Proceedings of SDR'11-WInnComm-Europe, 22-24 Jun 2011 Joint Optima Power Aocation and Reay Seection with Spatia Diversity in Wireess Reay Networks Md Habibu Isam 1, Zbigniew Dziong 1, Kazem Sohraby 2, Mahmoud F Daneshmand 3, and Rittwik Jana 4 1 Écoe de Technoogie Supérieure ETS, University of Quebec, Montrea, Quebec H5A 1K6, Canada e-mai: md-habibu.isam.1@ens.etsmt.ca, zbigniew.dziong@etsmt.ca 2 Department of Eectrica Engineering, University of Arkansas, 3217 Be Engineering Center Fayettevie, AR 72701 e-mai: sohraby@uark.edu 3 AT&T Labs Research, 200 S Laure Ave - Bdg D, Middetown, NJ e-mai: daneshmand@att.com 4 AT&T Labs Research, 180 Park Ave - Buiding 103, Forham Park, NJ e-mai: rjana@research.att.com Abstract We consider a wireess reay network WRN mutipe mobie stations MSs try to send their data to a base station BS either directy or via a set of fixed reay stations RSs. For this network, we study the probem of joint optima MS and RS power aocation and reay seection with the objective of minimizing the tota transmitted power of the system. The joint optimization agorithm must satisfy the minimum data demand of each MS. We formuate the probem as a mixed integer noninear programming MINLP probem and find the soution under different reaying architectures and spatia diversity schemes. The optima soution of the MINLP probem is exponentiay compex due to its combinatoria nature. We use the MATLAB based commercia software TOMLAB to find a near optima soution of the MINLP probem. We aso find an approximate soution of the origina probem by appying a simpe reay seection scheme based on the channe gains between MSs and RSs. Numerica resuts are presented to show the performance of this simpe scheme with respect to the near optima soution in terms of tota power consumption. I. INTRODUCTION The ever increasing demand for high data rate services has resuted in a significant amount of energy consumption by the communication component of information and communication technoogy ICT. As a consequence, the ICT is paying a major roe in goba cimate change that demands substantia reduction in word-wide energy consumption. Finding aternative ways to improve energy efficiency and thus reducing the energy consumption of wireess networks is vita for a greener future. Given the obvious need to reduce the energy consumption, the fundamenta chaenge is how to reduce the overa power consumption of wireess networks whie maintaining adequate coverage, quaity of services, and reiabiity. Wireess reay networks WRNs can provide a favorabe patform to address this chaenge. The underying technoogy of WRNs is cooperative communications, which is shown to be a promising approach to increase data rates and reiabiity in wireess networks 1] 3]. In WRNs, ower energy consumption is achieved via using ess transmission power due to smaer distances between reays and the terminas, spatia diversity, and using efficient signa processing schemes such as distributed beamforming 4], distributed space-time coding 5], 6], etc. On the other hand, power contro is recognized as a powerfu too to minimize tota transmission power of wireess communications systems. In a wireess reay network WRN, the choice of reay stations RSs to be optimay assigned to the mobie stations MSs is critica to the overa network performance. It has been observed that regardess of the reaying schemes appied, e.g. ampify-and-forward AF and decodeand-forward DF, the performance of cooperative communications highy depends on the efficient seection of reays for the sources and the power contro across the transmissions 7]. Joint power aocation and reay seection in muti-user scenarios have been studied in 7] 10]. In 8], in order to maximize the system capacity with ow computationa compexity and system overhead, the authors propose to design effective reaying agorithms by jointy optimizing reay node seection and power aocation for AF wireess reay networks with mutipe sources and a singe destination. In 9], the