Direction Of Arrival Estimation For Sparse Arrays

Direction-of-Arrival is an important branch of array signal processing.Since the beam lobe of the beam pattern will cause the problem of peak response ambiguity,so the conventional array structure of the array element spacing is generally not more than a half wavelength of the design.The resolution of the DOA estimation is usually affected by the array aperture.Moreover,due to the limitation of the number of physical array elements,the number of signal sources that the array can simultaneously process is less than the number of array elements.In the actual complex electromagnetic environment,the number of signal sources will always be larger than the number of array elements,i.e.underdetermined problem.Therefore,how to use a limited number of array elements array aperture as large as possible to improve the degree of freedom of the array,to improve resolution and process more signal sources it is a matter of concern and research.The current research in this area is mainly divided into two aspects.One is the research on array structure design,which mainly studies the layout of non-standard linear arrays;the other is the research on the direction of arrival estimation algorithm for sparse arrays.This article aims at the above problems,the main content is:(1)First,the layout of various sparse arrays is studied,and then different sparse arrays are analyzed,and their respective patterns are compared and analyzed to verify the advantages of sparse arrays over uniform arrays.(2)The DOA estimation algorithm for sparse arrays is studied.Firstly,aiming at the problem that the MUSIC algorithm cannot be directly applied to sparse arrays,the improved MUSIC algorithm based on covariance matrix vectorization is introduced.First,the received array covariance matrix is vectorized and sorted to reconstruct the sampling covariance matrix,thereby increasing the aperture of the virtual array,then the spatial smoothing algorithm is used for rank recovery,and finally the DOA is estimated using the MUSIC algorithm.For the DOA estimation algorithm based on sparse representation,the DOA estimation problem is converted into a line spectrum estimation problem,the covariance matrix fitting problem is converted into a convex optimization problem using the concept of atomic norms.Reconstruct it by using the properties of the data covariance matrix,thereby obtaining a more accurate DOA estimate.Aiming at the problem of information waste caused by the existence of holes in the virtual array of coprime arrays,an improved DOA estimation algorithm for Toeplitz matrix completion is proposed.First,the sampling covariance matrix is optimized by using the covariance fitting algorithm to obtain a Toeplitz data covariance matrix.Then use the matrix completion algorithm to fill in the missing data,complete the hole information of the virtual array,and obtain the complete covariance matrix for DOA estimation.As the available aperture of the virtual array increases,the array estimation performance is improved.(3)Aiming at the problem of sparse array design,a new improved array based on minimum redundant array is proposed,which solves the problem of design difficulty caused by the unresolved expression of minimum redundant array,and at the same time increases the aperture of virtual array and improves the estimation performance.(4)Aiming at the distributed array,a distributed minimum redundant array structure is designed,and the dual-scale ESPRIT algorithm is used to solve the problem of angular ambiguity of the distributed array,and then an accurate estimate of the direction of arrival is obtained.The superiority of the array structure is verified through simulation experiments.Finally,the above proposed algorithm and array structure were simulated,which verified the effectiveness of the listed algorithms and the superiority of the proposed array structure,reflecting the advantages of sparse array.