Real-valued DOA estimation for spherical arrays using sparse Bayesian learning

Spherical arrays have many advantages for direction-of-arrival (DOA) estimation in 3D space. In this paper, a new real-valued method is proposed to estimate DOAs for spherical arrays. It exploits the property of the complex conjugate of spherical harmonics to find a unitary matrix which can transform the complex array steering matrix into a real matrix. Based on the unitary transformation, a new real-valued array model is constructed to keep the same dimension as the complex-valued model. Then variational sparse Bayesian learning (VSBL) is used to model the joint sparsity between the real part and imaginary part of original data. We get the approximate posterior of the sparse components. The real-valued DOA estimation method acquires good estimation performance and simultaneously decreases the computational cost considerably. Simulation results demonstrate the performance of the proposed method.