Joint Power Allocation and Beamforming for Cooperative Networks

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1 It. J. Commuicatios, etwork ad System Scieces,, 4, doi:.436/ijcs Published Olie July ( Joit Power Allocatio ad Beamformig for Cooperative etworks Sodes Maadi,, oureddie Hamdi The atioal School of Egieerig of Tuis, El-Maar Uiversity, Tuis, Tuisia The Commuicatio System Laboratory, The atioal School of Egieerig of Tuis, El-Maar Uiversity, Tuis, Tuisia Received May 6, ; revised Jue 3, ; accepted Jue 5, Abstract I this paper, we ivestigate power allocatio problem with the use of trasmit beamformig i a dual hop MISO (multiple iput sigle output) relay chael. We cosider either amplify ad forwa () or decode ad forwa (DF) cooperative protocols at the relay ad optimize the power allocated to the relay ad the source, uder total trasmit power costrait, to miimize the bit error rate (BER) of relayig system. Cooperative commuicatio is viewed as a method for icreasig diversity gai ad reducig ed to ed path loss. The use of relay ca create a virtual atea array so that it allows users to exploit the advatages of multiple iput multiple output (MIMO) techiques. I this work, we solve cooperative ratio, which is defied as the ratio power used for cooperative trasmissio over the total power. This approach is the compared to a equal power assigmet method ad its performace ehacemet is verified by simulatio results. Keywos: Amplify ad Forwa, Decode ad Forwa, Trasmit Beamformig, Power Allocatio, MISO, Cooperative Commuicatio. Itroductio I recet years, cooperative diversity is cosidered as a potetial trasmit strategy for wireless etworks. The basic idea of cooperative trasmissio is to allow several trasmit odes i the etwork to help i oer to create a virtual atea array ad exploit spatial diversity at the destiatio [-3]. It has bee show i the literature [4], [5] that cooperative commuicatio ca avoid the difficulties of implemetig actual atea arrays ad covert the sigle iput sigle output (SISO) system ito a virtual multiple iput multiple output (MIMO) system. I this way, cooperatio betwee users allows them to exploit the diversity gai ad others advatages of MIMO system i a SISO wireless etwork. Several protocols have bee proposed to achieve the gais promised by the use of ode cooperatio. Two mai relay protocols are widely kow: amplify ad forwa () ad decode ad forwa (DF). meas that the received sigal is multiplied by a amplificatio gai ad the retrasmitted by the relay without performig ay decodig. I cotrast to this, the sigal is decoded at the relay ad re-ecoded for retrasmissio i (DF) strategy. A importat questio i cooperative commuicatio is power allocatio. Give the same total power, how much should be allocated to source iformatio trasmissio ad how much to relayig iformatio trasmissio. I [6], efficiet power allocatio strategy is ivestigated i a orthogoal etwork to satisfy the target SR requiremet. I [7], the achievable iformatio capacity is aalyzed to obtai optimal power allocatio ad parter selectio with the total power costraits for SIMO relay chaels. I [8], optimal power allocatio is studied to miimize the total eergy cosumptio satisfyig the BER target of the cooperative system. Most curret research cosiders trasmit beamformig ad distributed beamformig i relayig system. I [9], the performace of the DF protocol i multiple relay chaels with maximal ratio combiig (MRC) ad trasmit beamformig has bee aalyzed. I [], the performace of a two hop relay etwork with trasmit beamformig at the source ad MRC at the destiatio has bee aalyzed. Also, distributed beamformig over multiple relays is widely studied. For example, several distributed beamformig techiques usig strategy have bee recetly proposed i [,] that miimize the total relay trasmit power subject to the receive sigal-to- oise ratio (SR) costrait. Copyright SciRes. IJCS

