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This paper considers the design of an optimal beamforming weight matrix of multiple-antenna multiple-relay networks. It is assumed that each relay utilizes the amplify and forward strategy, i.e., it multiplies the received signal vector by a matrix, dubbed the relay weight matrix, and forwards the resulting vector to the destination. Furthermore, the authors assume that the source and the destination have the same number of antennas and that each transmit antenna is virtually paired to a different destination antenna. The relay weight matrices are concurrently designed to optimize the Mean Square Error (MSE) criterion at the destination, assuming each relay node is subject to a power constraint.
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