Robust Adaptive Beamforming Under Quadratic Constraint with Recursive Method Implementation

Abstract

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 performance degradation can occur because of data nonstationarity and small training sample size, when the signal steering vector is known exactly. In this paper, to account for mismatches, we propose robust adaptive beamforming algorithm for implementing a quadratic inequality constraint with recursive method updating, which is based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix. 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. The variable diagonal loading term is added at each recursive step, which leads to a simpler closed-form algorithm. Our proposed robust recursive 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. Moreover, the proposed robust adaptive beamforming can be efficiently computed at a low complexity cost compared with the conventional adaptive beamforming algorithms. Computer simulation results demonstrate excellent performance of our proposed algorithm as compared with the existing adaptive beamforming algorithms.