Beamspace Root-MUSIC

Motivated by the superior performance of Root-MUSIC relative to spectral MUSIC and ESPRIT in a uniform linear array scenario and the many advantages of operating in beamspace, a beamspace implementation of Root-MUSIC is developed. To facilitate reduced computational complexity, procedures are presented for designing orthogonal matrix beam-formers composed of conjugate centrosymmetric weight vectors and producing beams exhibiting common out-of-band nulls. It is shown that the former property enables one to work with the real part of the beamspace sample covariance matrix irrespective of the angle-of-arrival estimation algorithm employed. The latter property enables one to work with a reduced degree polynomial in the final stage of Root-MUSIC. The N x B discrete Fourier transform (DFT) matrix beamformer composed of B columns of the N x N DFT matrix, where N is the number of elements, is employed as a prototype matrix beamformer possessing the aforementioned properties. It is used to establish these two results and to derive other matrix beamformers having the desired features plus additional features, such as producing beams with reduced out-of-band sidelobes and/or common nulls at prescribed locations. Simulations are presented comparing the performance of beamspace Root-MUSIC with that of element space Root-MUSIC and that of beamspace spectral MUSIC.