The design of optimum transmission precoder for multi-input multi-output (MIMO) communication systems equipped with zero-forcing decision feedback (ZF-DF) receivers usually requires perfect knowledge of the channel state information (CSI) at both the transmitter and the receiver. In wireless communication systems, however, it is often difficult to provide sufficiently timely and accurate CSI feedback from the receiver to the transmitter for such designs to be practically viable. In this paper, we consider the transmission precoder design for a MIMO communication system having M transmitter antennas and N receiver antennas (M < N) in a wireless link in which the channels are assumed to be flat fading and possibly 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. The goal in this paper is to seek an efficient design of the optimal precoder for such a MIMO system by minimizing the total transmitting power of the ZF-DF receiver subject to a constraint on the average arithmetic mean square error (MSE). Utilizing majorization theory, we transform this non-convex optimization problem into a convex geometrical programming problem, which can then be efficiently solved using an interior point method. In the case of the MIMO random channel being uncorrelated, a closed-form solution to the optimization problem has also been obtained.