Auction-Based Power Allocation for Multi-Source Multi-Relay Cooperative Wireless Networks Mohammed W. Baidas and Allen B. MacKenzie Wireless @ Virginia Tech, Bradley Department of Electrical and Computer Engineering, Virginia Tech, Blacksburg, VA 24061, USA (email: baidas@ieee.org, mackenab@vt.edu) Abstract—In this paper, multi-source multi-relay power allocation in cooperative wireless networks is considered. An ascending-clock auction is proposed to efficiently allocate cooperative relay power among multiple source nodes in a distributed fashion. In particular, each source node reports its optimal power demand to each relay node based on the relays’ announced prices. It is proven that the proposed auction algorithm enforces truthful power demands and converges in a finite number of time-steps to the unique Walrasian Equilibrium allocation that maximizes the social welfare. Numerical results are presented to supplement the theoretical analysis and demonstrate the efficiency of the proposed distributed relay power allocation algorithm. Index Terms—Amplify-and-forward (AF), auction, cooperation, net- work coding, power allocation, truth-telling I. I NTRODUCTION Cooperative communications has recently been proposed as a promising transmission technique to exploit spatial diversity gains over single antenna nodes in wireless networks. In particular, several nodes act as relays and share their transmission resources to forward other nodes’ data. Such cooperation significantly improves system performance and reliability. To fully harness the benefits of cooperative diversity, efficient power allocation is essential. How- ever, such power allocation not only requires complete channel state information but also entails formidable centralized computations. In turn, the design of distributed power allocation algorithms where computations are carried out locally by the different network nodes is highly desirable. Recently, several works have considered game- and auction- theoretic resource allocation in cooperative wireless networks. For instance, in [1], a Stackelberg game is proposed for distributed relay selection and power allocation. However, the previous work did not consider the scenario where multiple source nodes are allocated power from the different relays in the network. In [2], two auction mechanisms are proposed, namely the SNR auction and the power auction, where it was shown that the former auction achieves effi- ciency while the latter yields a flexible tradeoffs between fairness and efficiency. In [3], single-object and multiple-object second- price auction-based mechanisms are studied for cooperative partner selection such that a desired quality-of-service is maintained. In this paper, a distributed ascending-clock auction-based algo- rithm is proposed for multi-relay power allocation. Specifically, each source node reports its optimal power demand to each relay node in response to the prices announced by the relay nodes. It is proven that the proposed distributed algorithm enforces truthful power demands and converges in a finite number of time-steps to the unique Walrasian Equilibrium (WE) allocation that maximizes the social welfare. To the best of the authors’ knowledge, no prior work has considered distributed multi-relay auction-based power allocation. The rest of the paper is organized as follows. The network model is presented in Section II. The utility functions of the source and relay nodes are discussed in Section III. The proposed ascending- clock auction-based power allocation algorithm is presented in Fig. 1. Cooperative Network - Broadcasting and Cooperation Phases Section IV while its properties are discussed in Section V. The numerical results are presented in Section VI and the conclusions are drawn in Section VII. II. NETWORK MODEL Consider a wireless network consisting of N source nodes (N ≥ 2), denoted S 1 , S 2 , ..., S N . The N nodes are assumed to have data symbols x 1 ,x 2 ,...,x N , respectively, and aim at communicating their data symbols to a common destination node D via a set of K relay nodes (K ≥ 2). The relay nodes are denoted R 1 , R 2 , ..., R K , each with transmission power P R k for k ∈{1, 2,...,K}. In this network (shown in Fig. 1), each node is equipped with a single antenna and the relays’ cooperative transmissions follow the amplify-and-forward (AF) protocol [4]. The channel between any two nodes is modeled as a narrowband Rayleigh fading channel with additive white Gaussian noise (AWGN). Let h j,k denote the channel coefficient representing the channel between any two nodes j and k, then h j,k ∼ CN (0,σ 2 j,k ), where σ 2 j,k is the channel gain. The communication between the source nodes and the destination node is performed over N + K time-slots and is split into two phases, namely the broadcasting phase (of N time-slots) and the cooperation phase (of K time-slots). A. Broadcasting Phase In this phase, each source node S j for j ∈{1, 2,...,N } is assigned a time-slot T j in which it broadcasts its data symbol x j to the rest of the network. The received signal y j,k at relay node R k for k ∈{1, 2,...,K} in time-slot T j is expressed as y j,k =  PB j h j,k xj + n j,k , (1) while the signal received at the destination is given by y j,d =  PB j h j,d xj + n j,d , (2) where PB j is the broadcast transmit power of source node S j while n j,k and n j,d are zero-mean AWGN samples with variance N 0 , at relay node R k and the destination, respectively. 978-1-4244-9268-8/11/$26.00 ©2011 IEEE This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2011 proceedings.