Capon beamforming is often applied in passive sonar to improve the detectability of weak underwater targets. However, we often have no accurate prior information of the direction-of-arrival (DOA) of the target in the practical applications of passive sonar. In this case, Capon beamformer will suffer from performance degradation due to the steering vector error dominated by large DOA mismatch. To solve this, a new robust Capon beamforming approach is proposed. The essence of the proposed method is to decompose the actual steering vector into two components by oblique projection onto a subspace and then estimate the actual steering vector in two steps. First, we estimate the oblique projection steering vector within the subspace by maximizing the output power while controlling the power from the sidelobe region. Subsequently, we search for the actual steering vector within the neighborhood of the estimated oblique projection steering vector by maximizing the output signal-to-interference-plus-noise ratio (SINR). Semidefinite relaxation and Charnes-Cooper transformation are utilized to derive convex formulations of the estimation problems, and the optimal solutions are obtained by the rank-one decomposition theorem. Numerical simulations demonstrate that the proposed method can provide superior performance, as compared with several previously proposed robust Capon beamformers in the presence of large DOA mismatch and other array imperfections.
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