Multi-target Direction Of Arrival Estimation Algorithm Based On Coprime Array

As an important technology in the field of signal processing,array signal processing is widely used in radar,sonar,wireless communication and other fields.Direction of arrival estimation is one of the most notable subjects.Traditional Do A estimation algorithms are mainly designed based on the uniform linear array which satisfies Nyquist sampling theorem.Their estimation performance are limited by the number of physical array elements,and the cost is large in practical applications.In recent years,coprime array with systematic sparse structure is proposed.When using the same number of physical array elements as the uniform linear array,the Do A estimation algorithm based on coprime array can achieve higher degrees of freedom and larger array aperture,so as to achieve higher resolution and estimation accuracy.It is of great significance to reduce the computational complexity and the cost in the actual system implementation.On the basis of synthesizing the latest technology research,this paper further proposes specific and effective algorithms based on the Do A estimation algorithm with coprime array,which have high efficiency and robustness.The specific work of this thesis is as follows:Firstly,a Do A estimation algorithm using coprime array with rank minimization-based Toeplitz reconstruction is proposed.Since the holes which exist in the derived non-uniform array in the virtual domain will limit the degree of freedom and array aperture,the proposed algorithm initializes it into a virtual uniform array to satisfy Nyquist sampling theorem by array interpolation.Based on the atomic norm minimization of multiple virtual measurements,the equivalent rank minimization expression of the continuous parameter Do A estimation problem is proved.Furthermore,a multi-convex parameter optimization problem,which reconstructs the covariance matrix of the interpolated virtual array in a gridless manner through bivariate cyclic iterative optimization is designed.Finally,the Do A estimation can be completed by using simple subspace method.This method realizes the full utilization of the virtual array signal,improves the degree of freedom and array aperture and completes the Do A estimation with high precision.Secondly,a Do A estimation algorithm using coprime array based on accelerated structured alternating projection is proposed.In the previous Do A estimation algorithms with coprime array,most of them need to solve semi-definite programming problems in the convex optimization,resulting in high computational complexity.The low-rank characteristic of Hankel matrix is utilized to construct a Hankel matrix which contains all the information of virtual array.Under certain conditions,the Hankel matrix and the hole signal correspond to low-rank matrix space and sparse vector space respectively.After initialization,accelerated low-rank approximation method is used to update the estimations through the iterative projection between the two spaces.Once the desired Hankel matrix with Do A information is restored,a simple subspace spectrum estimation algorithm can be used to obtain the Do As of targets.The non-convex projection operation used in this algorithm not only can ensure the performance of DOA estimation,but also greatly reduce the computational complexity.Compared with other convex optimization algorithms,it shows great advantages especially in efficiency.Finally,a Do A estimation algorithm using coprime array with very few snapshots based on Hankel matrix is proposed.In the practical system environment,the received signals are seriously insufficient,and the performances of the existing coprime array DOA estimation algorithms often declines.When there are only a few or even single snapshot,on the basis of the hole-free uniform linear array in the virtual domain,the algorithm can recover the rank of the signal covariance matrix and decompose the signal by using Hankel’s structural characteristics.At last,the directions of the incident signals are estimated based on the orthogonality between subspaces.The algorithm makes an improvement on performance degradation or even failure in the previous coprime array DOA estimation algorithms when there are only a few snapshots.Besides,it improves the angle measurement accuracy and target detection probability,which enhances the robustness in future practical applications and widens the application field for coprime array.