Optimal Precoder Design for Correlated MIMO Systems Using Decision Feedback Receivers

We consider the design of the precoder for a multi-input multi-output (MIMO) communication system equipped with a decision feedback equalizer (DFE) receiver. For such design problems, perfect knowledge of the channel state information (CSI) at both the transmitter and the receiver is usually required. However, in the wireless communications environment, 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 knowledge of CSI is available at the receiver. At the transmitter however, only the second order statistics of the channels are available. Our goal here 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 (ZF) decision feedback detection subject to a constraint on the total transmitting power. Applying some of the properties of the matrix parameters, this non-convex optimization problem can be transformed into a convex geometrical programming problem which can then be efficiently solved using an interior point method. The superior performance of our MIMO system equipped with the optimum precoder is verified by computer simulations.