Optimum Zero-forcing Beamforming with Per-antenna Power Constraints

We investigate optimum zero-forcing beamforming in multiple antenna broadcast channels with per-antenna power constraints. We show that standard zero-forcing techniques, such as the Moore-Penrose pseudo-inverse, considered mainly in the context of sum-power constrained systems are suboptimal when there are per-antenna power constraints. We formulate convex optimization problems to find the optimum zero-forcing beamforming vectors. Our results indicate that optimizing the antenna outputs based on the per-antenna constraints may improve the rate considerably when the number of transmit antennas is larger than the number of receive antennas. Having more transmit antennas gives rise to additional signal space dimensions that may be exploited effectively to reduce transmit power at particular antennas with limited power budget.