Low Rank Matrix Completion Based Research On Direction Of Arrival Estimation Algorithms

Direction of Arrival(DOA)estimation is an important research direction of array signal processing.It is widely used in many fields,such as radar,sonar,smart antenna and electronic countermeasures.The reason is that these applications use direction finding technology.Many domestic and foreign scholars have proposed many highprecision and high-resolution DOA estimation algorithms,but most of these traditional DOA estimation algorithms are proposed under the background of Gaussian white noise assumption.However,in practice,due to the imperfect hardware of the receiving channel and the external influence,the noise in each sensor may be uncorrelated nonuniform Gaussian white noise.In this scenario,the estimation performance of most classic algorithms will be significantly reduced.The low rank-matrix completion technology is an effective method to eliminate the interference of nonuniform noise.However,if the low-rank matrix completion technique is directly used to estimate DOA,it often requires a lot of computational complexity.The real-time performance cannot be satisfied.Therefore,researching DOA estimation algorithms with high-resolution,high-accuracy and low-complexity will be a hot spot for array signal processing.Based on the low-rank matrix completion technology,this paper studies the DOA estimation of circular and noncircular signals in non-uniform noise scenes.This article first introduces the basic theory of DOA estimation.Among them,the mathematical model of the array signal and the basic algorithm of spatial spectrum estimation(MUSIC algorithm,ESPRIT algorithm and spatial smoothing algorithm)are introduced in detail.And these basic algorithms are deduced.Simulation experiments were performed under different parameters to analyze and summarize the pros and cons of these algorithms' estimated performance.In addition,the nonuniform noise model is also introduced to lay the foundation for the subsequent algorithm research.Then,in order to solve the problems of high computational complexity and poor angle estimation accuracy of traditional DOA estimation methods under nonuniform noise,based on the complete theory of low-rank matric,a unitary low-rank matrix decomposition algorithm was proposed.In the proposed method,the complex-valued covariance matrix is turned into real-valued one by using the unitary transformation.Then the nonuniform noise covariance is removed in the real-valued array covariance,and the noise-free real-valued covariance matrix can be recovered by matrix completion technique.Simulation experiments show that this method can effectively suppress the interference of nonuniform noise,and can estimate the DOA of two coherent signals.This method has high angular resolution and estimation accuracy.For a special kind of signal,that is,noncircular signal,the definition and properties of noncircular signals and the mathematical model of coherent source signals are introduced.Then by using the characteristics of noncircular signals,a novel virtual array is designed,and a unitary matrix completion algorithm is proposed.This algorithm combines the unitary transform method with a virtual array to avoid the loss of array aperture.Moreover,the eigenvalue decomposition is performed in the real number domain,which reduces the computational complexity.Simulation experiments show that the algorithm can effectively suppress the interference of non-uniform noise and obtain high-resolution and high-accuracy DOA estimation performance.Moreover,the proposed method can identify more sources than the number of physical sensors.In the end,the complexity analysis of the algorithm and the Cramer-Rao bound under this model are also given in this paper.Finally,for coherent non-circular signal sources,the forward-backward smoothing technology is introduced into the virtual array.In addition,a novel selection matrix is designed to eliminate the interference of unknown non-circular phases.Simulation results show that this method can effectively reduce the correlation of signals.