Sum Throughput Maximization for Heterogeneous Multicell Networks with RF-Powered Relays

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1 Sum Throughput Maxmzaton for Heterogeneous Multcell etworks wth RF-Powered Relays Al A. asr, Duy T. go, Xangyun Zhou, Rodney A. Kennedy, and Salman Durran Research School of Engneerng, Australan atonal Unversty, Canberra, Australa Emal: {al.nasr, xangyun.zhou, rodney.kennedy, School of Electrcal Engneerng & Computer Scence, Unversty of ewcastle, Australa. Emal: Abstract Ths paper consders a heterogeneous multcell network where the base staton BS) n each cell communcates wth ts cell-edge user wth the assstance of an amplfy-and-forward relay node. Equpped wth a power spltter and a wreless energy harvester, the relay scavenges RF energy from the receved sgnals to process and forward the nformaton. In the face of strong ntercell nterference and lmted rado resources, we develop a resource allocaton scheme that jontly optmzes ) BS transmt powers, ) power splttng factors for energy harvestng and nformaton processng at the relays, and ) relay transmt powers. To solve the hghly non-convex problem formulaton of sum-rate maxmzaton, we propose to apply the successve convex approxmaton SCA) approach and devse an teratve algorthm based on geometrc programmng. The proposed algorthm transforms the nonconvex problem nto a sequence of convex problems, each of whch s solved very effcently by the nteror-pont method. We prove that our developed algorthm converges to an optmal soluton that satsfes the Karush-Kuhn-Tucker condtons of the orgnal nonconvex problem. umercal results confrm that our jont optmzaton soluton substantally mproves the network performance, compared to the exstng soluton wheren only the receved power splttng factors at the relays are optmzed. I. ITRODUCTIO Heterogeneous multcell networks have been proposed as a promsng soluton for 5G communcaton standard []. In multcell networks, users at the cell edges can experence poor sgnal recepton beng out-of-drect-communcaton-range from the base statons BSs) and due to strong ntercell nterference. The vable soluton to ths crtcal ssue s the opportunstcally deployed relays whch connect to the macrocell BSs va wreless lnks and provde network coverage to the cell-edge users []. In addton, the performance of a heterogeneous multcell network s further enhanced wth coordnated multpont transmsson and recepton CoMP) technques, n whch BSs and relays cooperate wth one another to best serve the cell-edge users [3]. The opportunstc nature of relay deployments may restrct the access to a man power supply. Ths problem can be crcumvented by mplementng wreless energy harvestng technques at the relays, where energy s scavenged from the ambent propagatng electromagnetc waves n the rado frequency RF) [4] [8]. Wreless energy harvestng solutons are feasble for heterogeneous relays, whch only requre sgnfcantly low transmt power due to ther restrcted network coverage [9]. In a heterogeneous multcell network wth RF-powered relays, the key factors that determne the system performance nclude: The work of A. A. asr, X. Zhou, and S. Durran was supported n part by the Australan Research Councl s Dscovery Project fundng scheme project number DP40033). The work of D. T. go was supported n part by the Unversty of ewcastle s Early Career Researcher Grant G308. ) how effectvely the ntercell nterference s managed, ) how the lmted transmt power s allocated at the BSs, and ) how the harvested RF energy s utlzed at the relays. Exstng research efforts have partally addressed these central ssues. Consderng the downlnk of a multcell multuser nterference network, [0] proposed coordnated schedulng and power control algorthms for the macrocell BSs only. In [], resource allocaton schemes were specfcally developed for the remote rado heads a form of heterogeneous relays. Assumng smultaneous wreless nformaton and power transfer, [] consdered the power control problem for multuser broadband wreless systems wthout relays. In [3], an optmal power splttng rule was devsed for energy harvestng and nformaton processng at the self-sustanng