Joint transceiver design for MIMO relay systems employing SC-FDE

In this paper, we propose a joint transceiver design for multiple-input multiple-output (MIMO) relay systems employing single-carrier frequency-domain equalization (SC-FDE). We first derive the optimal minimum mean-squared error (MMSE) frequency-domain linear equalization filter at the destination and the associated stream-wise MSEs at the output of the equalizer. Subsequently, we optimize the source and relay precoding matrices for various optimality criteria by minimizing a general function of the MSEs subject to separate source and relay power constraints. The structures of the optimal source and relay precoding matrices are obtained in closed form and the remaining power allocation problems are solved using an alternating optimization algorithm. Simulation results show that the proposed SC-FDE designs outperform orthogonal frequency-division multiplexing based MIMO relay systems in terms of both uncoded and coded bit error rate.