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It has been shown that the performance of multiple-input multiple-output (MIMO) spatial multiplexing systems is significantly degraded when spatial correlation exists between transmit and receive antenna pairs. In this paper, we investigate designs of a new statistical precoder for spatial multiplexing systems with maximum likelihood (ML) receiver which requires only correlation statistics at the transmitter. Two kinds of closed-form solution precoders based on rotation and power allocation are proposed by means of maximizing the minimum Euclidean distance of joint symbol constellations. In addition, we extend our results to linear receivers for correlated channels. We provide a method which yields the same profits from the proposed precoders based on a simple zero-forcing (ZF) receiver. The simulation shows that 2dB and 8dB gains are achieved for ML and ZF systems with two transmit antennas, respectively, compared to the conventional systems.