I. Introduction
Multiple-input multiple-output (MIMO) wireless systems [1] have been extensively investigated due to the potential for high-speed transmission in many different communication scenarios, such as unicast with single user and broadcast with multiple users. When the perfect channel knowledge is available at the transmit side, various precoding schemes can be employed to improve spectral efficiency as well as link reliability for the MIMO system. It's rational that for MIMO Gaussian channels with finite alphabet input, the bit-error-rate (BER) performance is essentially dominated by the minimum Euclidean distance between points in the received signal space. In this regard, a linear precoder, associated with the maximum likelihood (ML) receiver, is considered in this paper under the criterion of maximizing the minimum Euclidean distance with average transmit power constraint, which is referred to as minimum-distance precoder hereinafter.