Tomlinson-Harashima precoding with partial channel knowledge

Abstract—We consider minimum mean-square error Tom-linson–Harashima (MMSE-TH) precoding for time-varying frequency-selective channels. We assume that the receiver esti-mates the channel and sends the channel state information (CSI) estimate to the transmitter through a lossless feedback channel that introduces a certain delay. Thus, the CSI mismatch at the receiver is due to estimation errors, while the CSI mismatch at the transmitter is due to both estimation errors and channel time variations. We exploit a priori statistical channel knowledge, and we derive an optimal TH precoder, adopting a Bayesian approach. We use simulations to compare the performance of the so-derived TH precoder with that of the same-complexity MMSE decision-feedback equalizer (DFE). We observe that for low signal-to-noise ratios (SNRs) and sufficiently slow channel time variations, the optimal TH precoder outperforms the DFE, while at high SNR, the opposite happens. Index Terms—Intersymbol interference (ISI), partial channel knowledge, Rayeigh fading, Tomlinson–Harashima (TH) precoder