relays of a multuser nterference network. However, [3] dd not address the mportant ssue of optmally controllng the transmt powers at the BSs and the relays. In ths paper, we consder a heterogeneous multcell network n whch the BS n each cell communcates wth ts cell-edge user va the assstance of an energy-constraned relay node. Employng CoMP, we assume that multple BSs cooperate to share the channel qualty measurements and to schedule the transmssons, allowng for more effcent rado resource utlzaton. Each relay n multcell network s equpped wth a wreless energy harvester that scavenges part of the RF energy n the receved sgnal. A power spltter s ncluded n the relay to decde the porton of the receved sgnal energy to be harvested. Usng the harvested energy, an nformaton transcever wll later amplfy and forward AF) the receved sgnal to ts correspondng user. Our am s to devse an optmal resource allocaton polcy for both the BSs and the energy-harvestng relays n order to maxmze the network sum throughput. Dfferent from the exstng works, we jontly optmze the transmt powers at the BSs and the relays, along wth fndng an optmal power splttng rule for energy harvestng and sgnal processng at the relays. Snce the optmzaton varables are strongly coupled wth many nonlnear cross-multplyng terms, the formulated problem s hghly nonconvex and thus challengng to solve. The man contrbutons of ths work are: We propose to adopt the successve convex approxmaton SCA) method and transform the problem to a seres of convex programs. Here, we specfcally talor the generc SCA framework to allow for the applcaton of geometrc programmng GP). To arrve at the convex program, we use the arthmetc-geometrc nequalty to condense a posynomal to a monomal. At each step of our proposed teratve /5/$ IEEE 96

2 algorthm, we effcently solve the resultng convex problem by the nteror-pont method. We prove that our developed algorthm generates a sequence of mproved feasble solutons, whch eventually converges to the solutons that satsfy the Karush-Kuhn-Tucker KKT) condtons of the orgnal nonconvex problem. Whle a true globally optmal method does not exst for the formulated problem, t s noted that SCA-based soluton often emprcally acheves the global optmum n most practcal scenaros [4] [6]. We confrm va numercal examples that our jont optmzaton approach sgnfcantly outperforms the exstng soluton that only optmzes how the receved power s splt at the relays. Cell Base Staton Relay User CP h, h 3, g, g 3, g, h, g, h, Cell II. SYSTEM MODEL AD PROBLEM FORMULATIO Consder the downlnk transmssons n an -cell heterogeneous network wth unversal frequency reuse,.e., the same rado frequences are used n all cells. We adopt CoMP and assume that the base statons BSs) are connected to a central processng CP) unt whch coordnates the multcellular transmssons and rado resource management. Let = {,...,} denote the set of all cells. In a cell, the BS attempts to establsh communcaton wth ts sngle cell-edge user. Assume that the users n the network are located n the sgnal dead zones, where no drect sgnal from any BSs can reach. To provde the network coverage to these dstant users, a relay node s deployed n each cell to assst the communcaton from the BS to ts user. Denote the channel coeffcent from BS to relay j as h,j, and that from relay j to user k as g j,k. We assume that all BSs send the avalable channel state nformaton to the CP unt va a dedcated control channel. In Fg., an example 3-cell heterogenous network wth relays s llustrated. The relays are assumed to be energy-constraned nodes,.e., they do not have any energy supply of ther own. Each of these relays s equpped wth a wreless energy harvester that scavenges energy n the receved RF sgnals from all BSs ncludng ts servcng BS and other nterferng BSs). At each relay, the harvested energy s used by an nformaton transcever to process and forward the message sgnal to the ntended user. We propose to dvde the total transmsson block tme T nto two equal tme slots. The frst tme slot ncludes BS-torelay transmssons and RF energy harvestng at the relays. Ths s done whle all the relays do