Minimum bit error rate nonlinear precoding for multiuser MIMO and high SNR

This manuscript focuses on the minimization of the bit-error-rate in the high signal to noise ratio regime, for the downlink of a multiuser MIMO channel with NN transmit antennas and KK single antenna users. In the design of such a precoder the knowledge of the transmitted data and full channel state information at the transmitter are assumed. It is shown that, in the high signal to noise regime, the problem simplifies from a constrained quadratic nonlinear optimization to a single quadratic program, allowing to reduce the complexity. This quadratic problem is equivalent to maximize the minimum distance between the user received symbols and corresponding decision boundaries. The proposed algorithm selects and inverts part of the correlation matrix, unlike the zero-forcing where full inversion is required. This leads to a better performance as the selection allows us to get a better conditioned matrix. Also, this allows us to treat zero-forcing as a special case of the algorithm. The results show that the algorithm achieves a performance close to the optimum, with much lower complexity.