Downlink MU-MIMO With THP Combined With Pre- and Post-processing and Selection of the Processing Vectors for Maximization of Per-Stream SNR

In this paper, we consider a downlink multiuser multiple-input-multiple-output (MU-MIMO) system with multiple antennas at the transmitter and multiple antennas at each user, where the transmitter can send one or more data streams to each user. We propose a non-iterative method by combining Tomlinson-Harashima precoding (THP) with pre- and post-processing and selecting processing vectors based on the maximization of instantaneous signal-to-noise ratio (SNR) of the data stream at the input of the detector of each user. The postprocessing vectors for all users are found to be eigenvectors corresponding to the maximum eigenvalue of a certain matrix involving the channel matrix of the user. The transmitter computes the vectors of the linear processing matrix through an orthonormalization procedure in a single step. The feedback matrix at the transmitter is then obtained from the effective channel matrix and the linear processing matrix. We express the instantaneous SNR of all data streams in terms of eigenvalues of a Wishart matrix, obtained from the channel matrix of the user, and find the diversity order for each data stream. Considering multiple scenarios, we find the outage probability of the instantaneous SNR for all data streams and the cumulative distribution function (cdf) of the sum-rate capacity for all users using the proposed method and compare the results with those of recently proposed methods that provide a closed-form solution and with that of block diagonalization, channel inversion, and THP in scenarios where they are applicable.