Filterbank precoding for MIMO frequency selective channels: minimum redundancy and equalizer design

This paper deals with the problem of designing zero forcing finite impulse response (ZF-FIR) equalizers for multiple input multiple output (MIMO) FIR channels, in a polynomial matrix framework. When channel knowledge is available at the transmitter, a precoding operation, which introduces redundancy, can be performed to enable FIR equalization at the receiver. We derive the expression for the minimum redundancy required to render an arbitrary MIMO channel matrix polynomially invertible. The non-uniqueness of the FIR inverse can be used to design equalizers based on different criteria such as noise minimization, low delay and low complexity. We provide a solution for the equalizer which minimizes the output noise power. Simulation results are provided to demonstrate the effectiveness of the proposed design.