not transmt. The second tme slot ncludes sgnal processng at the relays and relay-to-user transmssons. Ths s done whle all the BSs suppress ther transmssons. The operatons n each tme slot are llustrated n Fg., whch wll be detaled n the followng subsectons. A. BS-to-Relay Transmssons and Wreless Energy Harvestng at Relays In the frst tme slot [0,T/], let x be the normalzed nformaton sgnal sent by BS,.e., E{ x } =, where E{ } denotes the expectaton operator and the absolute value operator. Let P be the transmt power of BS, d h,j the ote that the network analyss and proposed solutons n ths paper are general; hence, they are vald for any cellular network geometry and can be straghtforwardly extended to the case of multple relays and multple users n a cell. Cell 3 h 3,3 g 3,3 ntended sgnal nterferng sgnal Fg.. An example heterogeneous multcell network consstng of three cells and a central processng CP) unt. Each cell has a base staton, a relay and a cell-edge user. For clarty, we only show the nterferng scenaros n cell,.e., at the recevers of relay and user. In general, the nterference occurs at the recevers of all three relays and three users. dstance between BS and relay j, and β the path-loss exponent. Assumng thatn a s the zero-mean addtve whte Gaussan nose AWG) wth varance σ a at the receve antenna of relay, the receved sgnal at relay can be expressed as y R = h, P x,j h j, Pj x j n a, ) where h j, h j, d h j, ) β/,,j, s the effectve channel gan from BS j to relay ncludng the effects of both smallscale fadng and large-scale path loss). To mplement dual energy harvestng and sgnal processng at the relays, we assume that each relay s equpped wth a power spltter that determnes how much receved sgnal energy should be dedcated to each of the two purposes [5], [7], [3]. As shown n Fg., the power spltter at relay dvdes the power of y R nto two parts n the proporton of α : α ). Here, α 0,) s termed as the power splttng factor. The frst part α y R s processed by the energy harvester and stored as energy e.g., by chargng a battery at relay ) for the use n the second tme slot. The amount of energy harvested at relay s gven by E = ηα T P j h j,, ) where η 0,) s the effcency of energy converson. The second part α y R of the receved sgnal s passed to an nformaton transcever. In Fg., n r denotes the AWG 97

3 nterference P BS h, n a y R Power Spltter α y R α y R Wreless Energy Harvester y R I E AF Informaton Transcever nterference g, User Relay n r T Frst tme slot: [ 0, T ] T Second tme slot: [ T,T] Fg.. BS-to-user communcaton asssted by a RF-powered relay wth zero mean and varance σ r ntroduced by the baseband processng crcutry. Snce antenna nose power σ a s very small compared to the crcut nose power σ r n practce [7], n a has a neglgble mpact on both the energy harvester and the nformaton transcever of relay. For smplcty, we wll thus gnore the effect of n a n the followng analyss by settng σ a = 0. The sgnal at the nput of the nformaton transcever of relay can be wrtten as y I R = α y R n r = α h, P x α,j h j, Pj x j n r, where the frst term n 3) s the desred sgnal from BS, and the second term s the total nterference from all other BSs. B. Sgnal Processng at Relays and Relay-to-User Transmssons In the second tme slot [T/,T], the nformaton transcever amplfes the sgnal yr I pror to forwardng t to user. Denote the transmt power of relay transceveras. Wth the harvested energy E n ), the maxmum power avalable for transmsson at relay s gven by E T/, whch means that E T = ηα P j h j,. 