Realizable minimum mean-squared error channel shorteners

We present an analysis of realizable (i.e., causal, stable, and of finite degree) minimum mean-squared error (MMSE) channel shorteners for multiple-input multiple-output (MIMO) systems, driven by spatially and temporally white signals, and subject to a constant output power constraint. This is of interest since this design has recently been shown to result in near optimal rate performance in multitone transceivers, and the performance of conventional finite impulse response (FIR) shorteners is upper bounded by that of realizable schemes. The MMSE shortener is shown to consist of a prewhitening filter followed by an FIR postfilter of order equal to the sum of the overall delay and the target shortening length. It is shown that this design results in output decorrelation and that the shortener output enjoying the smallest MMSE sees a target impulse response without zeros inside the unit disk. The asymptotic behavior of the shortened system is explored, and performance bounds are provided in terms of the channel frequency response and the noise power spectral density.