authors consider joint optimization of power aocation and reay seection for AF reay networks with mutipe sourcedestination pairs. The joint schemes are proposed under two types of design criteria: i maximization of user rates, and ii minimization of the tota transmit power at the reays. Unike the above works, the authors in 10] deveop a strategy to minimize the tota transmit power in a DF user cooperative upink, such that each user satisfies its required data rate. In 10], the authors mode the tota power minimization probem as an optimization probem the objective function tota network power is a convex function of user powers and the constraints are target rates of users which are concave functions. They then sove the optimization probem by Lagrange mutipier method. A common assumption in a these works 8] 10] is that the transmissions from sources are orthogona to each other, i.e. the channe is not interference-imited. For interference-imited DF WRN with mutipe source-destination pairs and a poo of avaiabe reays, Gkatzikis and Kout- Copyrightc 2011 The Software Defined Radio Forum 209 Inc. - A Rights Reserved
sopouos 7] deveop ightweight joint power aocation and reay seection agorithms of at most poynomia compexity, amenabe to distributed impementation. In this paper, we focus on minimizing the tota transmit power of a WRN by expoiting reaying and cooperation at the physica ayer. We consider a network setup there are mutipe MSs acting as source nodes, mutipe RSs acting as reay nodes and a singe Base Station BS acting as the destination node. We assume that the number of RSs are ess than the number of MSs. We formuate a joint BS and RS aocation probem with power contro at MSs and RSs subject to the transmit power constraints of MSs and RSs, and minimum data rate constraint of RSs. We note that this probem formuation invoves integer variabes to characterize RS and BS seection decision and noninear constraints minimum data demand constraints. It is we known that in genera, a mixed-integer noninear program MINLP is NPhard, which is the main difficuty here. However, an MINLP formuation does not mean the probem itsef is NP-hard uness the probem is proved to be NP-hard. Using TOMLAB 11], a MATLAB based commercia software, we find the near optima soution of the combinatoria probem under different reaying architectures and schemes. We aso provide a simpe ow-compexity soution of the agorithm by fixing the BS and RS assignment variabes, each MS greediy seects either the BS or one or more RS which maximizes its transmission rate. Finay, we provide some numerica resuts to compare the performance of the agorithms under different system scenarios. II. SYSTEM MODEL We consider a hexagona service area, a number of MSs are uniformy distributed. A BS is depoyed at the center of the service area. Within the same area, mutipe RSs are aso depoyed and the ocations of RSs are fixed. It shoud noted that such a depoyment scenario is more representative of IEEE 806.16j type networks. Let the number of MSs and RSs be N MS and N RS, respectivey. An MS can either be directy connected to the BS or via one or more RSs. We assume that if an MS is directy connected to the BS, it cannot be connected to an RS, and vice versa. However, both BS and RSs can be accessed simutaneousy by different MSs at their assigned frequency bands using Orthogona Frequency-Division Mutipe Access OFDMA technique. In other words, orthogona transmissions are used for simutaneous transmissions among different MSs by using different channes and time division mutipexing is empoyed by the reaying schemes. We assume a conventiona two-stage AF reaying scheme 1], 9]. An MS can be assigned with a singe reay or mutipe reays depending on the transmission schemes empoyed. For the sake of simpicity, we consider the number of hops for reaying to be imited to 2. To keep the description simpe, we use MS k to denote the kth MS and RS m to denote the mth RS. Fat Rayeigh fading channes are