Limited Feedback Design of MIMO Systems with Zero-forcing DFE Using Grassmann Codebooks

We consider the design of multiple-input multiple-output communication systems with zero-forcing decision feedback equalization (DFE) in which perfect channel state information (CSI) is available only at the receiver. Based on its channel knowledge, the receiver will select a suitable precoder from a codebook and will feed back the index of this precoder to the transmitter using a limited number of feedback bits. We begin by developing a unified framework for the joint design of the precoder and DFE receiver that embraces a wide range of design criteria. We then 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 will minimize an upper bound on an average distortion measure. Our simulation study shows that using only a limited number of of feedback bits, the proposed scheme can achieve that same rate of decay of bit error rate with signal to noise ration (SNR) as that achieved with perfect CSI at the transmitter.