Optimal Multi-User Interference Balancing Using Transmit Beamforming

We study the problem of non-orthogonal spatial multiplexing under hard fairness constraints, assuming that the transmitter is equipped with multiple antennas and each of the independent receivers has a single antenna. Channel state information is available at the transmitter. All users are coupled by co-channel interference, thus maintaining individual QoS requirements requires the joint optimization of beamforming and power control. In this paper we study the problem in the absence of noise. The achievable signal-to-interference-ratios (SIR) of all user are limited by the amount of mutual cross-talk. The design question: at which level can the relative SIR levels be balanced under the given channel condition, and what are the optimal beamforming weights? Our approach is analytic. By exploiting the duality between uplink and downlink beamforming, we derive an iterative optimization scheme that is globally convergent and always finds the optimally balanced level. This provides a necessary and sufficient condition for the feasibility of the given scenario. Hence, the results will prove useful for the design of new beamforming algorithms as well as for new spectrally efficient resource allocation strategies.