Research On DOA Estimation Algorithm Based On Off-grid Compressed Sensing Under Compressed Sparse Array

Direction of arrival(DOA)estimation is a critical component of array signal processing and is widely employed in both military and commercial applications.Important reference indicators to quantify the DOA estimation performance include the estimation accuracy of the signal incidence angle in the airspace,the minimum angle resolution,and the number of estimable sources.To improve DOA estimation performance,the array aperture and number of array elements must be increased,which will result in a significant rise in the number of antennas in the receiving array,causing a slew of issues such as increased system complexity and expense.In order to address this issue,this paper investigates the DOA estimation algorithm with high accuracy and degree of freedom in an underdetermined environment with a fixed number of antennas utilizing the compressed sparse array structure.The main content of the paper is summarized to the following three parts:Aiming at the problem that traditional subspace algorithms can only estimate the number of signal sources that are less than the number of physical array elements,the paper introduces the concept of sparse array.By sparsely placing the antenna element positions in the receiving array,it can be implemented in the array.The effect of reducing the number of antennas on the premise that the aperture is unchanged or even increased,and the autocorrelation information of the received signal covariance matrix can also be used to improve the degree of freedom.The thesis first establishes a signal model based on sparse arrays,takes nested arrays as an example,introduces the principle of sparse arrays to achieve high degrees of freedom,and analyzes the advantages and characteristics of sparse arrays compared to traditional uniform linear arrays.Then,based on the sparse array signal model,two DOA estimation algorithms are introduced: the MUSIC algorithm based on spatial smoothing and the LASSO algorithm based on grid compressed sensing.The DOA space spectrum of the two algorithms is given to verify the sparse array.It has great advantages in terms of estimation accuracy and degree of freedom.The sparse array can expand the array aperture,thereby increasing the freedom of the array and improving the estimation accuracy of the algorithm.The application of compressed sensing in the DOA estimation structure,that is,the data compression structure,can better reduce the number of RF front-end channels through the combined network after the antenna output,thereby reducing the complexity of the system.Therefore,the combination of the two can further improve the performance of the estimation system,which is the Compressed Sparse Array(CSA)structure.This paper takes the compressed nested array as an example to model the general system of the CSA structure,and then introduces the MVDR algorithm under the compressed sparse array structure and the traditional LASSO algorithm in the grid based on the CSA signal model,and compares the advantages and disadvantages of the two algorithms and their application environment.Aiming at the problem of off-grid error in existing DOA estimation algorithms under CSA structure,this paper constructs an off-grid compressed sensing model of CSA structure,and proposes a joint sparse DOA estimation algorithm based on off-grid.The proposed algorithm uses the linear approximation of the first-order Taylor expansion to express the real array flow pattern matrix to establish the off-grid model of the CSA structure,and then uses the joint sparse method to convert the non-convex optimization model caused by the Taylor expansion into a standard convex optimization problem to complete the signal reconstruction.The comparison results of simulation experiments verify that the proposed algorithm can effectively solve the off-grid problem of signal incident angle.The propsed sparse Bayesian learning method in recent years has higher robustness than the subspace algorithm which does not need to estimate the covariance matrix in the DOA estimation process and has lower requirements on the signal-to-noise ratio and the number of snapshots.When the typical sparse Bayesian learning method is used to a sparse array,however,it will encounter issues such as array aperture loss and off-grid error.This paper was written in response to these shortcomings,as well as the aforementioned issues of system complexity and high cost.This paper extended the sparse Bayesian learning method to the CSA structure framework,and then proposed a DOA estimation algorithm based on the CSA structure for improved off-grid sparse Bayesian learning.In this paper,the noise is considered as a part of the signal to be estimated,and the SBL off-grid model under the CSA structure is established by using the first-order Taylor expansion,which realizes the automatic estimation of the noise variance and solves the grid mismatch problem and improves the accuracy of the estimation algorithm.The model retains all the virtual signals in the vectorized single snapshot covariance matrix,effectively avoids the information loss of the virtual array of the difference set,and becomes easier to deal with the error caused by the approximate covariance matrix.At the same time,the advantages of the CSA structure have been used to further reduce the dimensionality of the covariance matrix,thereby reducing the computational complexity and the amount of calculation.In addition,an improved grid update method is proposed by using the characteristic of repeated iterations in the SBL algorithm.The sampling grid points are regarded as parameter variables,and they are gradually approached to the true angle of incidence through repeated iterations to reduce the off-grid error.Through the numerical simulation experiments,it can be observed that the proposed algorithm can not only achieve accurate DOA estimation in an underdetermined environment,maintains a high degree of freedom of estimation,but also has good estimation accuracy,and can still maintain a large spatial grid spacing and have a good estimated performance.