Research On DOA Estimation Methods Based On Nested Array

Direction-of-arrival(DOA)estimation technology based on uniform non-sparse arrays has been relatively mature so far.As a new type of sparse array,nested array has various advantages,such as large aperture with equal physical sensors,low overhead of sensors with equal array aperture,small mutual coupling error and various array geometries.It can obtain higher array processing gains than uniform arrays and this has attracted the attention of many scholars at home and abroad.To exploit the advantages of nested array in estimation accuracy and degree-offreedom(DOF),this paper proposes several DOA estimation algorithms based on circular and non-circular signal separation,uncorrelated and coherent signal separation and complex mixed signal separation after thoroughly study of the joint utilization of array characteristics and signal characteristics.The main innovations of the paper are as follows:1.Research on DOA estimation methods for uncorrelated non-circular signals.Considering that using non-circular characteristic to expand the virtual array will introduce holes,this paper proposes a high degree of freedom DOA estimation algorithm which utilizes the nuclear norm minimization criterion to recover the missing elements of the covariance matrix.Firstly,the covariance and elliptic covariance are considered to average the received data from those repeated virtual sensors.Secondly,the missing values in covariance matrix are estimated through a matrix completion method called singular value thresholding(SVT).Note that the estimated values are the equivalent received data of virtual sensors corresponding to holes in virtual array and hence the holes in virtual array can be completed.Finally,classical multiple signal classification(MUSIC)algorithm is applied to resolve the DOA.Numerical results show that the proposed algorithm can complete the holes in virtual array so that the array aperture and degree of freedom are improved consequently,which has greatly increased the accuracy of DOA estimation.2.Research on DOA estimation methods for uncorrelated circular and non-circular signals.The virtual array can not be expanded due to the circular characteristics when there are coexistence of both circular and non-circular signals,thus the DOF and accuracy of estimation are restricted from further improvement.To cope with the problem,this paper proposes a DOA estimation algorithm based on covariance separation and reconstruction for mixed circular and non-circular signals.The algorithm separates the mixed signals according to characteristics of elliptic covariance.For DOA estimation of non-circular signals,the algorithm constructs an extended virtual array first by utilizing elliptic covariance(and its conjugate)according to their nonzero property.Then matrix completion technique and Root-MUSIC without spectral peak search are used to estimate DOA of non-circular signals.Furthermore,circular components can be separated from covariance matrix by using direct Toeplitz reconstruction technique and finally the DOA of circular signals can be obtained.Simulation results show that the proposed algorithm based on separation of mixed signals obtains a reduction of the number of signals to be estimated under the same number of array elements,which is equivalent to the improvement of DOF.And hence the proposed algorithm obtains better performance.3.Research on DOA estimation methods of mixed uncorrelated and coherent non-circular signals.Existing algorithms which deal with problems of coherent signals lose DOF when uncorrelated and coherent signals coexist.Moreover,the neglect of the non-circularity also leads to limited precision.As a result of these concerns,this paper utilizes non-circularity to construct a novel virtual array and proposes a DOA estimation algorithm which separates mixed signals based on conjugate symmetry invariance.The algorithm separates the coherent non-circular signals according to the conjugate symmetry invariance of uncorrelated non-circular signals and hence the DOA estimation of the two kind of signals can be conducted separately.After the construction of a novel virtual array,the proposed algorithm estimates DOA of each subarray first and then calculates all possible values according to common peak finding theory.Based on two solution sets,true DOA of uncorrelated non-circular signals can be obtained through common peak searching.Then,noise components and uncorrelated non-circular components are removed from covariance matrix by using conjugate symmetry invariance and the rest of covariance matrix is composed of coherent non-circular components only.Thus,one can resolve DOA of coherent noncircular signals subsequently.The simulations show that the proposed two-step DOA estimation algorithm based on signal separation improves the performance of DOF and DOA estimation effectively.4.In DOA estimation of multitype mixed signals,separation technique based on covariance separation and reconstruction lose efficacy if there are coherent signals.Besides,separation technique using conjugate symmetry invariance has poorer performance in the presence of circular signals.Considering about these problems,this paper proposes a high-degree-of-freedom DOA estimation algorithm based on sparse reconstruction theory which separates mixed signals first,and then resolve DOA.If non-circular signals contain uncorrelated components only,the proposed algorithm separates circular and non-circular signals first,then vectorizes covariance,elliptic covariance and it conjugate to construct an extended two-dimensional redundant dictionary.Actually,the process of separation improves the DOF equivalently.If non-circular signals contain uncorrelated and coherent components,a two-dimensional redundant dictionary can be constructed with covariance.Further more,the proposed algorithm performs convex relaxation on cost function and resolves two-dimensional DOA estimation results,among which the overlap values are chosen as estimation results of impinging signals.Numerical results and theoretical analysis demonstrate that the proposed algorithm avoids losing array aperture caused by spatial smoothing method by establishing a sparse reconstruction model,improving DOF and accuracy of DOA estimation.Meanwhile,a better performance is obtained because of separation of mixed signals based on signal characteristics.