assumed among MS-BS, MS-RS, and RS- BS inks, and channes are independent of each other. The channe gains from MS k to BS, from MS k to RS m, and from RS m to BS are captured by the parameters g k, h km, and d m, respectivey. A the channe gains may incude the effect of path oss, shadowing, and fading. Let P k denote the power transmitted by MS k if MS k is directy connected with the BS. Let Q km and F km be the powers transmitted by MS k and RS m, respectivey, in the inks MS k -RS m -BS if MS k is connected to BS via RS m. The maximum transmit power budget constraint of an MS and an RS are P max and F max, respectivey. The variances of additive white Gaussian noise AWGN at BS and RS are denoted by 2 and σr, 2 respectivey. Now, we define the foowing two sets of decision variabes which indicate if an MS is directy connected with a BS or it is assisted { by reays to transmit its data to BS. 1 if MSk, is directy connected with BS x k { 0 otherwise. 1 if MSk, is connected with RS y km m, 0 otherwise. If an MS is directy connected with the BS, it needs ony one time sot to transmit its data to BS. On the other hand, if an MS is connected to the BS via an RS, then in the first time sot, an MS transmits unit energy signa to an RS. In the subsequent time sot, assuming the RS knows the channe state information CSI for the MS-RS ink, the RS normaizes the received signa and retransmits to the destination BS. III. PROBLEM FORMULATION In this work, we want to sove the foowing joint optimization probem. Given the ocation of the BS and a set of fixed RSs, find the optima power aocations {P k }, {Q km }, {F km }, and optima seection variabes {x k }, {y km } such that the tota transmit power of the system is minimized whie the minimum data rate demand { } rk min of each MS is met. Using the notations defined in the previous section, the above optimization probem can be mathematicay expressed as foows. min k1 P k + k1 m1 Q km + k1 m1 F km 1a s.t. r k rk min, k 1b M x k + y km R, k 1c m1 x k y km 0, k, m 1d 0 P k P max x k, k 1e 0 Q km P max y km, k, m 1f 0 F km F max y km, k, m 1g R 0 F km F max, m 1h k1 x k {0, 1}, y km {0, 1}, k, m variabes: {x k }, {y km }, {P k }, {Q km }, {F km } 1i 1j The objective function 1a minimizes the tota transmitted power of the system. Constraint 1b ensures that the data 210
transmission rate of each MS is arger than its minimum rate requirements. In 1b, r k is the maximum achievabe transmission rate of MS k In the next section, we present the expressions for r k under different spatia diversity schemes. Constraint 1c aong with the constraint 1d states that an MS is either directy connected with the BS or via a singe or mutipe RSs, and if an MS is directy connected with the BS, it cannot be assigned with one or mutipe RSs and vice versa. In 1c, R is a predetermined system parameter which represents the exact number of RSs assigned with each MS if the MS is not directy connected with the BS. Based on the reaying architecture and spatia diversity schemes, in this work, we set R 1 or R 2. The non-negativity of the power aocation variabes as we as the power budget constraints of MSs and RSs are ensured by constraints 1e, 1f, 1g, and 1h. The conditions that if x k 0, P k 0, if y km 0, Q km 0, and if y km 0, F km 0, are aso captured in the constraints 1e, 1f, and 1g. Finay, constraint 1i satisfies the condition that MS-BS and MS-RS assignment variabes are binary. IV. TRANSMISSION RATES UNDER DIFFERENT SCHEMES In this paper, we sove the tota transmit power minimization probem 1 under different depoyment scenarios and spatia diversity schemes. Specificay, we consider the foowing scenarios: BS-ony architecture: Under this architecture, the network consists of BS and MSs ony. Since there are no reays, a MSs transmit directy to BS and x k 1, k 1, N MS ]. We consider this scenario to show the advantage of using reays over non-reay networks in terms of energy saving. Singe reay per MS: Under this scheme, if an MS is not