Blind Equalization Bounds for Tomlinson-Harashima Precoded Systems

Tomlinson-Harashima precoding (THP) and blind equalization are often viewed as incompatible equalization techniques. In this paper, we give multiple scenarios where the THP-blind equalization combination might arise. With this motivation we set out to answer the question, can a blind equalizer successfully acquire a THP-shaped signal? By bounding the kurtosis of the THP-shaped signal, we show that THP actually aids the initial convergence of blind equalization. We find that, as the symbol constellation size increases, the THP-shaped signal kurtosis approaches that of a uniform distribution, not a Gaussian. We then verify our analytical results using a Monte Carlo simulation of a VDSL channel.