Robust Adaptive Beamforming under the Quadratic Inequality Constraint

When adaptive arrays are applied to practical problems, the performances of the conventional adaptive beamforming algorithms are known to degrade substantially in the presence of even slight mismatches between the actual and presumed array responses to the desired signal. Similar types of degradation can occur when the signal array response is known exactly, but the training sample size is small. In this paper, based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix, we propose robust adaptive beamforming algorithm for implementing a quadratic inequality constraint. We show that the proposed algorithm belongs to the class of diagonal loading approaches, but diagonal loading terms can be precisely calculated based on the given level of uncertainties in the signal array response and data covariance matrix. Our proposed robust algorithm improves the overall robustness against the signal steering vector mismatches and small training sample size, enhances the array system performance under random perturbations in sensor parameters and makes the mean output array SINR consistently close to the optimal one. Computer simulation results demonstrate excellent performance of our proposed algorithm as compared with the existing adaptive beamforming algorithm.