MMSE FIR zero-forcing equalizer for shorten length trailing zero precoder

A systematic method for designing minimal mean square error (MMSE) FIR equalizer for shorten length trailing zero (TZ) precoder is proposed in this paper. The TZ precoder considered here based on nonmaximally decimated filterbank allows the number of inserted zeros to be as less as one zero per block of transmitted symbols for an arbitrary channel order. This overrides the minimal redundancy insertion constraint in traditional TZ precoding system, such that the proposed equalizer can maximize the channel throughput by minimizing the inserted redundancy. A systematic method for parameterizing the solution of ZF equalizer is derived. The parameterized solution is useful for analyzing and computing the optimal ZF equalizer with a given optimization criteria. Simulation results are presented to illustrate the advantages of the MMSE equalizers obtained by the proposed design method.