Abstract: The compact array structure in the two-level nested array is subject to mutual coupling effects. To solve this problem, a method for improving two different nested array structures (continuous translational nested array and spaced translational nested array structures) is proposed. By adjusting the position of the element of the original two-level nested array, two different translational nested array structures are formed. The difference coarrays of these two structures are both "no hole", and the degree of freedom and array sparsity are larger than those of the original nested array. The direction finding model for difference coarray of the nested array is a single measurement vector model; therefore, the sparse Bayesian learning direction finding algorithm has high complexity. In view of this problem, a restructure sparse Bayesian learning algorithm is proposed. In this algorithm, the single measurement vector model is changed into a multi-measurement vector model via spatial smoothing. Singular value decomposition is applied to the transformed observation matrix to reduce the dimensionality and the computational complexity. Simulation results show that when the signal-to-noise ratio and number of samples are the same, the proposed algorithm converges faster than Single Measurement Vector Sparse Bayesian Learning (SMV-SBL), and the accuracy of direction finding with the proposed algorithm is higher than that with SMV-SBL and spatial smoothing Multiple Signal classification (MUSIC) algorithm. In the presence of mutual coupling, the two translational nested arrays are less affected by the coupling than the original nested array.

Key words: nested array, Sparse Bayesian Learning(SBL), direction finding, computational complexity, multiple measuring vectors