Optimization of error probability of multi-antenna broadcast channel using convex optimization

We consider the problem of multi-antenna broadcast transmitter design which minimizes the probability of bit error subject to, alternatively, peak or average power constraints. The proposed transmitter represents a nonlinear one-to-one mapping of the broadcast data and is obtained as a solution to a convex error probability optimization problem that can be obtained 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.