Convolutional Beamspace for Linear Arrays

A new beamspace method for array processing, called convolutional beamspace (CBS), is proposed. It enjoys the advantages of classical beamspace such as lower computational complexity, increased parallelism of subband processing, and improved resolution threshold for DOA estimation. But unlike classical beamspace methods, it allows root-MUSIC and ESPRIT to be performed directly for ULAs without additional preparation since the Vandermonde structure and the shift-invariance are preserved under the CBS transformation. The method produces more accurate DOA estimates than classical beamspace, and for correlated sources, better estimates than element-space. The method also generalizes to sparse arrays by effective use of the difference coarray. For this, the autocorrelation evaluated on the ULA portion of the coarray is filtered appropriately to produce the coarray CBS. It is also shown how CBS can be used in the context of sparse signal representation with dictionaries, where the dictionaries have columns that resemble steering vectors at a dense grid of frequencies. Again CBS processing with dictionaries offers better resolution, accuracy, and lower computational complexity. As only the filter responses at discrete frequencies on the dictionary grid are relevant, the problem of designing discrete-frequency FIR filters is also addressed.