Convex optimization based minimum probability of error beamforming in the uplink of a multiuser system

Motivated by power-limited uplink access, this paper proposes a receiver optimization for the uplink of a spatial multiple access scenario based on the concept of minimum probability of error (MPE) beamforming. Although MPE beamforming is shown to be more effective than the classical beamforming methods, it results in a non-convex and a highly nonlinear optimization problem. To resolve this problem, a set of modulated-based constraints is added to the MPE beamforming technique. It is shown that the solution to the constrained problem is equivalent to the original one. Moreover, it is proved that the constrained problem does not suffer from the existence of local minima and also has a unique global minimum. Finally the constrained problem is transformed into a convex optimization problem which can be solved using the existing convex programming algorithms.