4) The transmtted sgnal from relay to user s gven by x R = ζ p yr I, 5) [ where ζ α ) / P j h j, σ] r s the amplfyng factor that ensures power constrant 4) be met. The receved sgnal at user s then gve by y U = ḡ, x R ḡ j, x Rj n u, 6),j 3) where ḡ j, g j, d g β/, j,),j, s the effectve channel gan from BS j to relay ncludng the effects of both smallscale fadng and large-scale path loss), d g,j denotes the dstance between relay and user j, n u the AWG wth zero mean and varance σ u at the recever of user. Usng x R n 5) and yr I n 3), we can wrte 6) explctly as y U = ζ ḡ, h, p P α )x ζ ḡ, p α ) ζ ḡ, p n r,j,j h j, Pj x j ζ j ḡ j, pj y I R j n u. 7) The frst term n 7) s the desred sgnal from BS to ts servced user, and the remanng terms represent the total ntercell nterference and nose. Wthout loss of generalty, let us assume σ r = σu = σ,. From 7), the sgnal-to-nterference-plus-nose rato SIR) at the recever of user s gven n 8) [see the bottom of ths page], where we defne ḡ, h j, σ ; h j, σ ; 3 ḡ j, σ ; φ,j,k 4 ḡ j, h k, σ. 9) For notatonal convenence, let us also defne P [P,...,P ] T,p [p,...,p ] T, and α [α,...,α ] T. From 8), the acheved throughput n bps/hz bts per second per Hz) of cell s then: τ ) = log γ ). 0) An mportant observaton from 8) and 0) s that by dedcatng more receved power at relay for energy harvestng.e. ncreasng α ), one mght actually degrade the end-to-end throughput n cell. Ths can be verfed upon dvdng both γ =,j P j α ) φ, P α ) ) P j α ) 3 p j,j k=,k 4 P k p j α ), 8) 98

4 the numerator and the denomnator of γ n 8) by α ). However f one opts to decrease α, the transmt power avalable at the nformaton transcever of relay wll be further lmted [see 4)], thus potentally reducng the correspondng data rate τ. Smlarly, ncreasng the BS transmt power P or the relay transmt power does not necessarly enhance the throughput τ of cell. The reason s that P and appear n the postve terms at both the numerator and the denomnator of γ. These observatons emphasze the mportance of fndng an optmal resource allocaton polcy for the consdered network. In ths paper, we wll devse an optmal tradeoff of all three parameters transmt power P at the BSs, transmt power p at the relays, and power splttng factor α at the relays. Wth the objectve of maxmzng the total network throughput, the desgn problem s formulated as follows max τ a) s.t. 0 α, b) P mn P P max, 0 ηα P j h j,,, c) d) where P max denotes the maxmum power avalable for transmsson at each BS andp mn s the mnmum transmt power requred at each BS to ensure the actvaton of energy harvestng crcutry at the relay. In ths formulaton, b) s the constrant for the power splttng factors at all relays. Constrants c) and d) ensure that the transmt powers at the BSs and relays do not exceed the maxmum allowable. Problem ) s hghly nonconvex n ) because the throughputτ n 0) s hghly nonconvex n these three varables. Even f we fx p and α and try to optmze P alone, τ would stll be hghly nonconvex n P due to the cross-cell nterference terms. Smultaneously optmzng P,p and α s much more challengng due to the nonlnearty ntroduced by the crossmultplyng terms, e.g., P k p j α n 8) and α P j n d). III. PROPOSED SCA SOLUTIO USIG GEOMETRIC PROGRAMMIG To effcently solve ), we propose to adopt the successve convex approxmaton SCA) approach [4] [6] to transform the orgnal nonconvex problems nto a sequence of convex subproblems. For our formulated problem, the key steps of the generc SCA framework are summarzed n Algorthm [8]. In applyng the SCA approach, there stll reman two key questons: ) How do we perform the approxmaton n Steps and 4 of Algorthm? ) Gven that the approxmaton s known, can we prove that the resultng algorthm converges to an optmal soluton? To answer the frst queston, we wll make use of the sngle condensaton approxmaton method [4] to form a relaxed geometrc program GP), nstead of drectly solvng the nonconvex problems ). A GP s expressed n the standard form as [9, Algorthm Successve Convex Approxmaton : Intalze wth a feasble soluton P [0],p [0],α [0] ). : At the m-th teraton, form a convex subproblem by approxmatng the nonconcave objectve functon and constrants of ) wth some concave functon around the prevous pont P [m ],p [m ],α [m ] ). 3: Solve the resultng convex subproblem to obtan an optmal soluton P [m],p [m],α [m] ) at the m-th teraton. 4: Update the approxmaton parameters n Step for the next teraton. 