Performance Tradeoffs Among Adaptive Beamforming Criteria

In this paper, we study the tradeoffs among three main criteria for adaptive beamformer design: maximal signal-to-interference-plus-noise ratio (MSINR), minimal mean-squared error (MMSE), and minimal least-squares error (MLSE). When the power and steering vector of the signal-of-interest (SOI) are exactly known, there are beamformers that can simultaneously meet the MMSE and MSINR criteria. However, this is no longer true when the exact knowledge of the steering vector is unavailable. To account for steering vector errors, a meaningful approach, which we adopt in this paper, is to model the actual steering vector as random. In this setting, we show that the MMSE and MSINR criteria cannot be simultaneously attained. Therefore, using convex analysis tools, we study the achievable region in the MSE-SINR plane and propose an adaptive beamformer that can attain the frontier of operating points on the boundary of this region, providing an optimal performance tradeoff between SINR and MSE. In contrast, we show that even in the presence of steering-vector uncertainties, the MLSE and MSINR criteria are simultaneously achievable, and develop an adaptive beamformer which is optimal under both these criteria.