2, te arveted power at Y need to be 1 2 P ηp p R <P, ηp p R P,andηP p R 1 2 P, repectively (or equivalently Y need to be inide H 2, H 1, and H, repectively). Tank to te fact tat te minimum carging power i alway larger tan or equal to 1 2 P in ti cae, we can determine te probability of te tranition from tate 1 to 2, i.e., from te battery power level in te range of [ 1 2 P,P ) to P, wic occur wen Y i (anywere) inide a arveting zone (ee Fig. 4(a)). Accordingly, te tatetranition probability matrix for te aumed 3-tate Markov cain (ee Fig. 4(b)) i given a P 2 = 1 p p 2 p 1 1 p p, (17) p g 1 p g were p 1 =Pr{Y H 1 } and p 2 =Pr{Y H 2 }. Notice tat p 1 + p 2 = p =1 e πr2 λp,inceh 1 H 2 = H and we ave aumed tat H 1 and H 2 are dijoint et. Similarly to (7), te probability p 1 i given a and p 2 i given a p 1 =Pr{Y H 1 } (18) =1 e π2 1 λp, (19) p 2 = p p 1 (2) = e π2 1 λp e πr2 λp. (21) Ten we can obtain p t for ti cae a given in te following propoition. Propoition 3.2: If ηp p r <P 2ηP p r or M =2 (double-lot carging), te tranmiion probability of a typical ST i given by p t = = p p + p g (1+ p2 p )p g (22) (1 e πr2 λp )e πr2 g λp 1 e πr2 λp + e πr2 g λp ( 1+ e π2 1 λp e πr2 λp 1 e πr2 λp ). (23) Proof: Te reult in (22) can be obtained by following te imilar procedure a in te proof of Propoition 3.1, i.e., by olving π 2 P 2 = π 2,wereπ 2 i te teady-tate probability vector given by π 2 =[π 2,,π 2,1,π 2,2 ]. Ten, we obtain p f = π 2,2 and ten (22) i obtained from (1).

6 LEE et al.: OPPORTUNISTIC WIRELESS ENERGY HARVESTING IN COGNITIVE RADIO NETWORKS X b(x, 1 ) a(x, 1, 2 ) a(x, 2,r ) Fig. 5. Divided arveting zone for te cae of M > 2. In ti cae, te amount of power arveted from PT X in a(x, 2,r ) i eiter overetimated a 1 P or underetimated a to obtain an upper/lower bound 2 on p t in Section III-C. It i wort noting from (23) tat p t in ti cae i a ( ) 1 decreaing function of P ince 1 = P ηp p in (23) i uc a function. In oter word, if P increae wit fixed P p and r, ten te ize of b(x, 1 ) (ingle-lot carging region) become maller, wic reult in an ST arveting for two lot to be fully carged more frequently, and tu a maller p f. Hence, p t become maller a well given p t = p f p g in (1). C. Multi-Slot Carging (M >2) For multi-lot carging wit P > 2ηP p r or M>2, te minimum carging power at te edge of te arveting zone, ηp p r, i maller tan 1 2 P. Unlike te previou two cae of M =1and M =2, te battery power level in ti cae cannot be caracterized exactly by a finite-tate Markov cain ince it i not poible in general to uniquely determine te tate-tranition probabilitie. 2 However, we ave own tat for te cae of M =2, te battery power level can indeed be caracterized wit a 3-tate Markov cain regardle of te fact tat we do not know te exact value of te battery power level in tate 1, but rater only know it range [ 1 2 P,P ), provided tat te minimum carging power ηp p r i no maller tan 1 2 P. Baed on ti reult, we obtain bot te upper and lower bound on p t for te cae wit M>2a follow. A own in Fig. 5, we divide te arveting zone into 3 dijoint region b(x, 1 ), a(x, 1, 2 ),anda(x, 2,r ), were < 1 < 2 <r wit 1 given in te cae of M =2 ( ) 1 and 2 = P 2ηP p. Note tat b(x, 1 ) i alo