Two-dimensional Direction-of-Arrival Estimation Based On Sparse Representation

Direction of Arrival(DOA) estimation is an important research subject of array signal processing, has been concerned about. But the majority of research concentrates on one dimensional(1-D) DOA estimation, because its model is simple and easy to explain the principles and of representative significance. Although the majority of 1-D DOA estimation algorithm can be directly extended to a two dimensional(2-D) airspace. But this simple extension method can cause some problems, two of the main problems is the increase of the amount of calculation and two dimensional parameter pairing difficult. Thus the 2-D DOA estimation research is necessary, and in the practical application of the 2-D DOA estimation is with realistic significance.DOA estimation of research has been in a period of rapid development, different types of algorithms emerge in endlessly. Such as beamforming algorithms, signal subspace-based algorithm, maximum likelihood estimation algorithm and so on. All these algorithms need a large number of samples to give an accurate estimation. In addition, the strong correlated sources lead to algorithm performance degradation. The sparse representation and compressive sensing provides a new method for DOA estimation. The algorithm based on the sparse representation have many advantages, which can have an accurate estimation with high correlations of sources, high observation noise and small samples. Therefore, this paper discusses DOA estimation problem based on sparse representation.This paper first introduces the traditional 1-D DOA estimation and 2-D DOA estimation signal model. The 2-D angular range enlarges the scale of the array manifold matrix which increases the computational complexity. And the traditional model does not take full advantage of the 2-D spatial sparse. The target location in the airspace of the elevation dimension and azimuth dimension are present sparse.In this paper, a new 2-D DOA estimation algorithm based on sparse representation is proposed. In the traditional 2-D DOA estimation algorithm, the elevation dimension is coupled with the azimuth dimension in the array manifold matrix. So we redefine the azimuth angle of airspace to split the array manifold matrix into two individual sub-matrices in azimuth and elevation. But this does not affect the final localization of the target according to the elevation angle and azimuth angle. A separable structure for manifold matrix is proposed to reduce the complexity of the algorithm and improve the speed and resolution of the estimation.In this paper, the Multitask Bayesian Compressive Sensing(MT-BCS) framework is engaged to propose a DOA estimation algorithm. The algorithm based on the MT-BCS is essentially to calculate the exact posterior density of the signal, rather than seeking a point estimate. The new MT-BCS based algorithm doesn't need to adjust the parameters or estimate the noise level of signal. So the new algorithm has a robust performance.Algorithms based on sparse representation are usually very sensitive to grid mismatch. The targets off the grid may cause performance degrading of DOA estimation. Existing literature mostly concentrated in 1-D DOA estimation of off-grid problem, it is very difficult to applicate in 2-D DOA estimation. Based on the array manifold separable model, the Taylor expansion is introduced to approximate the off-grid DOA. In that way, an algorithm for off-grid 2-D DOA estimation is proposed in this paper.