Achievable Rate Region for Downlink Beamforming in the Presence of Interference

We study in this paper optimal signaling for downlink transmission with mutual interference. Restricting each receiver to a single user detector, we show that computing the achievable rate region amounts to solving a family of non- convex optimization problems. Recognizing the intrinsic connection between the signal power at the intended receiver and the interference power at the unintended receiver, we convert the original family of non-convex optimization problems into a new family of convex optimization. Closed-form solutions to this new family of optimization problems are derived. Interestingly, with multiple-antenna transmitters and single-antenna receivers, the optimal downlink transmission with interference always reduces to a simple beamforming scheme. Finally, we note that similar procedure can be devised for systems with more than two pairs of mutually interfering users.