defined in te cae of M =2, wile te region a(x, 1, 2 ) conit of te location in b(x, r ) at wic te power arveted from PT X i larger tan or equal to 1 2 P, but maller tan P,and te region a(x, 2,r ) conit of te remaining location in b(x, r ) at wic te arveted power i maller tan 1 2 P. Ten, if we aume tat te power arveted from a PT in te region a(x, 2,r ) i equal to 1 2 P (an overetimation), 2 For intance, if M =3, following te previou two cae, we may divide te battery power level into 4 level a, [ 1 3 P, 2 3 P), [ 2 P,P), andp 3 and matc eac level to te tate, 1, 2, and3, repectively. Ten it can be eaily own tat te tranition probabilitie are unknown for ome of te tate tranition, e.g., from tate 1 to 2. r we can obtain an upper bound on p t ; owever, if we aume it i equal to (an underetimation), we can ten obtain a lower bound on p t, by applying a imilar analyi over te 3-tate Markov cain a for te cae of M = 2.For convenience, we define te following mutually excluive et A 1 = X Φ p b(x, 1 ), A 2 = X Φ p a(x, 1, 2 ), and A 3 = X Φ p a(x, 2,r ),werea 1 = H 1 and A 1 A 2 A 3 = H. Letp 2 =Pr{Y A 2 } and p 3 =Pr{Y A 3 }. It ten follow tat p 1 + p 2 + p 3 = p,werep 1 i given in (19) and p 2 =Pr{Y A 1 A 2 } Pr{Y A 1 } = e πλp2 1 e πλ p 2 2, (24) p 3 = p p 1 p 2 = e πλp2 2 e πλ pr 2. (25) Te following propoition i ten obtained. Propoition 3.3: If P > 2ηP p r or M > 2, tetranmiion probability of an ST i bounded a p 1 + p 2 p ) p g <p t < ( ) p g. (p 1 + p 2 (1+ )+pg p 2 p 1 p +p + p g 1+ p 2 +p 3 2 p (26) Proof: Pleae refer to te longer verion of ti paper [29]. It i wort mentioning tat te upper bound on p t i a ( ) 1 P decreaing function of P ince 1 = ηp p. Alo note tat te bound in (26) are tigt in te cae of M =1or M =2,incep 2 = p 3 =wit M =1,andp 2 = p 2 and p 3 =wit M =2, tu leading to te ame reult in (13) and (22), repectively. Note tat unlike te cae of M = 2, it i not poible to verify in general weter p t for te cae of M>2i a decreaing function of P or not; owever, it i conjectured to be o ince a larger value of P will generally render an ST pend more time to be fully carged. We verify ti by imulation in te following ubection (ee Fig. 6). D. Numerical Example To verify te reult on p t, we provide numerical example a own in Fig. 6, 7, and 8. For all of tee example, we et te pat-lo exponent a =4and te arveting efficiency a η =.1. In Fig. 6, we ow ST tranmiion probability p t veru ST tranmiion power P. It i wort noting tat M =1if <P ηp p r, M =2if ηp pr <P 2ηP p r,and M>2if P > 2ηP p r. It i oberved tat p t i contant if M =1, but i a decreaing function of P if M =2,wic agree wit te reult in (14) and (23), repectively. It i alo own tat if M > 2, p t i till a decreaing function of P a we conjectured. Moreover, te upper bound and lower bound on p t obtained in (26) for M>2are depicted in ti figure. Tee bound are oberved to be tigt wen M =1 and M =2, wile tey get looer wit increaing P wen M>2. Te reaon i tat te ize of te region a(x, 2,r ) own in Fig. 5, in wic we overetimate or underetimate te arveted power, enlarge wit increaing P.However, ince only mall value of P i of our interet, we can aume tat tee bound are reaonably accurate for mall value of M.

