Off-Grid DOA Estimation Based On Sparse Reconstruction In The Colored Noise Background

Array signal processing is an important research field in modern signal processing.It has been widely used and developed rapidly in radar,sonar,radio astronomy,wireless communication,biomedicine and seismic detection etc.At present,most conventional subspace based high resolution DOA estimation algorithms and sparse reconstruction algorithms for DOA estimation are based on white Gaussian noise whose statistical properties are known,and the spatial sources are located on the pre-defined grids.However,in practical applications,the background noise of the array is usually spatially colored with unknown statistical properties,and the sources are often not locating on the grids.These problems will degrade the performance of the existing algorithms or even lead to estimation failure,which restricts the practical applications seriously.Therefore,it is of great significance to study the DOA estimation method of in the background of color noise.The DOA estimation performance of traditional subspace based methods is greatly affected by the signal-to-noise ratio(SNR)and the snapshots.It fails to estimate the real DOAs when the sources are highly correlated.In practice,it is often difficult to obtain adequate samples,and the ambient noise is usually strong.With the emergence and improvement of compressed sensing theory,sparse reconstruction algorithm as its core theory can solve the defects of traditional subspace algorithms to a certain extent.In this paper,three off-grid sparse representation DOA estimation algorithms under color noise background are proposed.The main works are as follows:To solve the DOA estimation in the Gaussian colored noise background.Due to the property that the fourth-order cumulant is insensitive to the Gaussian process,a fourth-order cumulant matrix of the non-gaussian signals is constructed to eliminate the influence of Gaussian colored noise.In order to reduce the dimension of the fourth-order cumulant matrix and improve the estimation accuracy,a real fourth-order cumulants based off-grid DOA estimation algorithm is proposed.Firstly,a selection matrix is constructed to remove redundant data of the fourth-order cumulants and transform the virtual over-complete dictionary to conjugate symmetrical form.Then the de-redundant fourth-order cumulant matrix is transformed to a real-valued matrix via a unitary transformation which can be sparsely represented by a real-valued virtual over-complete dictionary.The real-valued sparse model is vectorized for transforming to a Single Measurement Vector(SMV)model,and a new real-valued virtual over-complete dictionary is constructed again.Based on the permutation characteristics of the new over-complete dictionary,the redundant data in the vector model is further removed by another selection matrix.Finally,an off-grid sparse model based on the real-valued single measurement vector is established and solved by utilizing the SBL strategy.The simulation results demonstrate the high estimation accuracy and low computational complexity of the proposed algorithm for DOA estimation in colored noise background.For non-Gaussian color noise situation,the covariance differencing method is used to suppress the color noise with symmetrical Toeplitz structure.The colored noise is eliminated by forming the difference of the original and the transformed covariance matrices.Two off-grid sparse representation DOA estimation algorithms based on the covariance difference matrix are proposed which can avoid the pseudo peaks caused by covariance differencing processing and greatly improve the estimation accuracy.For the difference model?R=R-JRJ,an off-grid sparse representation DOA estimation algorithm based on eigenvalue decomposition of covariance difference matrix is proposed.Since the eigenvalues of difference matrix are symmetric about zero,and the positive eigenvalues contain information of actual source,while the negative eigenvalues contain information of virtual mirror source.Taking the eigenvectors corresponding to the positive eigenvalue of the difference matrix as the new measurement model,the pseudo peaks can be avoided.Based on this measurement data,an off-grid sparse representation DOA estimation model is constructed,and the FOCUSS(Focal Undetermined System Solver)algorithm is used to solve the on-grid DOAs and the bias parameters by two-step optimization.For the difference model?R=R-JR~*J,an off-grid sparse representation DOA estimation algorithm based on real covariance difference matrix is proposed.Firstly,the difference matrix is transformed to a real-valued matrix via a unitary transformation.Since the imaginary part of the signal covariance matrix is retained in this process,the pseudo peaks can be avoided.Then the real-valued difference matrix is vectorized for transforming to a single measurement vector(SMV)model,which can be sparsely represented by the real-valued virtual over-complete dictionary.The Sparse Representation of Array Covariance Vectors(SRACV)algorithm is used to solve the on-grid DOAs and the biased parameters by two-step optimization.The above two algorithms can eliminate the colored noise without estimating the noise covariance matrix and avoid additional steps to distinguish pseudo peaks.Due to the off-grid model,high estimation accuracy is reached.