2994 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 56, NO. 7, JULY 2008 Optimized Power Allocation for Pairwise Cooperative Multiple Access Wessam Mesbah, Student Member, IEEE, and Timothy N. Davidson, Member, IEEE Abstract—Multiple access schemes in which the transmitting nodes are allowed to cooperate have the potential to provide higher quality of service than conventional schemes. In the class of pair-wise cooperative multiple access schemes in which channel state information is available at the transmitters, the allocation of transmission power plays a key role in the realization of these quality of service gains. Unfortunately, the natural formulation of the power allocation problem for full-duplex cooperative schemes is not convex. It is shown herein that this non-convex formulation can be simplified and recast in a convex form. In fact, closed-form expressions for the optimal power allocation for each point on the boundary of an achievable rate region are obtained. In practice, a half-duplex cooperative scheme, in which the channel resource is partitioned in such a way that interference is avoided, may be preferred over a full-duplex scheme. The channel resource is often partitioned equally, but we develop an efficient algorithm for the joint allocation of power and the channel resource for a modified version of an existing half-duplex cooperative scheme. We demon- strate that this algorithm enables the resulting scheme to attain a significantly larger fraction of the achievable rate region for the full duplex case than the underlying scheme that employs a fixed resource allocation. Index Terms—Achievable rate, convex optimization, cooperative communications, decode-and-forward, resource allocation. I. INTRODUCTION I N CONVENTIONAL multiple access schemes each node attempts to communicate its message directly to the desti- nation node; e.g., the base station in a cellular wireless system. While such schemes can be implemented in a straightforward manner, alternative schemes in which nodes are allowed to co- operate have the potential to improve the quality of service that is offered to the transmitting nodes by enlarging the achiev- able rate region and by reducing the probability of outage; e.g., [1]–[4]. The basic principle of cooperative multiple access is for the nodes to mutually relay (components of) their messages to the destination node, and hence the design of such schemes Manuscript received March 9, 2007; revised December 5, 2007. The as- sociate editor coordinating the review of this manuscript and approving it for publication was Prof. Qing Zhao.This work was supported in part by a Premier’s Research Excellence Award from the Government of Ontario. The work of T. N. Davidson is also supported in part by the Canada Research Chairs Program. Preliminary versions of this paper appeared in the Proceed- ings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Toulouse, France, May 2006, and the Proceedings of the IEEE International Conference on Communications, Istanbul, Turkey, June 2006. The authors are with the Department of Electrical and Computer Engi- neering, McMaster University, Hamilton, ON L8S 4K1, Canada (e-mail: mesbahw@mcmaster.ca; davidson@mcmaster.ca). Digital Object Identifier 10.1109/TSP.2008.917390 involves the development of an appropriate composition of sev- eral relay channels [5]–[7]. In particular, power and other com- munication resources, such as time-frequency cells/dimensions, must be allocated to the direct transmission and cooperation tasks. The realization of the potential improvement in quality of service provided by cooperation is contingent on this alloca- tion (among other things), and the development of efficient al- gorithms for optimal power and resource allocation for certain classes of cooperative multiple access schemes forms the core of this paper. We will focus on cooperative multiple access schemes in which the transmitting nodes cooperate in pairs and have access to full channel state information. The transmitting nodes will cooperate by (completely) decoding the cooperative messages transmitted by their partners, and hence the cooperation strategy can be broadly classified as being of the decode-and-forward type. We will consider an independent block fading model for the channels between the nodes, and will assume that the coherence time is long. This enables us to neglect the com- munication resources assigned to the feeding back of channel state information to the transmitters, and also suggests that an appropriate system design objective would be to enlarge the achievable rate region for the given channel realization. We will begin our development with the derivation (in Sections II and III) of closed-form expressions for optimal power allocations for cooperative schemes that are allowed to operate in full-duplex mode; i.e., schemes that allow each node to simultaneously transmit and receive in the same time-fre- quency cell. Although the demands on the communication hardware required to facilitate full-duplex operation, such as sufficient electrical isolation between the transmission and reception modules and perfect echo cancellation, are unlikely to be satisfied in wireless systems with reasonable cost, the full-duplex case represents an idealized scenario against which more practical systems can be measured. It also provides a simplified exposition of the principles of our approach. The performance required from the communication hardware can be substantially relaxed by requiring each node to communicate in a half-duplex fashion; e.g., [1]–[4]. However, half-duplex operation requires the allocation of both power and the channel resource. In Section V, we will develop an efficient jointly op- timal power and resource allocation algorithm for a (modified) block-based version of the half-duplex scheme in [2, Sec. III]. (The scheme in [2, Sec. III] employs a fixed, and equal, re- source allocation.) We will demonstrate that the ability of the proposed scheme to partition the channel resource according to the rate requirements of each node enables it to achieve a larger fraction of the achievable rate region of the full duplex case than the underlying scheme. 1053-587X/$25.00 © 2008 IEEE Authorized licensed use limited to: McMaster University. 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