Combined THP and Linear Precoding to Achieve Maximum Equalization Gain

In this paper, we propose a novel equalization scheme combining the Tomlinson-Harashima precoding (THP) and linear precoding for frequency selective fading channels. The newly introduced linear precoder at the transmitter is jointly designed with the feedforward filter (FFF) and the feedback filter (FBF) of the THP unit, aiming to minimize the mean-squareerror (MSE) of the receive signal. The final solutions obtained are closely related to a novel matrix decomposition named Geometric-Mean Decomposition. It is shown that the new scheme eventually attains the receive SNR/SINR upper bound of the conventional non-linear equalization systems, thus enjoys much better error performance. Furthermore, the implementation issue is considered by proposing a suboptimal scheme which enables the designer to take a tradeoff between the system performance and complexity. Numerical results are presented to demonstrate the superior performance of the proposed schemes.