Convex optimization of error probability of multi-antenna broadcast channel

In this paper, we propose a nonlinear convex optimization problem to minimize the average probability of error of all the users, subject to the peak or the average power constraints in the multi-input–multi-output broadcast channel. The proposed transmitter represents a nonlinear one-to-one mapping between the transmitted data vector and the symbol vector. The transmitted data vector going through the base station antennas is obtained as a solution to the proposed convex error probability optimization problem that can be solved using computationally efficient interior point algorithms. It is proved that the proposed transmitter is always optimal unless the signal-to-noise ratio (SNR) is too low or the channel is nearly singular. Simulation results demonstrate that the proposed transmission scheme significantly improves the probability of error as compared to several earlier approaches to multi-antenna broadcast transmitter design.