Adaptive Beamforming with Hydrophone Arrays Based on Oblique Projection in the Presence of the Steering Vector Mismatch

In sonar systems, the performance of adaptive beamformers severely degrades when mismatches occur between the actual and presumed steering vectors of the desired signal, mainly due to hydrophone position errors, amplitude-phase errors, and the scattered effect of arrays. Similarly, an inadequate number of “training” samples can lead to performance degradations similar to those caused by mismatches. In this paper, an adaptive beamforming algorithm based on oblique projection (OP-ABF) mismatch compensation is proposed to remove the degradation caused by the arbitrary-type steering vector mismatch of the desired signal. The proposed algorithm is motivated by the fact that the weight vector of adaptive beamforming can be represented as a linear combination of the optimal one and the oblique projection (OP) vector, which is generated by the steering vector mismatch and does not exist without this. Our algorithm was developed by constructing the oblique projection mismatch compensation vector (OPMCV) to provide the minimum variance distortionless response (MVDR) beamformer. Then, the algorithm could be implemented by the solution of the OP matrix with the formulation of the covariance matrix loading (CML). The simulation results of a uniform linear array (ULA) and a half-cylindrical conformal array (HCCA) show that the OP-ABF can optimize the original weight vector as much as possible without sacrificing the output signal-to-interference-plus-noise ratio (SINR) under different conditions. Experimental results for the HCCA also confirm the effectiveness of this algorithm.