7 4794 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 9, SEPTEMBER M=1 (P =.1): Simulation ST tranmiion probability M=1 M=2 M>2 Simulation Lower bound Upper bound ST tranmiion probability M=1 (P =.1): Analyi M=2 (P =.2): Simulation M=2 (P =.2): Analyi Guard zone radiu ST tranmiion power Fig. 6. ST tranmiion probability p t veru ST tranmiion power P, wit λ p =.1, r g =4, r =1.5, andp p =2. Fig. 8. ST tranmiion probability p t veru te radiu of guard zone r g, wit λ p =.1, r =1,andP p = ST tranmiion probability M=1 (P =.1): Simulation M=1 (P =.1): Analyi M=2 (P =.2): Simulation M=2 (P =.2): Analyi Cumulative ditribution function Exact I (P =.1) Approximated I (P =.1) Exact I (P =.2) Approximatec I (P =.2) PT denity Fig. 7. ST tranmiion probability p t veru PT denity λ p, wit r g =3, r =1and P p = x x 1 4 Fig. 9. Te CDF of exact I and approximated I (baed on Aumption 1) wit =4, η =.1, r g =3, r =1, λ =.2, λ p =.1, andp p =2. Fig. 7 ow p t veru PT denity λ p. It i oberved tat for bot M =1and M =2, p t firt increae wit λ p wen λ p i mall but tart to decreae wit λ p wen λ p become ufficiently large. Ti can be explained a follow. If λ p i mall, increaing λ p i more beneficial ince eac ST will get carged more frequently and tu be able to tranmit (i.e., p f increae more ubtantially tan te decreae of p g ). However, after λ p exceed a certain treold, increaing λ p will more pronounce te effect of guard zone and tu make ST tranmit le frequently (i.e., p g decreae more ubtantially tan te increae of p f ). In Fig. 8, we ow p t veru te guard zone radiu r g.iti oberved tat p t i a decreaing function of r g. Intuitively, ti reult i expected ince larger r g reult in ST tranmitting le frequently, i.e., maller value of p g, and it i known from (1) tat p t = p f p g. IV. OUTAGE PROBABILITY In ti ection, te outage probabilitie of bot te primary and econdary network are tudied. Let Φ t denote te point proce of te active (tranmitting) ST. In addition, let I p and I indicate te aggregate interference at te origin from all PT and active ST, repectively, wic are modeled by otnoie procee [28], given by I p = X Φ p g X P p X and I = Y Φ t g Y P Y, repectively. Note tat in general, due to te preence of te guard zone and/or arveting zone, in eac time lot, te point proce Φ t i not necearily an HPPP; tu, I i not te ot-noie proce of an HPPP. Accordingly, te outage probabilitie P (p) out and P () out for primary and econdary network, bot related to I, are difficult to be caracterized exactly. To overcome ti difficulty, we make te following aumption on te proce of active ST. Aumption 1: Te point proce of active ST Φ t i an HPPP wit denity p t λ. It i own in Fig. 9 tat te cumulative ditribution function (CDF) of I,givenbyPr{I x}, obtained by imulation, can be well approximated by tat of approximated I baed on Aumption 1. Furter verification of Aumption 1 will be given later by imulation (ee Fig. 11 and 12). Let Λ(λ) denote te HPPP wit denity λ >. Under Aumption 1, te ditribution of Φ t i te ame a tat of

