Beam-domain deconvolution beamforming algorithm enhanced by compressive sensing

Deconvolution beamforming can effectively suppress sidelobes and improve the azimuth resolution of multiple targets. However, traditional deconvolution beamforming methods mostly require the beam pattern to be shift-invariant, so they are only suitable for specific arrays such as linear arrays and circular arrays. Traditional deconvolution beamforming methods usually focus on beamforming intensity, which proves inadequate for handling coherent signals. To address this limitation, a deconvolution beamforming method for arbitrary arrays in beam domain is proposed, which is developed within the framework of compressive sensing. This method first uses conventional beamforming to obtain several complex output beams, and then applies the sparse Bayesian learning (SBL) algorithm to achieve deconvolution of complex output beams. This deconvolution process enhances the accuracy of direction of arrival (DOA) estimation for true targets. The proposed method effectively reduces computational complexity by optimizing the number of output beams generated during conventional beamforming. It is equally applicable to both uncoherent and coherent signals, outperforming conventional deconvolution beamforming methods. The simulation and experimental results demonstrate that the proposed method has azimuth resolution performance comparable to the traditional SBL beamforming in element domain, while outperforming conventional beamforming and minimum variance distortionless response (MVDR) method. When applied to short dense arrays, the proposed method achieves significantly lower computational complexity compared to traditional SBL in element domain, particularly when the number of output beams from conventional beamforming is much smaller than the number of array elements.