Error Analysis of Convolutional Beamspace Algorithms

Beamspace processing for DOA estimation offers low computational complexity and high DOA resolution. Moreover, unlike classical beamspace methods, convolutional beamspace (CBS) preserves the Vandermonde structure of uniform linear array output, so no additional preparation is needed to apply root-MUSIC. In this paper, theoretical MSE of CBS is given when MUSIC or root-MUSIC is used. Error variance can be derived from the asymptotic probability distribution of the eigenvectors of an average finite-snapshot covariance matrix. Meanwhile, the bias due to the filtered stopband sources is given by first-order perturbation analysis. Known advantages of CBS are confirmed by the MSE analysis. For example, CBS yields smaller MSE for correlated sources than element-space. The theoretical results are verified by simulations.