The application of genetic algorithm (GA) optimization has been proven to be highly successful in the area of non-linear optimizations. For a Multiple-Input, Multiple-Output (MIMO) wireless communication system, the optimum performance of the users with respect to the arrangement of antennas is a highly non-linear function which a genetic algorithm seems highly suited to. In this paper, a four-by-four MIMO system model is considered using a simplified 2-D LOS radio channel with additive white noise. Placing the users in a known arrangement, the optimum placement of the four antennas is determined through a genetic algorithm optimization using the average MSE of the four users as the fitness function. Initial results show a tendency towards an arrangement in which at least two antennas seen by the all transmitters are separated by a symbol wavelength.