Power loss analysis of Tomlinson-Harashima precoder with tilted constellation in flat fading MIMO channels

We analyze the power loss of Tomlinson-Harashima precoding with constellation tilting (THP-CT) method using M-QAM modulation in flat fading MIMO channels. To derive a new approximation of the power loss of THP-CT method, the effective channel components, the information symbols, the precoded symbols, and some of their combinations are analyzed stochastically. From the analysis of the signal components, the transmission power of the conventional THP is firstly approximated as the mean of the block average power for a fixed tilting angle. Then, the variance for a fixed angle and the dependence between the block average power terms with two tilting angles are approximated. Also, we modify the Clark's algorithm that approximates the expected minimum of dependent samples. By using the modified algorithm and also the mean, variance, and correlation factors, we provide a more accurate power loss approximation for THP-CT. Simulation results show that the proposed algorithm exploiting the analyzed dependence expression can reduce the approximation error up to about 60% and 70% for the case of 4-QAM and 16-QAM case, respectively.