Research On DOA Estimation Algorithm Based On Nested Array

With the situation of increasingly complex electromagnetic circumstance,as an important field of electromagnetic perception,the direction of arrival(DOA)estimation has very important research significance.Suitable DOA estimation algorithms can be used to measure the angle of the target accurately.In practical applications,the traditional uniform array often requires more array sensors to improve its degrees of freedom(DOF),but the hardware cost is huge and it is bad for the mobility of the system.In view of this situation,this thesis completes DOA estimation based on nested array.The nested array can break through the limitation of element size on DOF,and have the characteristic of "redundant and no-hole".Its virtual array elements are continuous and the number is more than physical elements,so it can achieve DOA estimation for signal source with more than the number of array elements accurately.This thesis first introduces the signal models of uniform linear arrays(ULAs)and nested linear array.Aiming at the problem that receiving data of virtual array under the nested array is coherent and the multiple signal classification(MUSIC)algorithm cannot directly be used to solve the coherent signal problem,two decoherent algorithms,spatial smoothing(SP)algorithm and toeplitz matrix reconstruction,are used to extract the coherent receiving data,then MUSIC algorithm is used to complete the DOA estimation.The performance including the resolution of the MUSIC,the estimation of multi-source directions,and change of root mean square error(RMSE)are analyzed.Compared with the ULAs,the nested array can effectively increase the numbers of elements available for estimation,solve the problem of under-determined source,and have a very high resolution.Compressed sensing(CS)algorithms are applied to solve under-determined signal problems.First,this thesis introduces the theoretical framework of CS,and then derives the mathematical model of CS for nested linear array,and also the performance of basic pursuit(BP)algorithm and orthogonal matching pursuit(OMP)algorithm under nested linear array are analyzed.The covariance matrix of the nested linear array after vectorization can be regarded as a single measurement vector(SMV)model,In view of the low accuracy of the above two algorithms in estimating multiple sources under the SMV model,this thesis draws on the idea of spatial smoothing algorithm,converts the SMV model into a multiple measurement vector(MMV)model,and then applies L1 Reconstruction after Singular Value Decomposition(L1SVD)algorithm to complete DOA estimation.The simulations compare the performance of the three algorithms when the number of sources is more than the number of elements,and prove the L1 SVD algorithm based on the MMV model is superior to the BP algorithm and the OMP algorithm under the SMV model,which can accurately estimate the DOA of the signal with more targets than the number of elements.To solve the two-dimensional angle of the signal in practical engineering applications,this thesis derives the planar nested array model,and the MUSIC algorithm based on SP algotithm is used to complete the DOA estimation.The planar nested array model based on CS is also derived.In view of the complexity of compressed sensing algorithm in planar array increases sharply,the fast sparse Bayesian learning(FSBL)algorithm is applied to the DOA estimation.Finally,the performance of the MUSIC algorithm and the FSBL algorithm are compared through simulations such as the resolution of the algorithm,the estimation of multi-source directions and the analysis of the RMSE curves.