Achievable Rates for Tomlinson-Harashima Precoding

This correspondence examines Tomlinson–Harashima precoding (THP) on discrete-time channels having intersymbol interference and additive white Gaussian noise. An exact expression for the maximum achievable information rate of zero-forcing (ZF) THP is derived as a function of the channel impulse response, the input power constraint, and the additive white Gaussian noise variance. Information rate bounds are provided for the minimum mean-square error (MMSE) THP. The performance of ZF-THP and MMSE-THP relative to each other and to channel capacity is explored in general and for some example channels. The importance of symbol rate to ZF-THP performance is demonstrated.