On asymptotics of Tomlinson-Harashima precoding with channel uncertainty

This paper analyzes the impact of uncertain channel information for a Tomlinson-Harashima precoder designed with the zero forcing criterion. The channel uncertainty is modeled as the channel matrix corrupted by additive Gaussian noise. General expressions are derived for the densities of the feedback and feedforward precoding matrices. Under an assumption of small variance in the channel uncertainty, asymptotic expressions are derived for both the two-user case and the general multiple users case.