8 LEE et al.: OPPORTUNISTIC WIRELESS ENERGY HARVESTING IN COGNITIVE RADIO NETWORKS 4795 Y o.55.5 r g r g d Outage probability Primary: Exact Primary: Approximation (Lemma 4.1) Secondary: Exact Secondary: Approximation (Lemma 4.2) SINR treold (θ or θ ) p Fig. 1. A typical SR located at te origin, for wic tere i no PT inide te aded region b(y o,r g). Λ(p t λ ). It tu follow tat I can be rewritten a I = g Y P Y. (27) Y Λ(p tλ ) Conider firt te outage probability of te primary network, P (p) out, wic can be caracterized by conidering a typical PR located at te origin. Slivnyak teorem [28] tate tat an additional PT correponding to te PR at te origin doe not affect te ditribution of Φ p. Terefore, te outage probability of te PR at te origin i expreed a { P (p) gp P p d } p out =Pr I p + I + σ 2 <θ p, (28) were g p i te cannel power between te PR at te origin and it correponding PT, and σ 2 i te AWGN power. Ten, P (p) out i obtained in te following lemma. Lemma 4.1: Under Aumption 1, te outage probability of a typical PR at te origin i given by were ( τ p = P (p) out =1 exp ( τ p ), (29) λ p + p t λ ( P P p ) 2 ) θ 2 p d 2 p ϕ + θ pd p σ 2 P p, (3) ϕ = π 2 Γ( 2 )Γ(1 2 ), wit Γ(x) = y x 1 e y dy denoting te Gamma function. Proof: Pleae refer to [29]. Next, conider te outage probability of te econdary network, P () out, wic can be caracterized by a typical SR located at te origin. Note tat tere mut be an active ST, denoted by Y o, correponding to te SR at te origin. Since an ST cannot tranmit if it i inide any guard zone, to accurately approximate P () out under Aumption 1, we conider te outage probability conditioned on tat Y o i outide all te guard zone and tu tere i no PT inide te dik of radiu r g centered at Y o (ee Fig. 1). Let te event in te above condition be denoted by E = {Φ p b(y o,r g )= }. Ten Fig. 11. Outage probability of primary and econdary network veru SINR treold, wit = 4, η =.1, d p = d =.5, r g = 3, r = 1, λ p =.1, λ =.1, P p =1,andP =.1. te outage probability of a typical SR at te origin can be obtained a { P () g P d } out =Pr I p + I + σ 2 <θ E, (31) were g i te cannel power between te SR at te origin and te correponding ST Y o. From te law of total probability we ave { } { gpd gp I p+i +σ <θ 2 Pr d } I p+i +σ <θ 2 Ē Pr{Ē} Pr P () out = Pr{E} (32) Note tat Ē = {Φ p b(y o,r g ) }. Ten we ave te following lemma. Lemma 4.2: Under Aumption 1, te outage probability of te typical SR at te origin i approximated by were ( τ = P () out 1 exp ( τ ) (1 p g ) p g, (33) λ p ( P P p ) 2 + pt λ ) θ 2 d 2 ϕ + θ d σ 2 P. (34) Proof: Pleae refer to [29]. Altoug I can be well approximated by (27) baed on Aumption 1, it i wort mentioning tat te approximated reult of P (p) out and P () out in Lemma 4.1 and 4.2, repectively, are valid only wen P p P,aaumedintipaperforte following reaon. Firt, to derive P (p) out under Aumption 1, ST are uniformly located and tu can be inide te guard zone correponding to te typical PR at te origin, and a a reult caue interference to te PR. However, if we aume P p P, te interference due to ST inide ti guard zone i negligible and tu can be ignored. Next, to derive P () { gp d. out,a } own in [29, Appendix C], te term Pr I p+i +σ <θ 2 Ē in (32) can be aumed to be 1 only wen P p P.In Fig. 11 and 12, we compare te outage probabilitie obtained by imulation and toe baed on te approximation in (29)

