Joint downlink transmit and receive beamforming under per-antenna power constraints

Conditioned with per-antenna power constraints, power allocation over transmit antennas must be controlled in joint optimization of transmit beamformers and receive beam-formers in multi-user multiple-input multiple-output (MIMO) downlink. In this paper, it is shown the Lagrangian dual of the per-antenna power constrained optimization problem is related to the network dual of a weighted sum power optimization problem without power constraints. From this perspective, the virtual uplink noises are found to be playing important roles. A scheme to manage power allocation over antennas by adjusting the virtual uplink noises during optimization is proposed. Under this scheme, two algorithms with different functions are designed and show good performance in simulations.