Sparse Representation Based Theory And Methods For Direction-of-arrival Estimation

With the development of modern communication and information technology,the signal environment faced by the array processing system becomes more and more sophisticated.The current study of array signal processing theory and techniques that are dominated by the subspace-based direction-of-arrival(DOA)estimation methods is very much limited by imperfect scenarios such as small snapshots,low signal-to-noise ratio(SNR)and correlated sources.Recently,based on sparse representation theory,the sparsity-based methods have been proposed to solve the DOA estimation problem.Different from the subspace-based methods,which use the orthogonality between the signal subspace and the noise subspace for direction finding,the sparsity-based DOA estimation methods use the fact that the DOAs of the sources are sparse among the whole angle space,and demonstrate excellent adaptability to the aforementioned imperfect scenarios.However,these methods often suffer from the limitation of the sparse reconstruction algorithms.More importantly,because of the high correlation and high complexity caused by the grid division,the sparsity-based methods cannot satisfy the requirement of different array processing system in terms of accuracy,computational complexity and adaptability as a whole.This dissertation is concerned with the development of new DOA estimation methods based on the sparse signal representation(SSR)with an objective to eliminate the limitation of the grid division,improve the estimation performance of the sparsity-based methods as well as reduce the computational complexity.Depending on the model adopted,the SSR based methods can be classified into three categories: on-grid,off-grid and gridless.The signal model of on-grid methods assumes that the true DOAs lie exactly on a set of predefined grid points.Off-grid sparse methods still use a grid set but the DOAs are not restricted to be on the grid.Finally,the gridless methods do not need a grid set and they operate directly in the continuous domain.This dissertation first conducts analysis of the on-grid methods and then proposes a new off-grid signal model based on which several algorithms are developed.By incorporating a bias parameter into the off-grid signal model to reduce the number of grids,and in turn the correlation between the columns of the manifold matrix,the estimation accuracy has been improved.Then some gridless methods are proposed that have avoided the problems caused by grid discretization.Finally,a gridless 2-dimensional(2-D)DOA estimation method is proposed with a higher accuracy and better adaptability than the subspace-based methods.With respect to the detailed research contributions,in this dissertation,firstly a DOA estimation method named off-grid reconstruction after Cholesky covariance decomposition(OGL1CCD)and its fast implementation named fast OGL1CCD(FOGL1CCD)are proposed based on the off-grid signal model.By analyzing the cramer-rao lower bound(CRLB)of the bias parameter,the influences of the sensor number,SNR and the DOAs of the impinged signals on the CRLB are discussed.Moreover,it is shown that the algorithm framework can be easily extended for any other on-grid methods to improve their estimation accuracy.To further improve the accuracy,another off-grid method named off-grid covariance matrix reconstruction approach(OGL1CMRA)is proposed based on the covariance matrix of the array output.Both theoretical analysis and computer simulation indicate that in the case of sufficient snapshots,OGL1 CMRA has a higher accuracy than OGL1 CCD.Secondly,a new off-grid signal model is proposed to meet the requirement of array system in computational efficiency.Through theoretical analysis,the new model is shown to have identical estimation accuracy compared with the first-order Taylor expansion based off-grid model.Based on the new model,an off-grid method named perturbed sparse Bayesian learning(PSBL)is proposed by applying the sparse Beyesian learning theory to array signal processing.PSBL is shown to be more efficient than OGL1 CCD and can be applied to both single snapshot and multiple snapshots cases.Then,a covariance-based method named perturbed covariance matrix(PCM)is proposed.Since PCM has a higher array output SNR than PSBL,PCM is more computationally efficient than PSBL.Finally,by using the rotational invariant property of the uniform linear array(ULA),an improved PCM(IPCM)method is presented.Thirdly,to avoid the drawbacks of the discretization,a gridless method named covariance matrix reconstruction approach(CMRA)is proposed based on the covariance matching criteria(CMC).Since the discretization procedure is no longer required,CMRA is able to completely resolve the grid mismatch problem,such as high computations and high correlations.CMRA is not only suitable for the ULA,but also can be used in the sparse linear array(SLA)to correctly locate more signals than sensors.The influence of the limited snapshots to the accuracy of the model is also analyzed.Then two algorithm implementations are presented based on the duality and the alternating direction method of multipliers(ADMM),respectively.Finally,we reveal the connection between CMRA and the atomic norm as well as the sparsity-based method and prove that CMRA is equivalent to the on-grid method with infinite number of grid points.Next,to further improve the accuracy of CMRA,a family of iterative DOA estimation methods named reweighted CMRA(RCA)is proposed based on several nonconvex penalties.As an extension of CMRA,RCA is also a gridless method and thus suitable for the ULA and SLA cases.Furthermore,because of the sparse-inducing ability of the coefficient in RCA,it has a sparser solution than CMRA,and hence enjoys a higher resolution.Then,a duality-based algorithm implementation and a fast implementation named fast RCA(FRCA)are provided,respectively.The connection between RCA and the atomic norm as well as the on-grid method is discussed.Finally,by extending the gridless method CMRA of linear array into the planar array version,a low-rank matrix reconstruction based model is proposed.Then,a 2-D gridless method named 2-D CMRA that is applicable to a variety of array structures is proposed to overcome the discretization problem faced by the current sparsity-based 2-D methods.A fast implementation named 2-D fast CMRA(2-D FCA)is also proposed by deriving a closed-form solution of the problem.Since the 2-D FCA avoids using the time-consuming CVX toolbox,it is much more efficient than the 2-D CMRA.It is shown that the proposed methods give automatically paired 2-D DOA estimates and can locate more sources in a sparse rectangular array(SRA).