Linear IIR-MMSE precoding for frequency selective MIMO channels

We consider the design of linear precoding filters with respect to the minimum mean square error (MMSE) criterion for systems that employ an additional scalar gain next to a fixed receive filter. The precoding filter and the scalar gain are to be jointly optimized. Currently, only the finite impulse response (FIR) solution to this problem is known. The goal of this paper is to derive the infinite impulse response (IIR) MMSE precoder both with and without causality constraint, i.e., finite and infinite latency time, respectively. We discuss the role of the scalar gain and its relationship to automatic gain control (AGC). We also show that causal precoding requires that the joint first arrival delay of channel and receive filter is not larger than the latency time, and that the IIR-MMSE precoder enjoys the same advantages over the FIR-MMSE precoder as the IIR-MMSE equalizer does over the FIR-MMSE equalizer, viz.: improved performance and no need for latency time optimization.