Unitary transformations for spherical harmonics MUSIC

Spherical arrays have been widely used in direction-of-arrival (DOA) estimation in recent years. In this paper, two unitary transformations for DOA estimation using spherical arrays are developed to transform the complex search vector to a real vector. Furthermore, the covariance matrix is transformed into a real matrix which has real eigenvalues and eigenvectors. Therefore, we can develop a real spherical harmonics multiple signal classification (RSHMUSIC) method to estimate the locations of signals. By exploiting the phase shift characteristic of the real search vector, the computation cost can be further reduced. Compared with the complex spherical harmonics MUSIC, the proposed methods have a lower amount of computations and better performance. Simulation results demonstrate the performance of the real SHMUSIC method.