A Design Framework for Limited Feedback MIMO Systems with Zero-Forcing DFE

We consider the design of multiple-input multiple-output communication systems with a linear precoder at the transmitter, zero-forcing decision feedback equalization (ZF-DFE) at the receiver, and a low-rate feedback channel that enables communication from the receiver to the transmitter. The channel state information (CSI) available at the receiver is assumed to be perfect, and based on this information the receiver selects a suitable precoder from a codebook and feeds back the index of this precoder to the transmitter. Our approach to the design of the components of this limited feedback scheme is based on the development, herein, of a unified framework for the joint design of the precoder and the ZF-DFE under the assumption that perfect CSI is available at both the transmitter and the receiver. The framework is general and embraces a wide range of design criteria. This framework enables us to characterize the statistical distribution of the optimal precoder in a standard Rayleigh fading environment. Using this distribution, we show that codebooks constructed from Grassmann packings minimize an upper bound on an average distortion measure, and hence are natural candidates for the codebook in limited feedback systems. We also show that for any given codebook the performance of the proposed limited feedback schemes is an upper bound on the corresponding schemes with linear zero-forcing receivers. Our simulation studies show that the proposed limited feedback scheme can provide significantly better performance at a lower feedback rate than existing schemes in which the detection order is fed back to the transmitter.