9 4796 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 9, SEPTEMBER Outage probability Primary: Approximation (Lemma 4.1) Primary: Exact Secondary: Approximation (Lemma 4.2) Secondary: Exact Optimal ST tranmiion power ε p =.1 ε p =.2 ε p = ST tranmiion power PT denity Fig. 12. Outage probability of primary and econdary network veru ST tranmiion power P, wit =4, η =.1, d p = d =.5, r g =4, r =1, λ =.2, λ p =.1, θ p = θ =5,andP p =2. Fig. 13. Optimal ST tranmiion power P veru PT denity λp, wit = 4, d p = d =.5, r = 1, r g = 3, P p = 2, ɛ =.3, and θ p = θ =5. and (33). It i oberved tat our approximation are quite accurate and tu Aumption 1 i validated. In addition, it can be inferred from (33) and (34) tat P () out i in general a decreaing function of P,inceτ i a decreaing function of P. Ti implie tat large ST tranmiion power P i beneficial to reducing te econdary network outage probability, altoug larger P alo increae te interference level from oter active ST. Ti can be explained by te fact tat if P i increaed, te increae of received ignal power by te SR at te origin can be own to be more ignificant tan te increae of interference power from all oter active ST. On te oter and, from (29) and (3), it i analytically i a decreaing or increaing function of P. Ti i becaue in general tere i a tradeoff for etting P to minimize te primary outage probability, ince larger P increae te interference level from active ST difficult to ow weter P (p) out (reulting in larger P (p) out ) but at te ame time reduce te ST tranmiion probability p t (ee Fig. 6) and tu te number of active ST (reulting in maller P (p) out ). In Fig. 12, we ow te outage probabilitie P (p) out i oberved tat P () P (p) and P () out veru P, repectively. It out i a decreaing function of P, werea out i quite inenitive to te cange of P. V. NETWORK THROUGHPUT MAXIMIZATION In ti ection, te patial trougput of te econdary network defined in (11) i invetigated under te primary and econdary outage contraint. To be more pecific, wit fixed P p, λ p, r g,andr, te trougput of te econdary network C i maximized over P and λ under given ɛ p and ɛ.te optimization problem can tu be formulated a follow. (P1) : max. P,λ p t λ log 2 (1 + θ ) (35).t. P (p) out ɛ p (36) P () out ɛ, (37) were P (p) out and P () out are given by (29) and (33), repectively. Wit oter parameter being fixed, te tranmiion probability p t i in general a function of P (cf. Section III). Tu, we denote p t a p t (P ) in te equel. Since log 2 (1 + θ ) in (35) i a contant and P (p) out, P () out are monotonically increaing function of τ p and τ, repectively (ee (29) and (33)), (P1) i equivalently expreed a max. P,λ p t (P )λ (38).t. τ p μ p (39) τ μ, (4) were μ p = ln(1 ɛ p ) and μ = ln((1 ɛ )p g ). Note tat μ p and μ are increaing function of ɛ p and ɛ, repectively. In general, it i callenging to find a cloed-form olution for (38) wit σ 2 >. However, if we aume tat te network i primarily interference-limited, by etting σ 2 =,a cloed-form olution for (P1) can be obtained a given in te following teorem. Teorem 5.1: Auming σ 2 =, te maximum trougput of te econdary network i given by C = μ (μ p ϕθ 2 p d 2 pλ p ) log θ 2 2 (1 + θ ), (41) d 2 μ pϕ were te optimal ST tranmit power i P = θ ( ) ( ) d μ 2 Pp, (42) θ p d p μ p and te optimal ST denity i λ = μ (μ p ϕθ 2 p d 2 p λ p). (43) p t (P )θ 2 d 2 μ p ϕ Proof: Pleae refer to [29]. Note tat ince p t (P ) a been obtained in cloe-form for te cae of <P 2ηP pr (i.e., M =1or M =2in Section III), te optimal ST denity λ in (43) can be obtained exactly for ti cae, according to (14) and (23). Oterwie, only upper and lower bound on λ can be obtained, baed on (26).