directy connected with a BS, it woud transmit to a BS via exacty a singe RS. Therefore, under this scheme, R 1. In this scheme, spatia diversity is achieved through AF reaying scheme. Mutipe reays per MS: Unike the scenario of singe reay per mobie, in this scenario, if an MS is not directy connected to a BS, it woud transmit to a BS via R > 1 reays. For the sake of simpicity, here, we consider R 2. Under this scheme, additiona spatia diversity is achieved due to the mutipath combining of the received signa from mutipe reays at the BS. Distributed beamforming: In this case, a maximum ratio transmission MRT based distributed beamforming scheme woud be empoyed by mutipe RSs to assist MSs to transmit their data to BS. Distributed space-time coding: In this scheme, mutipe RSs woud empoy the distributed space-time coding 5], 6] to assist MSs which are not directy connected to the BS. Under the BS-ony non-reay depoyment scenario, the maximum achievabe data rate of MS k, k 1, N MS ], can be expressed by the we-known Shannon capacity theorem: r k W og 2 1 + P k g k 2 2, 2 W is the bandwidth of the channe. Without the oss of generaity, we can assume W 1. Now, we ook at the case when the MSs which cannot directy transmit to BS are assisted by exacty R number of reays. In this case, under AF scheme 1], 9], the data rate of MS k is given by r k og 2 1 + x kp k g k 2 σ 2 0 + og 2 1 + 1 R y km Q km h km 2 F km d m 2 γ km y km F km d m 2 σr 2 + m1 y km Q km h km 2 + σ 2 r γ km, 3, 2 4 Note that in 3, R 1 represents the scenario each MS without any direct connection with BS is assisted by one RS, and R 2 represents the scenario each MS without any direct connection with the BS is assisted by two RSs. A. Distributed Beamforming For the distributed beamforming case, if an MS is not directy connected with the BS, it is assisted by R number of reays. For the sake of simpicity, we imit this to R 2. Given the coordinates of the ocations of RSs, for each RS, we seect the cosest RS as its pair. As a consequence, an RS might appear in a singe or mutipe RS pairs. Note that the above method of choosing RS pairs is not necessariy optima. Let N RSP be the tota number of RS pairs. Denote RSP, 1, N RSP ], as the th RS pair. To this end, we define the foowing binary assignment variabe. { 1 if MSk is assisted by RSP α k 0 otherwise With a itte abuse of notations, we denote the vectors of compex channe gains from MS ] k to RSP and from RSP ], to the BS as h k h 1 k, h2 k and d d 1, d 2 respectivey. In AF distributed beamforming, during the first time sot, MS k, k 1, K] transmits signa to RS i, i 1, 2] of RSP using the transmit power Q i k. In the second time sot, each RS i of RSP normaizes the received signa, mutipies it by a beamforming coefficient and transmit the ampified signa to the BS using its transmit power F i k. Let w k ] w 1 k, w2 k be the beamforming weight vector empoyed by RSP to transmit the signa of MS k to BS. Now, with AF distributed beamforming scheme, the data rate of MS k, k 1, N MS ], can be written as r dbf k og 2 1 + x kp k g k 2 σ 2 0 r k, 5 N RSP + 1 211
and γ i k α k F i k r k og 2 1 + 1 2 2 i1 γ i k, 6 α k Q i k F i k h i k 2 d i 2 w i k 2 d i 2 w i 2 σr 2 + h i 2 + σr 2 k Q i k k. 2 7 In this paper, we empoy the simpe maximum ratio transmission MRT beamforming scheme under which the beamforming vector w k can be expressed as f k w k f k, k 1, N MS], 1, N RSP ], 8 ] f k h 1 k d1, h 2 k d2 is the equivaent channe gain vector for the MS k -RSP -BS ink. It shoud be noted that MRT based distributed beamforming scheme requires a centraized contro with access to a channe information. We assume that BS has perfect knowedge of a channe information and it feeds back those information to RSs. B. Distributed Space-Time Coding In distributed space-time coding, ] if MS k wants to send the signa s k s 1 k,..., st k in the codebook { } s 1 k,..., sl k to BS via RSP, T is the ength of the time sot, then the received signa at RS i of RSP, and at