5: Go back to Step and repeat untl ) converges. p. 6]: mn y f 0 y) a) s.t. f y), =,...,m b) h l y) =, l =,...,M c) where f y), = 0,...,m are posynomals and h l y), l =,...,M are monomals. A GP n standard form s a nonlnear and nonconvex optmzaton problem because posynomals are not convex functons. However, wth a logarthmc change of the varables and multplcatve constants, one can turn t nto an equvalent nonlnear and convex optmzaton problem usng the property that the log-sum-exp functon s convex) [4], [9]. Frst, we express the objectve functon a) as max log γ ) max log mn γ ) 3a) γ, 3b) where 3b) follows from 3a) because log ) s monotoncally ncreasng functon. Upon substtutng γ n 8) to 3b) and replacng α by an auxlary varable t, t s shown that problem ) s equvalent to 4) [see the top of the next page], where t [t,,t ] T. It can be seen that 4) s not yet n the form of the GP ) because 4a) and 4d) are not posynomals. ow, let us defne: u x) v x),j P j t,j k= ) P jt 3 p j ) P j t P jt 3 p j,j k=,k 4 P k p j t, 5),k 4 P k p j t, 6) A monomal qy) s defned as qy) cy a ya...yan n, where c > 0, y = [y,y,...,y n] T R n, and a = [a,a,...,a n] T R n. A posynomal s a nonnegatve sum of monomals [9]. 99

5 mn,t,j P j t ) P jt 3 p j ) P j t P jt 3 p j,j k=,j k=,k 4 P k p j t,k 4 P k p j t s.t. t α, 4b) t 0, 0 ηα P,. j h j, 4d) b), c). 4a) 4c) where x = [P T,p T,t T ] T R 3. The objectve functon n 4a) can then be expressed as u x) v x). 7) As both u x) and v x) are posynomals, u x)/v x) s not a posynomal, confrmng that 4a) s also not a posynomal. To transform problem 4) nto a GP of the form n ), we would lke the objectve functon 7) to be a posynomal. To ths end, we propose to apply the sngle condensaton method [4] and approxmate v x) wth a monomal ṽ x) as follows. Gven the value of x [m ] at the m )-th teraton, we apply the arthmetc-geometrc mean nequalty to lower bound v x) by a monomal ṽ x) at the m-th teraton as [4, Lem. ] v x) ṽ x) v x [m ] )P j t P [m ] j v x [m ] )P j t P [m ] j t [m ],j k= v x [m ] )p j p [m ] j p [m ] t [m ] ) φ,j P[m ] t [m ] j v x [m ] ) ) φ,j 3 p[m ] j v x [m ] ) v x [m ] )P k p j t P [m ] k p [m ] j t [m ] ) φ,j P[m ] p [m ] t [m ] j v x [m ] ) v x [m ] ) ) φ,j,k 4 P [m ] k v x [m ] ) 8) p [m ] t [m ] j v x [m ] ) It can be verfed that v x [m ] ) = ṽ x [m ] ). In fact, ṽ x) s the best local monomal approxmaton to v x) near x [m ] n the sense of the frst-order Taylor approxmaton. Wth 8), the objectve functon u x)/v x) n 4a) s approxmated by u x)/ṽ x). The latter s a posynomal because ṽ x) s a monomal and the rato of a posynomal to a monomal s a posynomal. The upper bound u x)/ṽ x)) of 7) s also a posynomal snce the product of posynomals s a posynomal. ext, we wll approxmate the constrant d) by a posynomal for t to ft nto the GP form ). For ths, we lower bound. posynomal ηα P j h j, by a monomal as [4, Lem. ]: ηα P j h j, ηα P j k= P[m ] k h k, P [m ] j ) P[m ] h j j, k= P [m ] h k k, }{{} w α,p). 9) The rato /w α,p) s now a posynomal. Upon substtutng 8) and 9) nto 4), we can formulate an approxmated subproblem at the m-th teraton for problem ) as follows mn x,α s.t. u x) ṽ x) 0 w α,p), b), c), 4b), 4c). 0a) 0b) In 0a), snce v x) ṽ x) [see 8)], we are actually mnmzng the upper bound of the orgnal objectve functon n 4a). Wth 9), constrant 0b) s strcter than d) as: ηα P j h j,. ) w α,p) Referrng to ), t s seen that 0) belongs to the class of geometrc programmng,.e., a convex optmzaton problem. ote that the GP 0) s a convex approxmaton of the orgnal problem ). In Algorthm, we propose a GP-based SCA algorthm n whch an nstance of 0) s solved at each teraton. The followng result gves answer to the second queston stated at the begnnng of Secton III. Proposton : Algorthm generates a sequence of mproved feasble solutons that converge to a locally optmal pont x,α ) satsfyng the KKT condtons of the orgnal problem ). Proof: From 9), we have that ηα P j h j, ) /w α,p). Ths means that the optmal soluton of the approxmated problem 0) always belongs to the feasble set of the orgnal problem ). 00

