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For precoder design problems in a multi-input multi-output (MIMO) communication system, perfect knowledge of the channel state information (CSI) at both the transmitter and the receiver is usually required. However, it is often difficult to provide sufficiently timely and accurate feedback of CSI from the receiver to the transmitter for such designs to be practically viable. In this paper, we consider the optimum design of a precoder for a wireless communication link having M transmitter antennas and N receiver antennas (M < N), in which the channels are assumed to be flat fading and may be correlated. We assume that full CSI is known at the receiver, but only the first- and second-order statistics of the channels are available at the transmitter. Our goal is to come up with an efficient design of the optimal precoder for such a MIMO system by minimizing the average arithmetic mean-squared error (MSE) of zero-forcing decision feedback (ZF-DF) detection subject to a constraint on the total transmitting power. We transform this non-convex optimization problem into a convex geometrical programming problem, which can then be efficiently solved using an interior point method. For the case when the transmission channels are uncorrelated, a closed-form solution of the optimum precoder has been obtained. The superior performance of our MIMO system equipped with the optimum precoder is verified by computer simulations.