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A Modified Differential Beamforming and Its Application for DOA Estimation of Low Frequency Underwater Signal

Conventional beamforming (CBF) will lose its directivity once the signal frequency is much lower than the designed frequency of the array. In this paper, a modified differential beamforming (MDBF) method is proposed to deal with the underwater acoustic signal at low frequency band and then its application for direction of arrival (DOA) estimation with deconvolution technique is given. The MDBF proposed in this paper is a variation of the conventional differential beamforming (DBF) method and it constructs an optimization problem with an additional robustness constraint. The solution of MDBF solved via Lagrange multiplier technique owns a closed-form similar to that of DBF except two additional loading terms. Simulations with planar arrays show that for the frequency band where CBF owns an almost omnidirectional beampattern, MDBF outperforms DBF in robustness at the cost of some directivity loss. The application of MDBF for DOA estimation is demonstrated with both simulated and experimental data. The results show that the proposed MDBF outperforms both DBF and CBF in DOA estimation at low frequency band.