Real-Valued Sparse Bayesian Learning for DOA Estimation with Arbitrary Linear Arrays

Sparse Bayesian learning (SBL) has become a popular approach for direction-of-arrival (DOA) estimation, but its computational complexity for Bayesian inference is quite high because calculating inverse of a large complex matrix per iteration is required. It is known that the computational load can be reduced by transforming the complex-valued problem into a real-valued one. However, the commonly used real-valued transformation works for uniform linear arrays (ULAs) only. In this paper, we propose a new real-valued transformation for DOA estimation with arbitrary linear arrays by exploiting the virtual steering of linear arrays. Then, we introduce an alternating optimization algorithm based on the variational Bayesian inference (VBI) methodology to iteratively obtain a stationary solution to the real-valued sparse representation problem. Because of utilizing the additional real-valued structure, the VBI scheme can achieve a better performance in terms of both estimation accuracy and computational complexity. Moreover, we embed the generalized approximate message passing (GAMP) into the VBI-based method for further complexity reduction. Although there may be a performance loss for the GAMP variant, simulation results reveal its substantial performance improvement over existing methods.