10 LEE et al.: OPPORTUNISTIC WIRELESS ENERGY HARVESTING IN COGNITIVE RADIO NETWORKS 4797 Maximum econdary patial trougput ε p =.1 ε p =.2 ε p = PT denity Fig. 14. Maximum econdary patial trougput C veru PT denity λp, wit =4, d p = d =.5, r =1, r g =3, P p =2, ɛ =.3, and θ p = θ =5. in (39), i.e., reducing te network interference level. However, wen ɛ p i relatively larger (e.g., ɛ p =.2 or.3 in Fig. 14), (4) prevail over (39). A a reult, if λ p i increaed, ten o i μ in (4), and tu p t λ or C will be increaed. However, if λ p exceed a certain treold, p t λ will be decreaed to reduce τ in (4); a a reult, C decreae wit increaing λ p. It i revealed from (43) tat for given λ p, te optimal active ST denity p t (P )λ i fixed under a given pair of primary and econdary outage contraint. In oter word, λ i inverely proportional to p t (P ). Ti implie tat a p t converge to zero wit λ p (ee Fig. 7), λ diverge to infinity at te ame time, a own in Fig. 15. Tu, altoug te pare PT denity will lead to larger econdary network trougput (ee Fig. 14), a correpondingly large number of ST need to be deployed to acieve te maximum trougput, eac wit a very mall tranmiion probability p t. A a reult, only a mall fraction of te ST could be active at any time, reulting in large delay for econdary tranmiion or inefficient econdary network deign. Optimal ST denity ε p =.1 ε p =.2 ε p = PT denity Fig. 15. Optimal ST denity λ veru PT denity λ p, wit =4, d p = d =.5, r =1, r g =3, P p =2, ɛ =.3, andθ p = θ =5. Some remark are in order. It i wort noting tat μ = ln((1 ɛ )p g ) in (4) i an increaing function of PT denity λ p,incep g given in (4) i a decreaing function of λ p. Hence, te optimal ST tranmiion power P given in (42) decreae wit increaing λ p. Ti reult i own in Fig. 13, wit tree different value of ɛ p. In Fig. 14, we ow te maximum econdary patial trougput C given in (41) veru λ p wit ɛ p =.1,.2, or.3. Note tat from te perpective of RF energy arveting, larger λ p i beneficial to te econdary network trougput. However, it i oberved tat if ɛ p =.1, C decreae wit λ p, wlie for ɛ p =.2 or.3, C firt increae wit λ p wen λ p i mall but eventually tart to decreae wen λ p exceed a certain treold. Te reaon of ti penomenon can be explained a follow. Wen ɛ p i mall a compared wit ɛ (e.g., ɛ p =.1 in Fig. 14), te contraint in (39) prevail over tat in (4), i.e., atifying (39) i ufficient to atify (4), but not vice vera. Terefore, in ti cae, if λ p i increaed, te active ST denity p t λ or C will be decreaed to reduce τ p VI. APPLICATION AND EXTENSION In ti ection, we extend our reult on te CR network to te application cenario depicted in Fig. 2, were a et of ditributed wirele power carger (WPC) are deployed to power wirele information tranmitter (WIT) in a enor network. It i aumed tat wirele power tranmiion from WPC to WIT i over a dedicated band wic i different from tat for te information tranfer, and tu doe not interfere wit wirele information receiver (WIR). For implicity, we aume tat te pat-lo exponent for bot te power tranmiion and information tranmiion are equal to. Moreover, te network model for WPC and WIT a well a te energy arveting and tranmiion model of WIT are imilarly aumed a in Section II for PT and ST in te CR etup. For convenience, we tu ue te ame ymbol notation for PT and ST to repreent for WPC and WIT, repectively. A. Tranmiion Probability Unlike te CR cae, WIT in a enor network do not need to be prevented from tranmiion by guard zone, ince tere are no PT preent. A a reult, a WIT can tranmit at any time provided tat it i fully carged. By letting r g =,we ave p g = 1, and from (14), (23) and (26) we obtain te tranmiion probability of a typical WIT in te following corollary. Corollary 6.1: Te tranmiion probability of a typical WIT i given by 1) If <P ηp p r or M =1, 2) If ηp p r p t = <P 2ηP p r or M =2, p t = p 1+p. (44) p p +1+ p2 p. (45)