BS can be expressed, respectivey, as 5], 6] r i k x k Q k T h i k s k + u, 9 n 2 i1 d i t i k + v, 10 u and v are T 1 zero-mean compex AWGN vectors at RSs and BS, respectivey with component wise variances σr 2 and 2 and t i k F i k Q k + σr 2 A i k ri k, 11 T T dimensiona matrix A i k corresponds to the ith coumn of a proper T T space-time code. In 5], authors designed the distributed space-time codes such that A i k is a unitary matrix. With distributed space-time coding, the capacity of MS k, k 1, N MS ], can be written as 5], 6] rk dstc og 2 1 + x kp k g k 2 N RSP 2 + ρ k, 12 ρ k og 2 1 + 2 i1 µ i k 1 h i k di 2 13 µ i k 2 j1 α k Q k F i k α k Q k +σ 2 r α k F j k α k Q k +σ 2 r σ 2 r + σ 2 0 14 is the portion of the average symbo energy passing from the RS i of RSP to noise power ratio. V. SOLUTION APPROACH The optimization probem described in 1 is a mixed integer noninear programming MINLP probem, which is NP-hard in genera, due to the discrete nature of the BS and RS seection variabes, and the continuous nature of the power aocation variabes. The optima soution of 1 can be obtained by exhaustive search agorithm which is computationay intractabe due to its exponentia compexity with respect to the number of MSs and RSs. Some commercia software packages, e.g. TOMLAB 11], which uses branch-and-bound agorithm, may provide near-optima soutions. In this section, we provide a heuristic agorithm to get sub-optima soutions of the MINLP probem. The heuristic agorithm is simiar to the one-shot greedy agorithm proposed in 7]. Under this scheme, first transmit power of each MS and RS are set to P max and F max, respectivey. Then, each MS greediy seects either the BS or a singe or mutipe RSs based on different scenarios presented in Section IV such a way that its data rate is maximized. With x k and y km fixed, the optimization probem 1 is no more an MINLP probem and can be easiy soved using simpe non-inear programming NLP toos. However, since the seection of BS or RSs for each MS does not consider the channe in the second hop, the soution of the MS and RS power aocation woud be sub-optima. VI. NUMERICAL RESULTS In this section, we provide some numerica resuts to compare the performance of different schemes. In our simuation mode, we consider a hexagona ce with radius 1 km. The BS is ocated at the center of the ce. Within the ce, there are N RS 15 reays with their position fixed. The number of MSs is varied as N MS 30, 35, 40, 45, 50, 55, 60, and they are uniformy distributed within the ce. The normaized coordinates for the positions of BS, 15 RSs, and 30 MSs are shown in Fig 1 for a particuar snapshot. The path oss exponent is 4. It is assumed that a the receivers at RSs and BSs are subject to Additive White Gaussian Noise AWGN with zero mean and unit variance. Channe coefficients are generated as circuary symmetric AWGN with zero mean and unit variance. Minimum traffic demand of MSs are uniformy generated in 0, 1]. The resuts of the simuations are averaged over 1000 channe reaization. The ocations of BS and RSs, and required data rate of each MS are fixed over a channe reaizations. However, the ocations of MSs change from one channe reaization to another channe reaization. In Fig 2, we show the minimum tota transmit power of six different reaying architectures and schemes for different numbers of MS served. The resuts obtained by using TOM- LAB 11] are denoted by O, and the resuts obtained by 212
