Power Allocation in Wireless Relay Networks: A Geometric Programming-Based Approach Khoa T. Phan † , Tho Le-Ngoc ‡ , Sergiy A. Vorobyov † , and Chintha Telambura † † Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, CANADA ‡ Department of Electrical and Computer Engineering, McGill University, Montreal, QC, CANADA Email: khoa, vorobyov, chintha@ece.ualberta.ca, tho@ece.mcgill.ca Abstract— 1 In this paper, we consider an amplify-and-forward (AF) wireless relay system where multiple source nodes com- municate with their corresponding destination nodes with the help of relay nodes. While each user 2 is assisted by one relay, one relay can assist many users. Conventionally, each relay node is assumed to equally distribute the available bandwidth and power resources to all sources for which it helps to relay information. Realizing the sub-optimality of this approach, in this paper, we present efficient power allocation schemes to i) maximize the minimum end-to-end signal-to-noise ratio among all users; ii) minimize the total transmit power over all sources; iii) maximize the system throughput. Our approach is based on geometric programming (GP), a well-studied class of nonlinear and nonconvex optimization. Since a GP problem is readily transformed into an equivalent convex optimization problem, optimal power allocation can be obtained efficiently. Numerical results demonstrate the effectiveness of our proposed approach. Index terms– Power allocation, geometric programming, relay networks. I. I NTRODUCTION It has been shown that the operation efficiency and quality- of-service (QoS) of cellular and/or ad-hoc networks can be increased through the use of relay(s) [1], [2]. In such sys- tems, the information from the source to the corresponding destination is transmitted via a direct-link and also forwarded via relays. A critical issue for improving the performance of wireless networks is efficient management of available radio resources. Particularly, resource allocation via power control is commonly used to ensure the performance and stability of the wireless network. There have been numerous works that attempt to opti- mize the available communication resources, i.e., power and bandwidth to improve the system performance [7]-[10]. A single source-destination pair is typically considered in the aforementioned papers. In [7], for example, the authors derive closed-form expressions for the optimal and near-optimal relay transmission powers for the single relay and the multiple relays cases. Furthermore, the problem of minimizing the transmission power given that a target outage probability is achieved was tackled in [8]. In [9], the authors derive power allocation strategies for 3-node amplify-and-forward 1 This work was supported in parts by the Natural Science and Engineer- ing Research Council (NSERC) of Canada and Alberta Ingenuity, Alberta, Canada. 2 Hereafter, the term ’user’ refers to a source-destination (S-D) pair or only the source node depending on the context. (AF) relaying system based on the knowledge of channel means. Given either channel state information (CSI) or channel statistics, two power allocation schemes to minimize the outage probability are presented in [10]. We note, however, that very few existing works have con- sidered the 2-hop relay model with multiple users. The latter setup of multiple users is the more practical as compared to the previously considered configurations. Therefore, the above mentioned analysis is applicable only to a special case of the problem in hands, since each relay is usually delegated to assist more than one users, especially when the number of relays is usually (much) smaller than the number of users. An example of such scenario is the deployment of few relays in a cell at appropriate locations to assist mobile users operating in heavily scattering environment for uplink transmission. Resource allocation in a multi-user system usually has to take into account the fairness issue among users, their relative QoS requirements, channel quality and available resources. Mathematically, optimization of relay networks with multiple users is a difficult (if tractable) problem, especially for systems with large number of sources and relays. In this paper, we develop efficient power allocation schemes for multi-user wireless relay systems. Particularly, we derive optimal power allocation schemes to i) maximize the minimum end-to-end signal-to-noise ratios (SNRs) among all users; ii) minimize the total transmit power of all sources; iii) maxi- mize the system throughput. We show that the corresponding optimization problems can be formulated as geometric pro- gramming (GP) problems. Therefore, optimal power allocation can be obtained efficiently even for large-scale networks using convex optimization techniques. Note that GP has been successfully applied to solve the problem of power allocation in traditional cellular and ad hoc networks [5]–[6]. II. SYSTEM MODEL Consider a multi-user relaying model where a set of M source nodes S i ,i ∈{1, ...M } wants to transmit data to their corresponding destination nodes D i ,i ∈{1, ...M }. 3 Moreover, L relay nodes, denoted by R j ,j ∈ {1, ..., L} are employed for forwarding the information from source to destination nodes. The conventional two-stage AF relaying 3 This includes the case of one destination node for all sources, for example, base station in a cellular network, or central processing unit in a sensor network. This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings. 978-1-4244-2324-8/08/$25.00 © 2008 IEEE. 1 Authorized licensed use limited to: UNIVERSITY OF ALBERTA. Downloaded on December 17, 2009 at 15:01 from IEEE Xplore. Restrictions apply. "©2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE."