Two-stage MUSIC with reduced spectrum search for spherical arrays

Abstract

The multiple signal classification (MUSIC) algorithm is widely used in direction of arrival (DOA) estimation. Conventional MUSIC-like algorithms suffer from the heavy computational burden imposed by the two-dimensional (2-D) angle search and an exhaustive spectral search. We propose a two-stage unitary spherical harmonics MUSIC (TSU-SHMUSIC) that converts 2-D MUSIC into two new one-dimensional (1-D) MUSICs. The spherical harmonic steering vector is expressed in two forms, the linear weight of a uniform phase vector and the linear weight of a vector constructed by associated Legendre functions. These two expressions are used conjunction with Lagrange multiplier method to obtain two new corresponding search functions for the elevation and azimuth. We exploit the characteristics of real-valued spherical harmonics to construct virtual signals from the mirror directions of signal sources. A new noise subspace is computed from the covariance matrices of the virtual and real signals. We use this noise subspace to reduce the angle search ranges to half of the total angular field of view. The proposed methods have a considerably lower computational complexity than U-SHMUSIC. Numerical simulations demonstrate that the proposed methods provide perform better than the two-stage decoupled approach (TSDA).