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In this paper, the authors study the optimal structure of the source pre-coding matrix and the relay amplifying matrices for Multiple-Input Multiple-Output (MIMO) relay communication systems with parallel relay nodes. Two types of receivers are considered at the destination node: the linear Minimal Mean-Squared Error (MMSE) receiver; the nonlinear decision feedback equalizer based on the minimal MSE criterion. They show that for both receiver schemes, the optimal source pre-coding matrix and the optimal relay amplifying matrices have a beamforming structure. Using such optimal structure, joint source and relay power loading algorithms are developed to minimize the MSE of the signal waveform estimation at the destination.
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