Capacity bound analysis for FIR Bézout equalizers in ISI MIMO channels

We provide a quantitative analysis for the capacity performance of zero-forcing equalizers, also known as Bézout equalizers, in a multiple antenna, frequency-selective fading environment with either parallel or sequential structure. The capacity upper bound of the equalizers, when there is no restriction on the filter length, is derived by directly extending the flat-fading results in a previous paper by the present authors. The parallel structure presents an inherent capacity loss quantified as a function of the channel couplings, which can be avoided by adopting an interference cancellation procedure in the sequential structure. For practical implementation, two approaches are investigated for finite impulse response (FIR) sequential equalizers - truncated LaBést (Layered Bézout Space-Time) and perfect LaBést equalizers. For truncated LaBést equalizers, the percentage of achievable capacity is derived as a function of the filter length in analytical form, and the empirical optimum delay is also provided. For perfect LaBést equalizers, we demonstrate that the filter choice that yields an optimum signal-to-noise ratio (SNR) can also asymptotically achieve the optimum infinite impulse response (IIR) capacity bound. Both of the two designs can approach the IIR capacity upper bound arbitrarily closely, provided there are an adequate number of FIR taps.