Robust downlink beamforming based upon outage probability criterion

Abstract

We propose a new downlink beamforming algorithm that provides robustness against uncertainty of the assumed downlink spatial covariance matrix at a base station (BS) that uses 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 total downlink transmit power under the condition that the non-outage probability of each mobile station in the downlink is greater than a certain threshold value. Our approach leads to a semidefinite relaxation problem that can be solved efficiently using the well-established interior point methods. Computer simulations are used to compare the performance of our method with that of the robust transmit 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 the downlink spatial covariance matrices.