A Sparse Representation-Based DOA Estimation Algorithm With Separable Observation Model

Abstract

Conventional sparse representation (SR) based DOA estimation algorithms suffer from high computational complexity. To be specific, a wide angular range and a large-scale array will enlarge the scale of the spatial observation matrix, which results in huge computation cost for DOA estimation. In this letter, a new efficient DOA estimation algorithm based on the separable sparse representation (SSR-DOA for short) is derived, in which a separable structure for spatial observation matrix is introduced to reduce the complexity. Besides, a dual-sparsity strategy is engaged to make the algorithm tractable. Experimental results show that, high resolution performance can be obtained efficiently by the proposed algorithm.Index Terms-sparse representation, DOA, planar array I. INTRODUCTIONirection-of-arrival (DOA) estimation has attracted much interest due to its fundamental role in many application fields such as radar, sonar and wireless communications. Many high resolution algorithms have been developed to resolve the closely spaced sources, among which the subspace-based algorithms are the most prominent ones. However, these algorithms are very sensitive to the signal-to-noise ratio (SNR), the number of snapshot and the correlation between sources.Recently, the emerging field of Sparse Representation (SR) has aroused enormous attention. Based on the observation that signals impinging on an array are intrinsically sparse in the spatial domain, the DOA estimation problem can be formulated as a basis selection problem, where the basis entries are the discretized manifolds of a sensor array according to the angle. In [1], the concept of SR is first applied to the DOA estimation. Recently, the Bayesian theory is incorporated into the SR theory to improve the angular resolution [2]. Though these algorithms [1]-[5] have shown superior capability in improving resolution, they still suffer from one common problem, i.e., high computational complexity. In particular, the increase of the angular range and array size will result in an enormous growth of the spatial observation matrix, which brings a huge computation cost and hampers the application of SR theory in DOA estimation.In this letter, a separable observation structure is engaged to reduce the computation complexity by spliting the joint twodimensional (2-D) observation matrix into two individual observation sub-matrices in azimuth and elevation, respectively, then a new separable SR-based DOA estimation algorithm is

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