End-fire Beamforming for Small Element Space Linear Arrays Based on Acoustic Pressure Gradient Analysis

The main lobe width and side lobe level of beampattern are two most important performance measures in beamforming. Super-directivity beamforming method can gain a narrower main lobe compared with conventional beams at end-fire direction for small interelement space uniform linear arrays(ULAs), and the Dolph-Chebyshev(DC) amplitude weighting method can obtain the lowest side lobe level at specific main lobe width. A new beamforming method at end-fire direction for small aperture linear arrays based on acoustic pressure gradient analysis is proposed in this paper. The method combines the super-directivity theory and DC weighting method. The mode-filter matrix is used to extract higher order modes of pressure gradients at array center from the array manifold. The end-fire beam pattern is synthesized with DC weights in mode domain, and then the beam forming weights are transformed into element domain. Compared with the common DC weighted beam forming, this new approach can obtain better performance at end-fire direction. Simulation results show that this method is effective.