2 448 M. MAADI ET AL. I this paper, we focus o the optimal cooperative ratio i the sese to miimize the average BER. For both ad DF relays, we solve cooperative ratio, which is defied as the ratio power used for cooperative trasmissio over the total power. I particular, we focus o /DF cooperatio scheme i a eviromet with oe source equipped with multiple ateas ad usig beamformig trasmittig to the destiatio through a relay equipped both with sigle atea. The remaider of this paper is orgaized as follows: Sectio deals with system model i cosideratio. I Sectio 3, we formulate a optimal power allocatio solutio for protocol ad the i Sectio 4 for DF protocol. Sectio 5 presets simulatios results. The paper fially draws the coclusios i Sectio 6.. System Model Cosider a cooperative MISO etworks, the source s equipped with ateas ad usig trasmit beamformig ad commuicates with a destiatio d with the help of relay r equipped both with a sigle atea. We assume that the source does ot have a direct lik to the destiatio due to the large distace or the fadig obstacle. The whole trasmissio is accomplished i two phases: i the first phase, the source trasmits to the relay, ad the relay receives. I the secod phase, the relay amplifies () or decode (DF) the received sigal ad forwas to the destiatio. We assume that the relay is located i the straight lie betwee the source ad the destiatio. The distace betwee s to r, s to d ad r to d are deoted as d, d sd ad d respectively. We defie a ratio r as follows: d = r d sd ad d = ( r) d sd. I the first phase, the source uses beamformig to trasmit to the relay. The source-relay r sigal model y is give by: y h wx () s h hr, hr,, hr is ( ) chael vector from the source to the relay with complex Gaussia etries with zero mea ad uit variace. α is the path loss expoet ad K is a costat due to path loss at the referece distace. w is ( ) beamformig vector ad satisfies (w* w = ), (.)* deotes the cojugate traspose. x is the modulated trasmitted symbol, ad is the chael oise draw from a esemble of idepedet ad idetically distributed (i.i.d) complex Gaussia radom variables with zero mea ad variace. P s is the trasmittig eergy used at the source. Durig the secod phase, the relay trasmits to the destiatio. The relay-destiatio y sigal model is give as: y h x () r r h is the chael gai of relay-destiatio path which is complex gaussie with zero mea ad uit variace ad is the chael oise draw from a esemble of i.i.d complex Gaussia radom variables with zero mea ad variace. P r is the trasmittig eergy used at the relay ad x r is the relay sigal. Either or DF ca be used i this phase. We discuss them separately i the ext two sectios. 3. Amplify ad Forwa ad Optimum Power Allocatio If the relay use protocol, x Gy (4) r The relay-destiatio y sigal model is rewritte as: y h Gy (5) G r s hw The ed to ed SR (Sigal to oise Ratio) at the destiatio is give by: h w h s r r h G The ed to ed SR ca be simplified as: s h w ad h. r The form of the ed to ed SR i (8) ca be upper bouded by: (9) E ad E. Whe the sigal is trasmitted with coheret beamformig, the beamform- h ig weight is w ad the beamformig gai is h Ehw, we ca rewrite ad as: s r ad The goal of optimal power allocatio is to maximize the total system SR uder the total power costrait P (6) (7) (8) Copyright SciRes. IJCS

3 M. MAADI ET AL. 449 as: max Ps, Pr s.. tps Pr P The costrait ca be reformulated by itroducig ew variable, ad P s P ad Pr P. The average ed to ed SR ca the be calculated as follows: (). Optimum power allocatio ca be performed by takig the first derivatio of Equatio () ad equate it to zero. () This will result i polyomial degree i the form of a b c a P Kd P Kd b P Kd c P Kd () Solvig the above secod degree polyomial, optimum power allocatio ratio is obtaied as the positive real root which lies betwee zero ad oe. For a BPSK modulated sigal, the BER is calculated as follows: BER Q (3) 4. Decode ad Forwa ad Optimum Power Allocatio As i the case of the relay receives the broadcast from the source i Phase, but istead simply amplifyig ad forwaig the sigal, the relay tries to decode the sigal ad the forwa it. If the relay decodes the sigal correctly (x r = x). Cosiderig that the message will be received correctly at destiatio whe trasmissio of both phases is correct, the ed to ed error probability ca be foud usig: P P P e e e e e Pe Pe Pe Pe (4) P e ad P e are respectively the istataeous probability of decodig error at source-relay lik ad relay-destiatio lik ad ca be calculated as follows: Pe Q Ps Kd h (5) Pe Q Pr Kd h (6) t Qx x exp d t π (7) Sice h is the sum of squared i.i.d. zero mea circularly symmetric complex Gaussia radom variables, h has a chi-square distributio with degrees of freedom ad X h has a expoetial distributio. After applyig Cheroff Boud to (5) ad (6) ad itegratig them with respect to distributios of their terms, we obtai the average error probability: Pe exp r X exp X d X r (8) We recall that the Cheroff Boud for a Gaussia radom variable is: Q x x e (9) Pe exp d s p.5 s () The pdf (probability desity fuctio) of the radom variable is give by: p exp () Substitutig (8) ad () ito (4), we obtai the average ed to ed error probability as: ee Pe ( ) () Agai, optimal power allocatio ca be similarly Copyright SciRes. IJCS

