A Tomlinson-Harashima precoding for correlated MIMO channels

Highly correlated Multiple-Input Multiple-Output (MIMO) channels induce severe ill-conditioned MIMO channel matrices. MIMO receivers suffer from performance degradation due to the noise enhancement caused by the severe channel matrices. Precoding schemes, such as spatial Tomlinson-Harashima precoding (THP), can mitigate the performance degradation; however, the effect upon the highly correlated channels is insufficient. One way to avoid the noise enhancement is to turn off a few substreams related to the poor MIMO channels, which becomes possible by introducing an appropriate permutation matrix. We formulate a bit rate on the zero-forcing THP (ZF-THP) MIMO system, which shows that there is an optimum permutation matrix which maximizes the bit rate. We propose to apply a modified version of the sorted decomposition (SQRD) algorithm, which was originally developed for Vertical Bell Labs Layered Space Time (V-BLAST) receiver to carry out the QR decomposition of a MIMO channel matrix with permutation in its column direction simultaneously, to find a feasible permutation and create a precoder. Finally, it results in developing an efficient scheme to turn off the substreams. The proposed scheme is evaluated by computer simulations to verify its efficiency upon the correlated MIMO channels.