Convolutional Beamspace and Sparse Signal Recovery for Linear Arrays

The convolutional beamspace (CBS) method for DOA estimation using dictionary-based sparse signal recovery is introduced. Beamspace methods enjoy lower computational complexity, increased parallelism of subband processing, and improved DOA resolution. But unlike classical beamspace methods, CBS allows root-MUSIC and ESPRIT to be performed directly for ULAs without additional preparation since the Vandermonde structure for ULAs are preserved in the CBS output. Due to the same reason, it is shown in this paper that sparse signal representation problems can also be directly formulated on the CBS output. Significant reduction in computational complexity and higher probability of resolution are obtained by using CBS. It is also shown how the regularization parameter involved in the method should be chosen.