Relay design for SNR maximization in MIMO communication systems

In this paper a multi-input multi-output (MIMO) communication system is considered in which a relay with multiple antennas is used to assist the data transmission from the source to destination. We assume that the relay applies a linear transform matrix on its received signal vector and retransmit the transformed vector to the destination node. We optimize the transform matrix by maximizing the average end-to-end SNR. The relay transfer matrix is related to the eigenvectors of correlation matrices of the two channels. For some special cases, we derive the optimum solution and the best unitary excitation matrix. We show that this solution is applicable in some cases where the instantaneous end-to-end SNR has to be maximized. Interestingly, the optimum transfer matrix is the dominant mode excitation, for the specific case where either the source-to-relay (SR) channel enticers or the relay-to-destination (RD) channel enticers are uncorrelated and have identical variances, i.e., in such a case all the relay power must be dissipated in the direction of dominant eigenvectors of SR and RD channels correlation matrices. Computer simulations are used to evaluate the effect of different relaying matrices on the end-to-end SNR.