Research On Gridless Direction-of-Arrival Estimation Algorithm

With the accurate reconstruction condition of sparse signal proposed,the theory of compressed sensing has been improved,which has been widely used in signal processing,image compression,medical imaging,radio astronomy and radar detection.The rapid development of compressed sensing theory also has greatly promoted the direction of arrival(DOA)estimation technology,and forms a new kind of DOA estimation algorithm based on sparse signal reconstruction and compressed sensing theory,which is different from the traditional subspace algorithms.Compared with subspace algorithms,the sparse DOA estimation algorithm based on sparse signal reconstruction and compressed sensing theory has better robustness to noise,snapshot number and correlation of incident sources.It has more stable and excellent estimation performance in the case of less snapshots and low SNR,and can directly process the correlated incident sources.However,the traditional sparse algorithm relies on the discrete grid in the spatial angle domain,and the estimation performance will be significantly degraded in the case of off-grid.Therefore,the gridless DOA estimation algorithm which does not depend on spatial angle discretization has been widely studied in recent years.This paper focuses on the research of gridless DOA estimation algorithm and the main achievements of this paper are as follows:1.Aiming at the problem that the fast interior point method is only suitable for single snapshot model of atomic norm minimization(ANM),this paper proposes a DOA estimation algorithm based on multi snapshot fast interior point method,which can improve the solution efficiency of multi snapshot DOA estimation problem.In this algorithm,a new observation vector is constructed by using the weighted sum of the eigenvectors corresponding to the large eigenvalues of the covariance matrix of the multi snapshot data received by the antenna array.It is proved that the observation vector conforms to the single snapshot atomic norm minimization model.Finally,the semi positive definite Toeplitz matrix is established by the optimal solution of the semi positive definite programming problem,From the Vandermonde decomposition of the matrix,the DOA parameters of the incident source can be estimated.On the one hand,the algorithm uses multiple snapshot data to improve the estimation accuracy,while abandoning the small eigenvalue part of the covariance matrix,so it has better robustness to noise.On the other hand,it uses fast interior point method to solve the semi definite programming problem,which realizes the dimension reduction of the algorithm model and improves the operation efficiency.2.Aiming at the defect that the gridless DOA estimation algorithm based on ANM is only suitable for uniform linear array,this paper proposes an ANM-DOA estimation algorithm based on sparse linear array,which expands the application scenario of ANM-DOA estimation algorithm,so that the ANM-DOA estimation algorithm can obtain greater degrees of freedom and higher estimation accuracy on the premise of the same number of array elements.On the one hand,for the traditional sparse linear array structures,this paper first uses the virtual linear array interpolation technology to statistically process the covariance data of the received signal of the sparse linear array,and then obtains the single snapshot received data vector of the continuous virtual linear array with the largest array aperture formed by the sparse linear array,Then,the dual problem of minimizing the atomic norm of the vector on the atomic set composed of continuous virtual linear array steering vector is derived.Finally,the DOA parameters of the incident sources are estimated according to the position of the zero point of the dual polynomial with the optimal solution of the dual problem as the coefficient.Combined with sparse linear array,the model expands the degree of freedom of the algorithm.At the same time,the process of estimating DOA parameters through the optimal solution of dual problem avoids complex operations such as spatial spectral peaks search and matrix decomposition,and can reduce the complexity of the algorithm.On the other hand,aiming at the problem that there are one or more adjacent elements whose spacings are half wavelength of the incident sources in the existing sparse linear array structures,a second-order minimum redundant array structure and an ANM-DOA estimation algorithm based on second-order minimum redundant array are proposed in this paper.In this sparse array structure,the array element position is determined by introducing the minimum array element spacing constraint,the maximum array aperture constraint and the second-order array element spacing set constraint.The atomic norm minimization model is established according to the fourth-order cumulant of the received signal of the antenna array,and then the DOA estimation results are obtained.The algorithm can further improve the degree of freedom and antenna array aperture under the same number of array elements,and effectively improve the performance of the estimation algorithm.3.Aiming at the defects of the full rank of the linear mapping matrix in the gridless DOA algorithm based on generalized finite rate of innovation(FRI)signal reconstruction and the inability to guarantee the convergence of the algorithm for solving the bivariate optimization problem,a FRI estimation algorithm based on continuous covariance data vector is proposed in this paper,which can solve the problem that the traditional FRI-DOA estimation algorithm is not suitable for linear array DOA estimation model and the number of iterations needs to be set manually.In this algorithm,the covariance data vector of multiple snapshot signals received by continuous antenna array is solved by covariance fitting criterion and kernel norm minimization method,and the bivariate optimization problem is established.The optimal solution is obtained by using the near end gradient descent algorithm.The zero point of the complex polynomial with the optimal solution as the coefficient corresponds to the DOA parameters of the incident source.The algorithm avoids the construction process of linear mapping matrix column in the generalized finite innovation rate signal reconstruction model,which not only makes the algorithm model still suitable for sparse linear array,but also effectively solves the problem of linear mapping matrix column under rank.In addition,the introduction of the proximal gradient descent algorithm can effectively guarantee the convergence of the solving process of bivariate optimization problems.4.Aiming at the problem of two-dimensional DOA estimation,a two-dimensional gridless DOA estimation algorithm suitable for planar antenna arrays with arbitrary geometry is proposed in this paper,which makes the gridless DOA estimation algorithm suitable for a wider range of application scenarios.On the premise of the same number of array elements,compared with two-dimensional MUSIC algorithm and other planar antenna arrays with special geometry,the proposed algorithm has higher estimation accuracy.Firstly,a kind of Bessel function is used to expand the covariance matrix of the received signal of the planar antenna array in two orthogonal directions,and the uniform sampling values in the two orthogonal directions are obtained.Then,according to the calculation method of the atomic norm in the matrix form,the two-dimensional DOA estimation problem is transformed into an equivalent positive semidefinite programming problem.Finally,the estimation results of DOA parameters of incident source are obtained by Vandermonde decomposition of Toeplitz matrix,two-dimensional spatial angle transformation and pairing.The gridless DOA estimation algorithm studied in this paper can effectively solve the grid mismatch problem in sparse DOA estimation algorithm based on sparse signal reconstruction and compressed sensing theory.The corresponding algorithms are proposed to solve the key and difficult problems in DOA estimation field,such as sparse linear array,multi snapshot observation vector and two-dimensional DOA estimation.The application scenarios of gridless DOA estimation algorithm are added,and the estimation performance of the algorithm is improved.