Research On Sparse Iterative Covariance-based Algorithm For DOA Estimation

As an important branch of signal processing,array signal processing has developed rapidly in recent decades,and direction of arrival(DOA)is a major problem in array signal processing.However,the current research on traditional subspace DOA estimation algorithm is very much limited by imperfect conditions,such as low signal-to-noise ratio(SNR),small snapshots and correlated sources.Recently,Stoica P et al.proposed a novel sparse iterative covariance-based estimation approach,abbreviated as SPICE,for DOA estimation.SPICE has several unique features not shared by other sparse estimation methods,it has a simple,sound statistical foundation and global convergence properties.Not only useful in many-snapshot,SPICE-type methods also can be used in single-snapshot situation.In addition,an estimation of the incident signal power can be obtained after DOA estimation.Therefore,this paper mainly focuses on the research on the SPICE algorithm and its variants.The main contents can be summarized as follows:Firstly,the classical subspace-based DOA estimation methods are studied including MUSIC,Root-MUSIC and the spatial smoothing algorithm for coherent signals.Secondly,the principle of SPICE algorithm is studied,including the signal model,covariance fitting criterion and the method of cycle minimization.The DOA estimation performance of SPICE algorithm is verified under the condition of small and large snapshots,the same and different noise power.To solve the problem that the signal power estimated by SPICE algorithm is not accurate and the estimation accuracy is limited by space grid,a SPICEML algorithm based on maximum likelihood estimation is proposed.Theoretical and simulation results show that the SPICE-ML algorithm can improve the estimation accuracy of the incident signal power and the DOA estimation accuracy compared to the SPICE algorithm.Thirdly,the general form of the SPICE named Weighted-SPICE is derived through the gradient algorithm.By changing the weight function,the IAA and LIKES algorithms are obtained.Simulation results illustrate the characteristics of IAA,SPICE,LIKES algorithms in DOA estimation.The IAA algorithm has the lowest calculation computation cost and an accurate signal power estimation,but a low angular resolution.The SPICE algorithm has a high level of resolution,and the estimation accuracy is improved compared with IAA algorithm.However,the error of signal power estimation is large in the case of correlated signal.The LIKES algorithm maintains the high resolution of the SPICE algorithm,and improve the accuracy of signal power estimation compared with SPICE algorithm,but at the expense of the computation cost.At last,we study the theory of gridless SPICE(GLS)and atomic norm minimization(ANM)DOA estimation algorithms.It is proved that the GLS optimization problem is equivalent to the ANM when the number of snapshots is less than the number of array elements.When the number of snapshots is greater than the number of array elements,the GLS algorithm is equivalent to the weighted ANM.