Robust Minimum Variance Adaptive Beamformers and Multiuser MIMO Receivers: From the Worst-Case to Probabilistically Constrained Designs

Two related problems of the design of robust adaptive beamformers and multiuser multiple-input multiple-output (MIMO) receivers are considered. A popular recent solution to these problems is based on the worst-case performance optimization. Unfortunately, in practical applications the actual worst case occurs with a very low probability and, as a result, the worst-case based designs may be overly conservative. As a less conservative alternative to the worst-case designs, the so-called probabilistically constrained designs are introduced. The latter approach guarantees that the distortionless response constraint is satisfied for a mismatched array response with a certain selected probability. Improved flexibility and performance of the robust probabilistically constrained designs with respect to the worst-case designs are illustrated via simulations.