1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 RS BS MS 1 1 0.5 0 0.5 1 Fig. 1. A WRN depoyment scenario with N RS 15 and N MS 30. Tota Transmit Power db 40 38 36 34 32 30 28 26 24 22 20 BS Ony SRMS O SRMS G DRMS O DRMS G DBF O DBF G DSTC O DSTC G 30 35 40 45 50 55 60 Number of MSs Fig. 2. Tota transmit power vs. number of MSs the greedy agorithm are denoted by G. We use the egends BS-ony, SRMS, DRMS, DBF, and DSTC to refer to the scenarios of BS-ony architecture, singe reay per MS, dua reay per MS, distributed beamforming, and distributed space-time coding, respectivey. As can be seen from Fig 2 that the BS-ony architecture requires more transmitted power to serve a MSs than the other five architectures. This resut is expected since the MSs far from BS require to use more power to send their data to BS and achieve the target data rate. The singe reay per MS architecture using both optima TOMLAB and greedy schemes performs better than the BSony architecture. It is aso observed DRMS scheme performs better than SRMS scheme due to the mutipath diversity captured by the DRMS scheme. On the other hand, DBF scheme provides both spatia diversity and array gain and thus performs better than the DRMS scheme that ony takes the benefits of mutipath diversity. Finay, our resuts show that DSTC scheme outperforms a other schemes in terms of minimum tota power requirement. It is more ikey that for the specia case of 2 distributed antennas, coding and diversity gain achieved by DSTC is higher than the diversity and array gain provided by the DBF scheme. Finay, for a reay depoyment scenarios, as expected, the performance of the greedy agorithm is worse than that of the optima agorithm. VII. CONCLUSION We have studied the joint optima MS and RS power contro and BS and RS assignment to each MS for the upink of a WRN, mutipe MSs send their data to BS either directy or via a singe or mutipe RSs. With the objective of minimizing the tota transmit power of the system with the constraints on minimum data rate of each MS, and maximum transmit power budget of MSs and RSs, we have formuated the probem as an MINLP probem and then soved it under different system scenarios. The near-optima soution of the MINLP probem has been obtained by the commercia software TOMLAB 11]. We have provided a heuristic soution based on a greedy approach and compared its performance with that of the near-optima soution. Numerica resuts show that a gain of around 5-7 db, in terms of tota transmit power, can be achieved by expoiting spatia diversity inherent to the reaying architectures compared to the BS-ony architecture. REFERENCES 1] J. N. Lanemen, D. N. C. Tse, and G. W. Worne, Cooperative diversity in wireess networks: Efficient protocos and outage behavior, IEEE Trans. Inf. Theory, vo. 50, no. 12, pp. 3062 3080, Dec. 2004. 2] A. Sendonaris, E. Erkip, and B. Aazhang, User cooperation diversity - Part I: System description, IEEE Trans. Commun., vo. 51, no. 11, pp. 1927 1938, Nov. 2003. 3], User cooperation diversity - Part II: Impementation aspects and performance anaysis, IEEE Trans. Commun., vo. 51, no. 11, pp. 1939 1948, Nov. 2003. 4] Z. Ding, W. H. Chin, and K. K. Leung, Distributed beamforming and power aocation for cooperative networks, IEEE Trans. on Wireess Commun., vo. 7, no. 5, pp. 1817 1822, May 2008. 5] Y. Jing and B. Hassibi, Distributed space-time coding in wireess reay networks, IEEE Trans. on Wireess Commun., vo. 5, pp. 3524 3536, Dec. 2006. 6] B. Maham and A. Hjørungnes, Power aocation strategies for distributed space-time codes in ampify-and-forward mode, EURASIP J. Adv. Signa Process, vo. 2009, pp. 1 13, Jan. 2009. 7] L. Gkatzikis and I. Koutsopouos, Low compexity agorithms for reay seection and power contro in interference-imited environments, in Proc. WiOPT, Avignon, France, Aug. 2010, pp. 308 317. 8] J. W. M. J. Cai, S. Shen and A. S. Afa, Semi-distributed user reaying agorithm for ampify-and-forward wireess reay networks, IEEE Trans. on Wireess Commun., vo. 7, no. 4, pp. 1348 1357, Apr. 2008. 9] K. T. Phan, H. N. Nguyen, and T. Le-Ngoc, Joint power aocation and reay seection in cooperative networks, in Proc. IEEE GLOBECOM09, HI, USA, Nov. 2009. 10] K. Vardhe, D. Reynods, and B. D. Woerner, Joint power aocation and reay seection for mutiuser cooperative communications, IEEE Trans. on Wireess Commun., vo. 9, no. 4, pp. 1255 1260, Apr. 2010. 11] K. Homstrm, TOMLAB - an environment for soving optimization probems in MATLAB, in Proc. the Nordic Matab Conference 97. 213