Transceiver optimization for MIMO multi-relay systems using projected gradient approach

In this paper, we develop the optimal source precoding matrix and relay amplifying matrices for non-regenerative multiple-input multiple-output (MIMO) relay communication systems with parallel relay nodes using the projected gradient (PG) approach. We show that the optimal relay amplifying matrices have a beamforming structure. Exploiting the structure of relay matrices, an iterative joint source and relay matrices optimization algorithm is developed to minimize the meansquared error (MSE) of the signal waveform estimation at the destination using the PG approach. The performance of the proposed algorithm is demonstrated through numerical simulations.