On SINR Loss-Based Robust ABF Under Mismatch and Signal Contamination

The widely used diagonal loading approach for robust adaptive beamforming (RABF) is based on maximizing the signal-to-interference plus noise ratio (SINR) while constraining the gain against white noise of the desired beamforming weight vector. Alternatively, the SINR loss-constrained beamformer (SLCB) proposed by Richmond maximizes the gain against white noise while constraining the SINR loss relative to the optimal Capon beamformer. This paper investigates certain aspects of the SLCB under non-ideal conditions such as steering vector mis-match and unavailability of signal-free training data (challenges common to sonar processing). Under the ideal assumption of known data covariance, the expression for the output SINR under array position errors provided by Gilbert and Morgan is utilized to demonstrate the utility of the SLCB as well as the diagonal loading approach. In a practical scenario, the SLCB requires an estimate of the SINR loss based on the sample covariance matrix. The distribution for such an SINR loss estimate is derived under the scenario of steering vector mismatch, and the effect of the presence of the desired signal in the data covariance is discussed. An approach for estimating the interference-only covariance matrix, motivated by maximum likelihood estimation is also outlined.