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In this paper, we investigate a unified linear transceiver design with mean-square-error (MSE) as the objective function for a wide range of wireless systems. The unified design is based on an elegant mathematical programming technology namely quadratic matrix programming (QMP). It is revealed that for different wireless systems such as multi-cell coordination systems, multi-user MIMO systems, MIMO cognitive radio systems, amplify-and-forward MIMO relaying systems, the MSE minimization beamforming design problems can always be solved by solving a number of QMP problems. A comprehensive framework on how to solve QMP problems is also given.