Research On DOA Estimation Based On Matrix Completion Under Complicated Environment

Signal direction-of-arrival(DOA)estimation which is a key issue of array signal processing has been widely used in many applications involving radar,wireless communication,wireless sensor networks and radio astronomy.The traditional DOA estimation algorithm can improve the DOA estimation accuracy and resolution significantly with Gaussian white noise,but it is limited by the physical size of the array,which restricts its wide application.Moreover,noise within each sensor is spatially uncorrelated and non-uniform due to the receiver differences and external influences in application.Besides,the interaction between the elements may also lead to the mutual coupling effect.On the other hand,coherent sources are inevitable due to the multipath effect and so on.As a sequence,the performance of the traditional DOA estimation algorithm will degrade considerably.Hence one can see that DOA estimation algorithm with high resolution,high precision and low complexity is a hot field in array signal processing.In this thesis,the methods for DOA estimation based on matrix completion under complicated environment are discussed,which can be depicted as following:(1)Focusing on the issue of huge computational complexity produced by the traditional DOA estimation algorithms that requires a large number of sampling data,following the compressive sensing theory,a beamspace-domain based regularized multi-vectors focal undetermined system solver DOA estimation algorithm is proposed in this paper,which based on the spatial sparsity characteristic of targets of interest.The proposed algorithm maps the compressive received signals from the element-space to the beamspace,which overcomes the flaw that the sparse reconstruction algorithm cannot be used in the scenarios of the low SNR to some extent.Numerical simulations demonstrate that,compared to the traditional Capon,MUSIC and L1-SVD algorithms,the proposed algorithm outperforms the traditional DOA algorithms,can offer higher angle resolution and estimation accuracy and estimate the DOA associated with the coherent signals.Besides,the proposed method has a lower computational complexity as compared to the element-space based RMFOCUSS and L1-SVD algorithms.(2)Focusing on the problem of poor accuracy and low resolution of traditional DOA estimation algorithm in the presence of non-uniform noise,based on the matrix complement theory,a weighted L1 sparse reconstruction DOA estimation algorithm(MC-WLOSRSS)is developed under the second-order statistical domain in this paper.Following the matrix completion approach,the regularization factor is firstly introduced to reconstruct the signal covariance matrix reconstruction as a noise-free covariance matrix.After that,the multi-vector problem of the noise-free covariance matrix can be transformed into a single vector one by exploiting sum-average operation for matrix in the second-order statistical domain.Finally,the DOA can be complemented by employing the sparse reconstruction weighted L1 norm.Numerical simulations show that the proposed algorithm outperforms the traditional DOA algorithms such as MUSIC(multiple signal classification),IL1-SRACV(Improved L1-SRACV),L1-SVD(L1-norm-singular value decomposition)subspace and sparse reconstruction weighted L1 methods in the following respects: suppressing the influence of the non-uniform noise significantly,bettering DOA estimation performance,as well as improving angle estimation accuracy and resolution in the case of the low SNR(signal-noise ratio).(3)Focusing on the problem of poor accuracy and low resolution acquired by the traditional DOA estimation algorithm in the cases of the coherent signals and non-uniform noise,based on the spatial smoothing method,a DOA estimation approach via minimizing the rank of the covariance matrix of the received signal is developed in this paper.Following the traditional spatial smoothing approach,the covariance matrix of the received signal is multiplied by a certain switch matrix in the left and right sides in the proposed method,respectively,and then the spatial backward smoothing covariance matrix can be obtained.In what follows,the covariance matrix can be reconstructed into a noise-free one by exploiting the low rank property of the smoothing matrix.Finally,the DOA can be implemented by the traditional MUSIC algorithm.Simulation results demonstrate that,compared to the traditional MUSIC,matrix completion based MUSIC(MC-MUSIC)and rank and trace minimization(RTM)algorithms,the proposed method can suppress the non-uniform noise considerably,and improve the DOA estimation performance significantly in the case of the coherent signals.(4)Focusing on the problem of poor accuracy and low resolution of the DOA estimation of coherent signals obtained by the array with mutual coupling in the case of non-uniform noise,a DOA estimation method,which is based on the joint optimization of noise-free covariance matrix and mutual coupling coefficient,is developed in this paper.Following the least squares(LS)theory,the noise-free covariance matrix in the presence of mutual coupling can be obtained by alterative iteration approach.In what follows,the mutual coupling matrix can be reconstructed on the basis of the principle of signal subspace to acquire the noise-free covariance matrix after compensating the mutual coupling.Finally,the coherent signal can be decorrelated based on the spatial smoothing method,and the DOA can be implemented by employing the traditional MUSIC algorithm.Simulation results demonstrate that,compared to the traditional MUSIC and DOA estimation algorithms in the cases of non-uniform noise and mutual coupling,the proposed method can suppress the non-uniform noise significantly,alleviate the effect of mutual coupling on spatial smoothing algorithm obviously,as well as improve the DOA estimation performance in the case of coherent signals considerably.