Transmit beamforming for multiuser downlink with per-antenna power constraints

We consider the transmit beamforming design for a multi-user downlink with multiple transmit antennas at the base station. Different from the conventional sum-power constraint across the transmit antennas, we assume individual power constraints per antenna. Assuming that perfect channel state information (CSI) is available at the base station, we develop an efficient algorithm to find the optimal beamforming scheme for the classic max-min signal-to-interference-plus-noise ratio (SINR) problem based on solving a sequence of “dual” per-antenna power balancing problems as second-order cone programs. It is proven that the proposed algorithm can find the max-min SINR beamforming solution with guaranteed global optimality and fast convergence speed. Relying on robust optimization techniques, the approach is also generalized to obtain the robust beamforming design that maximizes the worst-case user SINR when the channel uncertainty is bounded by a spherical region. Numerical results are provided to demonstrate the merits of the proposed transmit beamforming schemes.