Research On Key Technologies Of DOA Estimation Of Sparse Array Based On Compressed Sensing

Array signal processing is an important part in modern signal processing.It has wide and important applications in wireless communication,radar,sonar and other fields.It includes array error calibration,array opti mization,spatial spectrum estimation,namely direction of arrival(DOA)estimation and other technologies.But most of the array signal processing technologies are based on the uniform array.In order to improve the performance of the array,the most commonly used method is increasing the number of array elements.However,this method has high requirements on the hardware complexity and the cost of the whole antenna system.And the complexity of signal processing will also increase.In order to reduce the cost and the complexity of the system,a feasible scheme is using sparse array with non-uniform distribution to replace the uniform linear array.But in the same aperture,compared with the uniform array,the performance of sparse array will decline because of the decrease of the number of array elements.In addition,most of the sparse array signal processing technologies are used under ideal conditions.In the actual systems,because of the non-linearity of devices and other factors,the existence of the gain/phase uncertainties is inevitable,and it will lead to the degradation of array performance.In order to solve the problems of sparse array calibration and DOA estimation in the presence of errors,this thesis studies the sparse array DOA estimation technology based on compressed sensing theory.The main research contents are as follows:1)Based on the compressed sensing theory and sparse array optimization algorithm,a sparse array optimization method based on invasive weed algorithm is proposed.Based on the optimized sparse array,the signal reconstruction model of sparse linear array is established under the condition of the gain/phase uncertainties,and the basic principle of DOA estimation of sparse linear array based on compressed sensing is introduced.In this model,the signal receiving model of sparse array is transformed into an EIV(Errors in Variables)model,and the estimation of the gain/phase uncertainties matrix is then transformed into a solution to the error matrix.Then,based on this model,the influence of gain/phase uncertainties on signal reconstruction is analyzed through the RIP(Restricted Isometric Property)of matrix.2)Aiming at the change of the RIP to the measurement matrix and the degradation of signal reconstruction performance because of the gain/phase uncertainties,SOMP-TLS(Simultaneous Orthogonal Matching Pursuit-Total Least Square)algorithm combining the greedy algorithm and total least square algorithm is proposed,and its convergence is analyzed theoretically.Th e algorithm firstly estimates the sparse coefficients of the signals by the initial error matrix value,then the error matrix is estimated by the least square algorithm,and the sparse coefficients of the signals is estimated with the estimated error matrix.Finally,the estimation of the gain/phase uncertainties matrix is obtained by using the estimated error matrix.This algorithm can achieve the gain/phase uncertainties calibration of sparse array,reconstruct the signal and obtain the DOAs of the targets under the condition of low snapshot number.3)In order to solve the grid mismatch problem in the compressed sensing based signal receiving model,two grid optimization algorithms are proposed under the condition of the gain/phase uncertainties.Firstly,the theory of gridless compressed sensing is introduced,and based on the EIV model,an algorithm of the gain/phase uncertainties estimation and signal reconstruction based on gridless compressed sensing: SDP-TLS(Semi-definite Programming-Total Least Square)algorithm is proposed.This algorithm estimates the sparse coefficients of the signals through semi-definite programming,and then estimates the error matrix by the total least square algorithm.The algorithm solves the problem of grid mismatch,and estimates the gain/phase uncertainties by gradient descent algorithm.However,this method needs to solve the semi-definite programming problem in every iteration,and it increases the computational complexity.This algorithm can only deal with the data of single snapshot.For the data of multiple snapshots,we need to deal with them one by one,which increases the operation time.When the angles of the targets are close,it is difficult to distinguish the targets effectively.In order to solve these problems,an algorithm based on sparse Bayesian theory is proposed.In this algorithm,the gain/phase uncertainties is regarded as a super parameter to be estimated,the grid is regarded as an adjustable parameter,and the grid can be adjusted adaptively.Compared with SDP-TLS algorithm,this algorithm reduces the computational complexity and the accuracy of signal reconstruction is improved.The data of multiple snapshots can be processed at one time.4)A gain/phase uncertainties and DOA estimation algorithm based on compressed sensing theory is proposed for sparse rectangular array,sparse circular array and sparse L-shaped array.Firstly,a sparse two-dimensional array signal reconstruction model with gain/phase uncertainties is established.The signal receiving model of sparse array is also transformed into an EIV model.Then,based on the model,algorithms are proposed and the joint estimation of gain/phase uncertainties and DOA is achieved.The compressed sensing based method can not avoid the problem of grid mismatch caused by the deviation of grid division.In order to solve this problem,a new algorithm of signal reconstruction and gain/phase uncertainties estimation based on the improved greedy algorithm is proposed.The algorithm firstly estimates the sparse coefficients of the signals and the deviation value of grid division,updates the grid by using the improved orthogonal matching pursuit algorithm iteratively.Then,the sparse coefficients of the estimated signals and the updated grid are used to reestimate the error matrix.The gain/phase uncertainties matrix is then estimated through the error matrix.Finally,the gain/phase uncertainties calibration and DOA estimation of sparse two-dimensional array are achieved.