Point-to-point MIMO MMSE vector precoding and thp achieving capacity

Non-linear precoding for point-to-point (P2P) multiple-input multiple-output (MIMO) systems is considered. First, the minimum mean square error (MMSE) optimal vector precoding (VP) is presented for different receiver structures, viz., weighted identity matrix, diagonal matrix, weighted unitary matrix, and matrix without particular structure. Whereas the former two structures can also be applied to the vector broadcast channel, the latter two are only realizable for cooperative receivers. Second, VP is derived that minimizes the MSE but is restricted to maximize the mutual information of the MIMO channel. Third, the corresponding Tomlinson-Harashima precoding (THP) is found by applying the nearest-plane approximation to the computation of the perturbation signal. The resulting maximum mutual information THP clearly out-performs the state-of-the-art P2P-MIMO THP based on the generalized triangular decomposition (GTD) with respect to MSE and BER.