Multiuser spatio-temporal Tomlinson-Harashima precoding for frequency selective vector channels

We derive and compare different approaches to Tomlinson-Harashima precoding (THP) in frequency-selective multiuser scenarios with a centralized multiantenna transmitter and single-antenna receivers. Starting with spatio-temporal THP, we discuss how to simplify this relatively complex approach to systems that perform either spatial THP or temporal THP only. For each approach, we give a MMSE design rule for computing the feedforward and the feedback filters as well as the optimum latency time and the optimum order in which to encode the multiple data streams. Since the zero-forcing variants are special cases of the MMSE THP types, we only explain how zero-forcing THP can be obtain from MMSE THP. We compare the three THP approaches in terms of complexity and, using simulations, in terms of BER performance. While both simplifications to spatio-temporal THP can significantly reduce complexity, simulation results show that in frequency-selective scenarios, the temporal THP component is of particular importance with respect to BER performance