4 45 M. MAADI ET AL. foud by replacig P s ad P r respectively by P ad P. Optimum power allocatio ca be foud from Equatio (). Takig the first derivatio ad equate it to zero, the optimizatio problem traslates ito solvig polyomial degree +. I this paper, we cosider = 4. So, power allocatio problem cosists of solvig a polyomial degree equal to ( a b c d e f ) PKd PKd 4 3PKd PKd 6 4PKd PKd 8P 5 Kd PKd a P Kd P Kd b P Kd P Kd c P Kd P Kd d P Kd P Kd e P Kd P Kd f P Kd P Kd (3) atea at the source) r =.5 ad r =.6 with beamformig at the source. Figure displays the average BER versus r for DF protocol at SR = 5 db. Similar observatios about BER performace compared to equal power allocatio ca also be made. It is iterestig to see that the amelioratio i performace is still observed as r icreases. The lowest BER is achieved by optimal power allocatio whe r =.8 Figure 3 shows the differece i average BER betwee ad DF evaluated at SR = 5 db. We ote that DF protocol outperform protocol for r from. to Coclusios I this work, we studied the performace of optimal power allocatio with trasmit beamformig i two hop /DF relay. We first derive a aalytical study of optimal power allocatio of the proposed system. ext, our 5. Simulatio Results I this sectio, we evaluate the performace of our scheme i term of ed-to-ed BER. We cosider equal ad optimal power allocatios for both ad DF ad evaluate their performace assumig that the relay is allowed to be i ay positio alog a straight lie betwee the source ad the destiatio. The simulatio is coducted for = 4 trasmit ateas at the source ad we recall that the relay ad the destiatio are equipped both of a sigle receive atea. Throughout the simulatio, the parameters d sd ad α are set to km ad 3.6 respectively. We defie the SR (Sigal to oise Ratio) as the ratio betwee system total power P ad oise variace ad we replace d by sd ad d by ( r) d sd i the differet expressios of BER. Figure shows the average bit error rate (BER) versus r for protocol at SR = 5 db. It is observed that amplify ad forwa with optimal power allocatio ca brig sigificat performace improvemet compared to equal power allocatio with ad without beamformig (BF) especially whe the relay is away from the source. The lowest BER is achieved whe r =.7 as with equal power allocatio ad without beamformig (sigle Figure. BER performace of with equal ad optimal power allocatio. Figure. BER performace of DF with equal ad optimal power allocatio. Copyright SciRes. IJCS

5 M. MAADI ET AL. 45 Figure 3. BER performace of ad DF with equal ad optimal power allocatio. aalytical results are cofirmed by simulatios. It is show that by usig our optimized method, we provide better performace tha equal power allocatio with ad without beamformig. Especially, whe the relay is away from middle poit betwee the source ad the destiatio, optimal power allocatio techique should be used to esure better performace. Moreover, i our case the BER ca be made low by movig the relay closer to the destiatio. 7. Refereces [] A. Sedoaris, E. Erkip ad B. Aazhag, User Cooperatio Diversity Part I: System Descriptio, IEEE Trasactios Commuicatios, Vol. 5, o., 3, pp doi:.9/tcomm [] A. Sedoaris, E. Erkip ad B. Aazhag, User Cooperatio Diversity Part II: Implemetatio Aspects ad Performace Aalysis, IEEE Trasactios Commuicatios, Vol. 5, o., 3, pp doi:.9/tcomm [3] G. Kramer, M. Gastpar ad P. Gupta, Cooperative Strategies ad Capacity the Idepedet ad Idetically Distributed Theorems for Relay etworks, IEEE Trasactios o Iformatio Theory, Vol. 5, o. 9, September 5, pp doi:.9/tit [4] A. Bletsas, A. Khisti, D. P. Reed ad A. Lippma, A Simple Cooperative Diversity Method Based o etwork Path Electio, IEEE Joural o Selected Areas i Commuicatio, Vol. 4, o. 3, March 6, pp [5] K. Azaria, H. E. Gamal ad P. Schiter, O the Achievable Diversity Multiplexig Tradeoff i Half-Duplex Cooperative Chaels, IEEE Trasactios o Iformatio Theory, Vol. 5, o., 5, pp doi:.9/tit [6] D. R. Brow III, Resource Allocatio for Cooperative Trasmissio i Wireless etworks with Orthogoal Users, Proceedigs of the 38th Asilomar Coferece o Sigals, Systems ad Computers, Pacific Grove, Vol., 7- ovember 4, pp [7] C. Pa, Y. Cai ad Y. Xu, Capacity, Power Allocatio ad Parters for SIMO Relay Chaels, Wireless Commuicatios ad Mobile Computig, Vol. 7, o. 8, May 7, pp. 3-. doi:./wcm.59 [8] V. Mahitha, L. Cai, J. W. Mark ad S. She, Parter Selectio Based o Optimal Power Allocatio i Cooperative Diversity Systems, IEEE Trasactios o Vehicular Techology, Vol. 57, o., Jauary 8, pp doi:.9/tvt [9] Y. Fa, A. Adioyi, J. S. Thompso, H. Yaikomeroglu ad H. V. Poor, A Simple Distributed Atea Combiig Approach for Cooperative Diversity, IEEE Trasactios o Commuicatios, Vol. 57, March 9, pp [] R. H. Y. Louie, Y. Li ad B. Vucetic, Performace Aalysis of Beamformig i Two Hop Amplify ad Forwa Relay etworks, Proceedigs of IEEE Iteratioal Coferece o Commuicatios, Beijig, 9-3 May 8, pp [] Y. Jig ad H. Jafarkhai, etwork Beamformig Usig Relays with Perfect Chael Iformatio, Proceedigs of IEEE Iteratioal Coferece o Acoustics, Speech ad Sigal Processig, Hoolulu, Vol. 3, 5- April 7, pp [] V. Havary-assab, S. Shahbazpaahi, A. Grami ad Z. Q. Luo, Distributed Beamformig for Relay etworks Based o Secod-Oer Statistics of the Chael State Iformatio, IEEE Trasactios o Sigal Processig, Vol. 56, o. 9, September 8, pp doi:.9/tsp Copyright SciRes. IJCS