Robust uplink beamforming based upon minimum outage probability criterion

In this paper, we propose a new uplink beamforming algorithm that provides robustness against the uncertainty of the assumed spatial covariance matrix at a base station (BS) which employs antenna arrays. This uncertainty arises due to the difference between the presumed and the actual array response as well as the estimation errors of the fading coefficients. In our method, we exploit the assumed statistical distribution of the uncertainty to minimize the outage probability of each mobile station in the uplink. Our approach leads to a semidefinite relaxation problem that can be solved efficiently using the well-established interior point methods. Simulation results show that our method slightly outperforms the robust adaptive beamforming based upon worst-case performance optimization. Moreover, the proposed technique avoids the necessity of the knowledge of the norm bounds of the uncertainty of spatial covariance matrices.