Computationally Efficient Robust Beamforming for SINR Balancing in Multicell Downlink With Applications to Large Antenna Array Systems

We address the problem of the downlink beamformer design for signal-to-interference-plus-noise ratio balancing in a multiuser multicell environment with imperfectly estimated channels at base stations. We first present a semidefinite program (SDP)-based approximate solution to the problem. Then, as our main contribution, by exploiting some properties of the robust counterpart of the optimization problem, we arrive at a second-order cone program (SOCP)-based approximation of the balancing problem. The advantages of the proposed SOCP-based design are twofold. First, it greatly reduces the computational complexity compared to the SDP-based method. Second, it applies to a wide range of uncertainty models. As a case study, we investigate the performance of proposed formulations when the base station is equipped with a massive antenna array. Numerical experiments are carried out to confirm that the proposed robust designs achieve favorable results in scenarios of practical interest.