Cooperative amplify-and-forward beamforming with multiple multi-antenna relays - Liang, Yang-Wen; Schober, Robert (IEEE Transactions on Communications, 2011)
In this paper, we consider beamforming (BF) for cooperative networks with one multiantenna source, multiple multiantenna amplifyandforward (AF) relays, and one singleantenna destination. The source BF vector and the AFBF matrices at the relays are optimized for maximization of the signaltonoise ratio (SNR) at the destination under three different power constraints. In particular, we consider individual relay power constraints, a joint relay power constraint, and a joint power constraint for the source and the relays. We solve the associated optimization problems in two stages. In the first stage, we find the optimal AFBF matrices for a given BF vector at the source. For the cases of individual and joint relay power constraints, closedform solutions for the AFBF matrices are provided, respectively. Furthermore, for the case of a joint sourcerelay power constraint, the AFBF matrices are obtained in closed form up to a scalar power allocation factor and an efficient numerical algorithm for the power allocation between the source and the relays is given. In the second stage, the optimal source BF vectors are computed. Thereby, we show that for the joint relay and the joint sourcerelay power constraints, the resulting problem can be transformed into a nonconvex polynomial programming problem which allows for an exact solution for smallscale networks. For largescale networks and networks with individual relay power constraints, we propose efficient suboptimal optimization methods for the source BF vector. Simulation results show the benefits of having multiple antennas at the source and/or multiple multiantenna relays and illustrate the performance differences introduced by the three different power constraints. © 2006 IEEE.
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Keywords: beamforming; Cooperative network; multiple antennas; multiple relays