6 Algorthm Proposed GP-based SCA Algorthm : Intalze m :=. : Choose a feasble pont x [0] P [0],p [0],t [0]) ) ;α [0]. 3: Compute the value of v x [0] ), accordng to 6). 4: repeat 5: Usngv x [m ] ), form the approxmate monomalṽ x) accordng to 8). 6: Usng the nteror-pont method, solve GP 0) to fnd an approxmated soluton x [m] P [m],p [m],t [m]) ) ;α [m] of ) at the m-th teraton. 7: Compute the value of v x [m] ), by 6). 8: Set m := m. 9: untl Convergence of x, α) y coordnate m) Cell Cell 3 Base Staton BS) Relay R) User U) Cell ext, snce v x) ṽ x), x R 3, t follows that: u x [m] ) v x [m] ) u x [m] ) ṽ x [m] ) = mn x u x) ṽ x) u x [m ] ) ṽ x [m ] ) = u x [m ] ) v x [m ] ), ) where the last equalty holds because ṽ x [m ] ) = v x [m ] ). As the actual objectve value of ) s non-ncreasng after every teraton, Algorthm wll eventually converge to a pont x,α ). Fnally, t can be verfed that and u x) v x)) x=x [m ] = ηα P j h j, = w α,p) ) ) u x), 3) ṽ x) x=x [m ] α=α [m ] ;P=P [m ] ) α=α [m ] ;P=P [m ], 4) where denotes the gradent operator. The results n 3)-4) mply that the KKT condtons of ) wll be satsfed after the seres of approxmatons nvolvng GP 0) converges to the pont x,α ). Ths completes the proof. IV. RESULTS Fg. 3 shows an example heterogeneous network where all cells have an equal cell radus of 00m. In cells and 3, we set the BS-relay and relay-user dstances as 4m and 5m, respectvely. In cell, the correspondng dstances are 4m and 48m. ote that the BS, relay and user n each cell do not le on a straght lne. We set the path loss exponent as β = 3. For small-scale fadng, we assume that the channel coeffcents h,j and g j,k,,j,k are crcularly symmetrc complex Gaussan random varables wth zero mean and unt varance. In the block fadng model, the randomly-generated values of h,j and g j,k reman unchanged n each tme block durng whch the resource allocaton takes place. Wth the channel bandwdth of 0kHz and the nose power densty of 74dBm/Hz, the total nose x coordnate m) Fg. 3. Topology of the heterogeneous multcell network used n the numercal examples. power s σ = 3dBm. At the relays, we set the energy harvestng effcency to η = 0.5 [0]. We ntalze Algorthm wth P [0] = ςp max ; α [0] = ς; t [0] = α [0] ; p [0] = P[0] j ςηα [0] h j,,, where ς 0,). To solve each convex problem n Algorthm, we resort to CVX, a package for specfyng and solvng convex programs []. Fg. 4 plots the convergence of the network sum throughput τ by Algorthm. Here, each teraton corresponds to solvng of a GP 0) by CVX. For all the parameter settngs that we consder, t s observed that the proposed algorthm quckly converges n around 4 teratons. As expected, the sum rate s almost doubled when a hgher BS transmt power budget of 46dBm s allowed nstead of 40dBm. In a multcell network settng, ncreasng the allowable transmt powers may trgger the power racng phenomenon among the users, thus worsenng the nterference stuaton. Our numercal results, on the other hand, confrm that the Algorthm effectvely manages the strong ntercell nterference n such cases and offers a maxmzed network performance. It s nfeasble to compare the performance of Algorthm wth that of a globally optmal soluton. There s no global optmzaton approach avalable n the lterature to solve the hghly nonconvex problem ). A drect exhaustve search would ncur a prohbtve computatonal complexty. However, Fg. 4 shows that the acheved throughput s nsenstve to the ntal ponts of Algorthm, further suggestng that the attaned soluton corresponds to the global optmum n our specfc example [4], [5]. Fg. 5 demonstrates the advantages of jontly optmzng P, p, α) as n Algorthm over ndvdually optmzng the power splttng factor α as proposed n [3]. In the latter approach, we set P = P max and = ηα P j h j,,. To obtan the results presented n the fgure, we average the sum throughput over, 000 ndependent smulaton runs where we take ς = 0.5. For P max n the range of 43 49dBm, the throughput acheved by Algorthm ncreases whereas that of [3] does not ncrease. It s also clear from Fg. 5 that 0

