Optimum Power Control for a Multi-User MIMO System with Beamforming

A multi-user multiple input multiple output (MIMO) system with beamforming based on maximum ratio transmission (MRT) is analyzed in a Rayleigh fading environment. A simple closed and compact form approximate expression for the outage probability of a mobile station for the downlink of such a system is obtained by considering that all the mobile stations are power controlled by a single base station. An interesting observation of the analysis is that an optimum power control problem can be formulated based on the outage probability of each mobile station in the downlink because the outage probability computation is easily simplified for a cellular environment where all the mobile stations are power controlled by the single base station. The objective is to minimize the base station transmission power by keeping the outage probability of all mobile stations below a specified threshold value. The optimization problem is non-convex and non-linear. We use an evolutionary strategy (EV) (T.P. Runarsson and X. Yao, 2000) to solve such a non-convex optimization problem