11 4798 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 9, SEPTEMBER 213 WIT tranmiion probability M=1 (P =.1): Simulation M=1 (P =.1): Analyi M=2 (P =.2): Simulation M=2 (P =.2): Analyi WPC denity Fig. 16. WIT tranmiion probability p t veru WPC denity λ p, wit =4, η =.1, r =1, r g =3,andP p =1. 3) If P > 2ηP p r p 1 + p 2 p 1 + p p 2 p 1+p 2 or M>2, p t p p +1+ p 2 +p3 p, (46) were p =1 e πr2 λp i given in (9); p 1 =1 e π2 1 λp and p 2 = e π2 1 λp e πr2 λp are given in (19) and (21), repectively; p 2 = e πλp2 1 e πλ p 2 2 and p3 = e πλp2 2 e πλpr2 are given in (24) and (25), repectively. It i wort noting tat unlike te CR etup, p t in ti cae i in general an increaing function of λ p ince tere are no guard zone and tu larger λ p alway elp carge WIT more frequently, a own in Fig. 16. B. Network Trougput Maximization Note tat unlike te CR etup, ere we only need to conider te outage probability of a typical WIR at te origin due to te interference of oter active WIT. Similar to Aumption 1, we aume tat active WIT form an HPPP wit denity p t λ ; tu, te outage probability of a typical WIR at te origin can be obtained by implifying Lemma 4.1 a { P () g P d } out =Pr I + σ 2 <θ (47) =1 exp ( τ ), (48) were in ti cae τ i given by τ = θ 2 d 2 ϕp t λ + θ d σ 2. (49) P For te enor network trougput maximization, Problem (P1) can be modified uc tat only te outage contraint for te WIR i applied. Tu we ave te following implified problem. (P2) : max. p t (P )λ log 2 (1 + θ ) (5) P,λ.t. P () out ɛ. (51) Te olution of (P2) i given in te following corollary, baed on Teorem 5.1. Corollary 6.2: Auming σ 2 =, te maximum network trougput i given by μ C = log θ 2 2 (1 + θ ), (52) d 2 ϕ were μ = ln(1 ɛ ), and te optimal olution (P,λ ) R + R + i any pair atifying p t (P )λ = μ. (53) θ 2 d 2 ϕ Proof: Pleae refer to [29]. Note tat unlike te reult in Teorem 5.1, te maximum network trougput remain contant regardle of λ p.ti i becaue tere i no primary outage contraint in ti cae and tu te optimal denity of active WIT p t (P )λ i determined olely by te outage contraint of WIR. On te oter and, if λ p i increaed, we can effectively reduce te required WIT denity λ for acieving te ame C ince p t in general increae wit λ p. VII. CONCLUSION In ti paper, we ave propoed a novel network arcitecture enabling econdary uer to arvet energy a well a reue te pectrum of primary uer in te CR network. Baed on tocatic-geometry model and certain aumption, our tudy revealed ueful inigt to optimally deign te RF energy powered CR network. We derived te tranmiion probability of a econdary tranmitter by conidering te effect of bot te guard zone and arveting zone, and tereby caracterized te maximum econdary network trougput under te given outage contrain for primary and econdary uer, and te correponding optimal econdary tranmit power and tranmitter denity in cloed-form. Moreover, we owed tat our reult can alo be applied to te wirele enor network powered by a ditributed WPC network, or oter imilar wirele powered communication network. REFERENCES [1] T. Le, K. Mayaram, and T. Fiez, Efficient far-field radio frequency energy arveting for paively powered enor network, IEEE J. Solid- State Circuit, vol. 43, no. 5, pp , May 28. [2] A. M. Zungeru, L. M. Ang, S. Prabaaran, and K. P. Seng, Radio frequency energy arveting and management for wirele enor network, Green Mobile Device and Netw.: Energy Opt. Scav. Tec., CRC Pre, pp , 212. [3] R.J.M.Vuller,R.V.Scaijk,I.Dom,C.V.Hoof,andR.Merten, Micropower energy arveting, Elevier Solid-State Circuit, vol. 53, no. 7, pp , July 29. [4] D. Boucouica, F. Dupont, M. Latrac, and L. Ventura, Ambient RF energy arveting, 21 Int. Conf. Renew. Energie and Power Qual. [5] T. Paing, J. Son, R. Zane, and Z. Popovic, Reitor emulation approac to low-power RF energy arveting, IEEE Tran. Power Electron., vol. 23, no. 3, pp , May 28. [6] H. Jabbar, Y. S. Song, and T. T. Jeong, RF energy arveting ytem and circuit for carging of mobile device, IEEE Tran. Conumer Electron., vol. 56, no. 1, pp , Feb. 21. [7] C. K. Ho and R. Zang, Optimal energy allocation for wirele communication wit energy arveting contraint, IEEE Tran. Signal Proce., vol. 6, no. 9, pp , Sep [8] O. Ozel, K. Tutuncouglu, J. Yang, S. Uluku, and A. Yener, Tranmiion wit energy arveting node in fading wirele cannel: optimal policie, IEEE J. Sel. Area Commun., vol. 29, no. 8, pp , Sept. 211.

