Optimal joint source and relay beamforming for MIMO relays with direct link

In this letter, we investigate the optimal structure of the source precoding matrix and the relay amplifying matrix for non-regenerative multiple-input multiple-output (MIMO) relay communication systems with the direct source-destination link. We show that both the optimal source precoding matrix and the optimal relay amplifying matrix have a beamforming structure. Based on this structure, an iterative joint source and relay beamforming algorithm is developed to minimize the mean-squared error (MSE) of the signal waveform estimation. Numerical example demonstrates an improved performance of the proposed algorithm.