7 Sum throughput, τ bps/hz) P max = 46 dbm P max = 40 dbm ς = 0.0 ς = Iteratons Average Sum Throughpout bps/hz) Fg. 4. Convergence process of Algorthm. Algorthm Proposed) Algorthm n [3] P max dbm) Fg. 5. Performance comparson of Algorthm and the proposal n [3]. our proposed algorthm always outperforms that of [3]. Also for P max = 46dBm, whch s a typcal power constrant value [0], the proposed algorthm acheves double the throughput of algorthm n [3]. V. COCLUSIOS Ths paper has consdered the challengng problem of sum throughput maxmzaton n a heterogeneous multcell network wth RF-powered relays. Specfcally, we have attempted to jontly optmze the BS transmt powers, the relay power splttng factors and the relay transmt powers. To resolve the hghly nonconvex problem formulaton, we have proposed a successve convex approxmaton algorthm based on geometrc programmng. We have proven that the devsed algorthm converges to a locally optmal soluton that satsfes the KKT condtons of the orgnal nonconvex problem. umercal examples have demonstrated the clear advantages of our proposed algorthm over exstng approaches. REFERECES [] J. Andrews, S. Buzz, W. Cho, S. Hanly, A. Lozano, A. Soong, and J. Zhang, What wll 5G be? IEEE J. Sel. Areas Commun., vol. 3, no. 6, pp , Jun. 04. [] Y. A. Sambo, M. Z. Shakr, K. A. Qaraqe, E. Serpedn, and M. A. Imran, Expandng cellular coverage va cell-edge deployment n heterogeneous networks: Spectral effcency and backhaul power consumpton perspectves, IEEE Commun. Mag., vol. 5, no. 6, pp , Jun. 04. [3] P. Marsch and G. Fettwes, Coordnated Mult-Pont n Moble Communcatons From Theory to Practce. Cambrdge Unversty Press, 0. [4] Z. Chen, B. Wang, B. Xa, and H. Lu, Wreless nformaton and power transfer n two-way amplfy-and-forward relayng channels, ArXv Techncal Report, 03. [Onlne]. Avalable: v [5] Z. Dng, S. M. Perlaza, I. Esnaola, and H. V. Poor, Power allocaton strateges n energy harvestng wreless cooperatve networks, IEEE Trans. Wreless Commun., vol. 3, no., pp , Feb. 04. [6] I. Krkds, S. Tmotheou, and S. Sasak, RF energy transfer for cooperatve networks: Data relayng or energy harvestng? IEEE Commun. Lett., vol. 6, no., pp , ov. 0. [7] Z. Dng, I. Krkds, B. Sharf, and H. Poor, Wreless nformaton and power transfer n cooperatve networks wth spatally random relays, IEEE Trans. Wreless Commun., vol. 3, no. 8, pp , Aug. 04. [8] A. A. asr, X. Zhou, S. Durran, and R. A. Kennedy, Relayng protocols for wreless energy harvestng and nformaton processng, IEEE Trans. Wreless Commun., vol., no. 7, pp , Jul. 03. [9] H. S. Dhllon, Y. L, P. uggehall, Z. P, and J. G. Andrews, Fundamentals of heterogeneous cellular networks wth energy harvestng, IEEE Trans. Wreless Commun., vol. 3, no. 5, pp , May 04. [0]. Ksar, P. Banch, and P. Cblat, early optmal resource allocaton for downlnk OFDMA n -D cellular networks, IEEE Trans. Wreless Commun., vol. 0, no. 7, pp. 0 5, Jul. 0. [] D. W. K. g and R. Schober, Resource allocaton for coordnated multpont networks wth wreless nformaton and power transfer, n Proc. IEEE GLOBECOM, Austn, TX, USA, Dec. 04. [] K. Huang and E. Larsson, Smultaneous nformaton and power transfer for broadband wreless systems, IEEE Trans. Sgnal Process., vol. 6, no. 3, pp , Dec. 03. [3] H. Chen, Y. L, Y. Jang, Y. Ma, and B. Vucetc, Dstrbuted power splttng for swpt n relay nterference channels usng game theory, IEEE Trans. Wreless Commun., vol. 4, no., pp , Jul. 05. [Onlne]. Avalable: [4] M. Chang, C. W. Tan, D. P. Palomar, D. O ell, and D. Julan, Power control by geometrc programmng, IEEE Trans. Wreless Commun., vol. 6, no. 7, pp , Jul [5] J. Papandropoulos and J. S. Evans, SCALE: A low-complexty dstrbuted protocol for spectrum balancng n multuser DSL networks, IEEE Trans. Inf. Theory, vol. 55, no. 8, pp , Aug [6] D. T. go, S. Khakurel, and T. Le-goc, Jont subchannel assgnment and power allocaton for OFDMA femtocell networks, IEEE Trans. Wreless Commun., vol. 3, no., pp , Jan. 04. [7] L. Lu, R. Zhang, and K. C. Chua, Wreless nformaton and power transfer: a dynamc power splttng approach, IEEE Trans. Commun., vol. 6, no. 9, pp , Sep. 03. [8] A. A. asr, D. T. go, X. Zhou, R. A. Kennedy, and S. Durran, Jont resource optmzaton for multcell networks wth wreless energy harvestng relays, ArXv Techncal Report, 05. [Onlne]. Avalable: [9] S. Boyd and L. Vandenberghe, Convex Optmzaton. Cambrdge Unversty Press, 004. [0] X. Lu, P. Wang, D. yato, D. I. Km, and Z. Han, Wreless networks wth RF energy harvestng: A contemporary survey, IEEE Commun. Surveys Tuts., 04. [] M. Grant and S. Boyd, CVX: Matlab software for dscplned convex programmng, verson., Mar