IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 7, NO. 11, NOVEMBER 2008 4681 Joint Power and Channel Resource Allocation for Two-User Orthogonal Amplify-and-Forward Cooperation Wessam Mesbah, Student Member, IEEE, and Timothy N. Davidson, Member, IEEE Abstract—We consider the jointly optimal allocation of the radio resources for a two-user orthogonal amplify-and-forward (AF) cooperation scheme. In particular, we derive a simple effi- cient algorithm for determining the power and channel resource allocations required to operate at any point on the boundary of the achievable rate region. The algorithm is based on two results derived herein: a closed-form solution for the optimal power allocation for a given channel resource allocation; and the fact that the channel resource allocation problem is quasi- convex. The structure of the optimal power allocation reveals that at optimality at most one user acts as a relay, and hence a fraction of the channel resource will be idle. We propose a modified orthogonal AF cooperation scheme that uses the channel resources more efficiently and hence provides a larger achievable rate region. Index Terms—Amplify-and-forward relaying, cooperative mul- tiple access, achievable rate region, quasi-convexity. I. I NTRODUCTION T HE growing demand for reliable spectrally-efficient wire- less communication has led to a resurgence of interest in systems in which nodes cooperate in the transmission of mes- sages to a destination node; e.g., [1]. (See Fig. 1.) An achiev- able rate region for a full-duplex two-user cooperative multiple access system was obtained in [1], based on earlier work in [2], and this achievable rate region was shown to be larger than the capacity region for conventional multiple access without cooperation between the source nodes. However, full-duplex cooperation requires sufficient electrical isolation between the transmitting and receiving circuits at each node in order to mitigate near-end cross-talk (e.g., [3], [4], [5], [6]), and this is often difficult to achieve in practice. In order to avoid the need for stringent electrical isolation, the cooperation scheme can be constrained so that the source nodes do not simultaneously transmit and receive over the same channel, and such schemes are often said to be half-duplex; e.g., [3], [7]. The subclass of half-duplex schemes with orthogonal components (e.g., Manuscript received July 9, 2007; revised January 5, 2008; accepted June 14, 2008. The associate editor coordinating the review of this paper and approving it for publication was M. Uysal. This work was supported in part by a Premier’s Research Excellence Award from the Government of Ontario. The work of the second author is also supported in part by the Canada Research Chairs program. Preliminary versions of portions of this work appear in Proc. 2008 IEEE Wireless Commun. Networking Conf. and in Proc. 2008 IEEE Int. Conf. Acoust., Speech, Signal Processing. The authors are with the Department of Electrical and Computer Engineer- ing, McMaster University, Hamilton, Ontario, Canada (e-mail: {mesbahw, davidson}@mcmaster.ca). Digital Object Identifier 10.1109/T-WC.2008.070748 [3]) further constrains the source nodes to use orthogonal subchannels. (These subchannels can be synthesized by time division, e.g., [3], or by frequency division, e.g., [6].) This enables “per-user” decoding at the destination node, rather than joint decoding, and hence simplifies the receiver at the destination node. Motivated by this simplicity, we will focus on orthogonal (half-duplex) cooperation schemes in this paper. A feature of orthogonal cooperation schemes is that they can be decomposed into parallel relay channels, each with orthogonal components [5], [8], [6]. Therefore, the remaining design issues reduce to the choice of the relaying strategy, and the allocation of the radio resources to the parallel relay channels. For the relaying strategy, a number of choices are available (e.g., [9], [10], [3], [11], [12], [13], [14]), and we will focus on the amplify-and-forward (AF) strategy, because it is the simplest in terms of the hardware requirements of the cooperating nodes. As such, the cooperative scheme that we will consider is a generalization of the orthogonal AF scheme in [3]. One of our contributions will be the development of a simple efficient algorithm for joint power and channel resource allocation for this scheme, for scenarios in which full channel state information (CSI) is available. (That is, the design is based on knowledge of the (effective) channel gain on each of the four links in Fig. 1.) As mentioned above, the design of an orthogonal AF coop- eration scheme requires the appropriate allocation of powers and the channel resource (typically time or bandwidth) to the components of each of the underlying parallel relay channels. Unfortunately, the problem of joint power and resource al- location so as to enable operation on the boundary of the achievable rate region is not convex; a fact that might suggest that this is a rather difficult problem to solve. Some progress has been made by considering power allo- cation alone [15]. 1 In particular, it was shown in [15] that for a given resource allocation, the problem of finding the power allocation that maximizes a weighted-sum of achievable rates can be written in a quasi-convex (e.g., [24]) form. In this paper, we will consider the problem of jointly allocating the power and the channel resource. In particular, we will show that for a given target rate of one node, the maximum 1 See [16] for some related work on a non-orthogonal AF cooperation scheme, [17] for some related work with an outage objective, and [18], [19] for some related work on half-duplex cooperation with decode-and-forward relaying. There has also been a considerable amount of work on power and resource allocation for a variety of relaying schemes with achievable rate or outage objectives; e.g., [5], [6], [20], [14], [21], [22], [23]. 1536-1276/08$25.00 c  2008 IEEE Authorized licensed use limited to: McMaster University. Downloaded on July 13,2010 at 04:54:22 UTC from IEEE Xplore. Restrictions apply.