In this paper, we investigate the source precoding matrix and the relay amplifying matrix for nonregenerative Multiple-input Multiple-output (MIMO) relay communication systems with the direct source-destination link. The Minimum Mean-squared Error (MSE) is taken as the design criterion. The power-constrained optimal design of source and relay precoder require to solve the complicated optimization problem that involves matrix variables. We propose a suboptimal joint source and relay beamforming precoding structure that convert the problem into an optimization problem involves only scalar variab...