Zero-forcing equalization for time-varying systems with memory

In this article, we derive conditions for existence of zero-forcing multiuser detectors which achieve perfect reconstruction of the transmitted symbols. Compared to similar works in the literature, the derived conditions allow a reduction in the length of the equalizer filters, while imposing no constraints on the channel order and on the order of the precoder filters. Since the analysis is carried out in time domain, time varying filters are also considered.