Convexity analysis of the feasible MSB region of sum-power constrained multiuser MIMO systems

We study the geometry of the feasible MSE region of multiuser MIMO systems with fixed transmitters and receivers. The sum of all powers is assumed to be constrained. We consider both linear processing and non-linear processing, i.e., interference precompensation in the downlink and successive interference cancellation in the uplink. We show that, for both cases, the feasible MSE region of uplink and downlink is a convex set. In addition, we show for adaptive multiuser reception/precoding, that the maximal feasible MSE region for two-user beamforming systems with adaptive MMSE filtering are convex.