| The spatial spectrum estimation technique for array signals is to estimate parameters of spatial sources using sensor array,which is an active research topic due to its importance in a wide range of applications on wireless communication,radar,sonar,and electronic surveillance.In recent years,the sparse representation(SR)theory has attracted wide attention in signal processing,aiming at representing the signal in a given redundant dictionary matrix with as few atoms as possible.Then it is easier to obtain valid information from the acquired signal by a more concise representation.Exploiting the sparsity of the targets in the whole airspace angle,the SR theory can be used in the spatial spectrum estimation of array signal,which has a number of advantages over conventional direction of arrival(DOA)algorithms,including correlation of the sources,increased resolution,and improved accuracy,especially in fewer snapshots and lower signal-to-noise(SNR).Therefore,the DOA estimation methods based on SR have important research significance and practical application value since it can overcome or avoid many shortcomings of traditional methods.On the research background of the spatial spectrum estimation of array signal,the shortcomings of the existing DOA methods based on SR are analyzed and solved in this dissertation.In narrowband signals,we analyze the essential cause of the performance degradation of the algorithms based on covariance matrix SR under the scene of fewer snapshots and introduce the fast maximum likelihood(FML)algorithm to solve the corresponding problem.In addition,a new off-grid model for nest array is proposed.A scheme of sparse Bayesian learning(SBL)is derived to estimate off-grid DOAs based on the proposed model.In wideband signals,the main goal is to research how to reduce the computation complexity of wideband DOA methods based on SR.The main contributions of this dissertation are summarized as follows.1.The performance of the L1-norm-based sparse representation of array covariance vectors(L1-SRACV)algorithm significantly degrades with the number of samples decreasing.The essential cause of this performance degradation is analyzed in this part and a new DOA estimation method based on FML algorithm is proposed.Firstly,the FML algorithm is employed to estimate the covariance matrix,which attenuates the instability of the small eigenvalues of the covariance matrix under the fewer snapshots.Then the sparse representation model based on FML is formulated for DOA estimation and finally,optimized by removing the diagonal elements of the covariance matrix to obtain better performance.The proposed method outperforms the L1-SRACV with higher accuracy and detection possibility,particularly under small samples support.2.An off-grid DOA estimation method using SBL based on array covariance matrix is proposed.By the vectorization operator of the covariance matrix of the nest receive data,a new off-grid model is built,which has a wider aperture and can therefore detect an increased number of sources.Then,a SR model for the corresponding measurements is established and the error vector between the sample covariance matrix and theoretical covariance matrix is whitened.Finally,a scheme of SBL is utilized to estimate off-grid DOAs without needing to know the number of sources.Comparing the existing methods,the proposed method cannot only improve the angle resolution but also enhance the accuracy of DOA estimation,owing to the extended aperture and off-grid model.3.A novel wideband signals DOA estimation method based on SR in direct data domain is proposed.The storage content and computation complexity of the traditional SR methods in wideband signals process are reduced by the proposed algorithm,which is caused by the large dimension of base matrix.The over-complete dictionary is constructed by using one-frequency to replace the 2D combination of frequency and angle.The column number of constructed dictionary only equals to that of single-frequency redundant dictionary.Firstly,focused thought is adopted to stack the different frequency data to the reference frequency and the redundant dictionary with a single frequency is founded.Then,a sparse recovery model is established to obtain the DOA estimations,which are coming from following the focus process.At the same time,the singular value decomposition(SVD)is used to summarize each frequency to reduce computation burden further.Finally,an automatic selection criterion for the regularization parameter involved in the proposed approach is introduced,which means how much of error we wish to allow and plays an important role in the final performance.The proposed algorithm can effectively distinguish the correlative signals without any decorrelation processing,and has higher accuracy and detection possibility.Moreover,it has a low computational cost,which is preferable in practical applications.4.The computational complexity for wideband DOA estimation methods based on SR greatly restricts the application in practical system.For this issue,an efficient method for wideband direction finding based on SR is proposed.The proposed algorithm combines the focusing operation with weighted subspace fitting(WSF)not only to decrease the computational complexity but also to improve the performance of DOA estimation.Firstly,each sub-band data of array signals after the focusing operation is obtained and the covariance matrix at each frequency is estimated.Secondly,the covariance matrix using to give the final DOAs comes from the mean of the covariance matrix at each frequency.Then SR reconstruction model based on WSF is established to estimate the DOAs,which reduces the sensitivity to the noise owing to WSF.Finally,second order cone programming(SOCP)is exploited to solve the optimal model and given the spatial spectrum estimation.The regularization parameter is derived from the asymptotic distribution of the WSF cost function and a method of adaption grid refinement is proposed.The proposed algorithm can provide good performance and has a low computational cost. |
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