Study On Sparse Representation Based Direction Finding Methods In Complex Noise

’All things being equal,the simplest solution tends to be the best one.’ As Occam’s razor deeply influenced principles from ancient to modern times,such as philosophy,art,and science,Sparse Representation,together with its derivative called Compressive Sensing,have concentratedly revealed their advantages of costless in modern statistics,machine learning,signal processing,etc.On the other hand,parameter estimation of array signal processing,which takes a fundamental position in RADAR,SONAR,and Communication systems,has been continuously kicking in the direction-finding(DF),locationing,target tracking,and other potential tasks,such as Unmanned Aerial Vehicle(UAV),unpiloted systems,3D printing,etc.However,to fight against the consistent improvement of the DF systems,a large variety of miniaturized RADARs have been coming out cost-effectively.Meanwhile,the electromagnetic environment becomes quite complex,which is caused by the iterations of stealth and RF jamming techniques.Under these adverse conditions,it is hardly accomplished the DF tasks for traditional sub-space scenarios,especially in non-ideal scenarios such as insufficient snapshots,low SNR,and spatial proximity signals and complex noise background.Fortunately,parameter estimation has been refurnished by sparse representation in the past two decades,which shows extreme capability under several non-ideal circumstances.From the perspective of noise suppression,this dissertation focuses on distinctions and relationships between sparse reconstruction and classical array signal processing methods,considering the influences of additional grids on array parameter estimation.Moreover,we study the sparse representation based DF algorithms under backgrounds of Gaussian white noise,Gaussian colored noise,alpha white noise,and alpha colored noise,respectively.As a result,some meaningful results and discussions have been obtained consequently.The main works and results of this dissertation can be summarized as follows:First,to overcome the resolution limit of the greedy algorithm for Direction of Arrival(DOA)estimation,we propose the Noise Subspace Reprojection Orthogonal Matching Pursuit(NSR OMP)algorithm using sub-space information.Two eigenspaces are fused organically under the framework of Matching Pursuit(MP),which considers signal subspace as the reconstructed signal to reduce the workload of optimization as well as to release noise interference on supporting-set selection.As the selection rule of the supporting set is modified by the noise subspace,the resolution could be improved.The proposed method inherits the excellent performance of a small snapshot of MP and the advantage of calculation saving.In the meantime,low angle resolution can also be greatly improved.In the next place,we propose a double matrix transformation process to transfer the DOA problem from a Multiple Measurement Vectors(MMV)problem in the complex domain into a Single Measurement Vector(SMV)problem in the real domain,which is inspired by the symmetric Toeplitz property of covariance matrices of array output.In this process,DOA estimation of Uniform Linear Array(ULA)can be simplified when ensuring the DF performances.On the other hand,a linear transformation is defined to reduce the dimension of the fourth-order cumulant covariance matrix of array output from the perspective of de-redundancy.Consequently,this process can be generalized to the fourth-order cumulant category by meeting aforementioned real-valued constraints.On another hand,to release the computational burden of current Basis Pursuit(BP)methods for DF,we propose the BP method for the background of Gaussian white noise and Gaussian colored noise respectively,based on real-valued vectorization model on second-order and high-order statistics,which are mentioned on the second part.Since only fewer variables of the SMV problem are needed to be solved,the proposed algorithm is more computationally efficient than the existing BP.Moreover,no eigenvalue decomposition is needed in the proposed methods,so the precise estimation of the number of sources will be insensitive.Furthermore,to deal with the difficulty in setting regularization parameters of the fourth-order cumulant-based convex optimization algorithm,Improved Smooth L0(ISL0),which has been used to handle real-valued SMV,is introduced into the DF problem,because of its low accuracy limit of regularization parameter settings.On fourth,we build a real-valued off-grid model to decrease computational workload.With the implementation of the aforementioned algorithm in the third part that alternatively calculates DOA and off-grid error,an off-grid DF scheme under Gaussian white noise and Gaussian colored noise is proposed respectively,which fills the gap that no off-grid schemes work in Gaussian colored noise environment.On the other hand,the proposed schemes are more computational friendly compared with others to some extent so that the practicability is improved.Computer simulations verify the effectiveness of the proposed algorithms.In the fifth place,since there is insufficient DF performance of Fractional Lower Order Statistics(FLOS)based subspace method under additional alpha noise unless enough snapshots and SNR gateway are accomplished,we propose two gridless algorithms for alpha white noise background.In these algorithms,we first analyze the criteria of Phase Fractional Lower Order Moment(PFLOM)covariance matrices for the Vandermond decomposition theorem and then combine PFLOM and covariance matching criterion.Simulation verifies that DOA estimation can be effectively accomplished by the proposed methods under the background of strong impulsive white noise with lower SNR and fewer snapshots compared with existing schemes.Finally,when focusing on DF under additional alpha noise that only conditions in white noise can be solved,a new statistic,called Fractional Order Cumulant(FOC),is introduced into the DF problem.We first analyze the suppression mechanism of this statistic on alpha-colored noise.Secondly,we propose several off-grid and gridless sparse methods for DF with the help of FOC suppression over alpha-colored noise,which fills the gap.And the effectiveness of the proposed methods is verified by simulation results.