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Trend in Netw., NOW Publier, vol. 5, no. 2-3, pp , 212. [28] J. F. C. Kingman, Poion Procee. Oxford Univerity Pre, [29] S. Lee, R. Zang, and K. Huang, Opportunitic wirele energy arveting in cognitive radio network, Available: ttp://arxiv.org/ab/ Seungyun Lee received te B.S. degree in Scool of Electrical and Electronic Engineering from Yonei Univerity, Seoul, Korea, in 212. He i currently working toward i P.D. degree in te Electrical and Computer Engineering Department at te National Univerity of Singapore. Hi current reearc interet include wirele networking uing tocatic geometry, convex optimization, energy arveting, and wirele information and power tranfer. Rui Zang (S M 7) received te B.Eng. (Firt- Cla Hon.) and M.Eng. degree from te National Univerity of Singapore in 2 and 21, repectively, and te P.D. degree from te Stanford Univerity, Stanford, CA USA, in 27, all in electrical engineering. Since 27, e a worked wit te Intitute for Infocomm Reearc, A-STAR, Singapore, were e i now a Senior Reearc Scientit. Since 21, e a joined te Department of Electrical and Computer Engineering of te National Univerity of Singapore a an Aitant Profeor. Hi current reearc interet include multiuer MIMO, cognitive radio, cooperative communication, energy efficient and energy arveting wirele communication, wirele information and power tranfer, mart grid, and optimization teory. Dr. Zang a autored/coautored over 12 internationally refereed journal and conference paper. He wa te co-recipient of te Bet Paper Award from te IEEE PIMRC in 25. He wa te recipient of te 6t IEEE ComSoc Aia- Pacific Bet Young Reearcer Award in 21, and te Young Invetigator Award of te National Univerity of Singapore in 211. He i now an elected member of IEEE Signal Proceing Society SPCOM and SAM Tecnical Committee, and an editor for te IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS. Kaibin Huang (S 5 M 8) received te B.Eng. (firt-cla on.) and te M.Eng. from te National Univerity of Singapore in 1998 and 2, repectively, and te P.D. degree from Te Univerity of Texa at Autin (UT Autin) in 28, all in electrical engineering. Since Jul. 212, e a been an aitant profeor in te Dept. of Applied Matematic at Te Hong Kong Polytecnic Univerity (PolyU AMA), Hong Kong. He ad eld te ame poition in te Scool of Electrical and Electronic Engineering at Yonei Univerity, S. Korea from Mar. 29 to Jun. 212 and preently i affiliated wit te cool a an adjunct profeor. From Jun. 28 to Feb. 29, e wa a Potdoctoral Reearc Fellow in te Department of Electrical and Computer Engineering at te Hong Kong Univerity of Science and Tecnology. From Nov to Jul. 24, e wa an Aociate Scientit at te Intitute for Infocomm Reearc in Singapore. He frequently erve on te tecnical program committee of major IEEE conference in wirele communication. He will cair te Comm. Teory Symp. of IEEE GLOBECOM 214 and a been te tecnical co-cair for IEEE CTW 213, te track cair for IEEE Ailomar 211, and te track co-cair for IEE VTC Spring 213 and IEEE WCNC 211. He i an editor for te IEEE WIRELESS COMMUNICATIONS LETTERS and alo te IEEE/KICS JOURNAL OF COMMUNICATION AND NETWORKS. He i an elected member of te SPCOM Tecnical Committee of te IEEE Signal Proceing Society. Dr. Huang received te Outtanding Teacing Award from Yonei, Motorola Partnerip in Reearc Grant, te Univerity Continuing Fellowip at UT Autin, and Bet Paper Award from PolyU AMA and IEEE GLOBECOM 26. Hi reearc interet focu on te analyi and deign of wirele network uing tocatic geometry and multi-antenna limited feedback tecnique.