Robust Adaptive Beamforming under Quadratic Constraint

Adaptive beamforming has received considerable attention in the past decades due to its wide applications in the flelds of radar, sonar, seismology, radio astronomy, and wireless communications. One of the main problems that occur in practical adaptive array processing is the mismatches between the presumed and actual signal steering vectors. The performance of adaptive beamforming methods is known to degrade severely in the presence of such slight signal steering vector mismatches that may occur due to signal pointing errors, imperfect array calibration, source local scattering, wavefront distortions, etc. Similar types of performance degradation can take place because of the small training sample size. Quadratic constraints on the weight vector of an adaptive linearly constrained minimum power beamformer can improve robustness to the signal steering vector mismatches. 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 under a quadratic inequality constraint. To improve robustness, the weight vector is optimized to involve minimiza- tion of the output power function subject to the norm of error between the actual and assumed array beampatterns. We can show that the proposed algorithm belongs to the class of diagonal loading approaches, but the diagonal loading term can be precisely calculated based on the given level of uncertainties in the signal array response and data covariance matrix. Our proposed robust adaptive beamforming algorithm provides a signiflcantly improved robustness against the signal steering vector mismatches and small training sample size, enhances the array system per- formance under random perturbations in sensor parameters and makes the mean output array SINR consistently close to the optimal one. Computer simulation results validate substantial performance improvement of our proposed algorithm as compared with the existing adaptive beamforming algorithms.