On beamforming for overlay cognitive multiple antenna systems

We determine the maximum achievable rate in a cognitive multiple antenna system based on the overlay approach. The primary system is assumed to be oblivious to the cognitive system and thus non-adaptive. Furthermore, a primary receiver with a single antenna is considered. Thus, the covariance matrices for the primary messages are chosen according to beamforming strategies. We establish an iterative method for determining the optimum covariance matrix for the transmit strategy considered here. The optimum solution allows for the evaluation of suboptimum strategies. We investigate two suboptimum methods for determining the covariance matrix with the advantage that closed form solutions are available. The results reveal that the suboptimum solutions achieve performances close to the optimum.