Research On Spatial Spectrum Estimation Using Array Covariance Matrix Sparse Representation

The estimation of plane wave’s wavenumber or direction-of-arrival (DOA) estima-tion (also called spatial spectrum estimation) is an important subject in array signal processing,playing a fundamental role in many applications involving radar, sonar, med-ical diagnosis and radio astronomy, etc. The theory and algorithms in DOA estimation have a rapid development over the past30years, but there are many unsatisfactory aspects. High resolution, low complexity, few number of sensors, and robust DOA estimation method is the goal of many scholars.Recently, the sparse signal representation (SSR), a topic bearing a close affinity with compressive sensing (CS), has attracted extensive and enormous attention and have many potential applications, including Radar imaging, underdetermined blind source separation, DOA estimation, to name a few. The sparsity spatially of signals make it possible to use for DOA estimation with SSR, so the DOA estimation based SSR have received a lot of attentions because of its many merits such as decorrelation, small number of snapshots,few number of needed sensors, superresolution, and so on. Many DOA estimation based on SSR have emerged in recent years. In order to achieve a higher resolution and improve the resolution in DOA estimation, we focus on how to use the array covariance matrix sparse representation to implement DOA estimation, and main contents can be summarized as follows:1. For far-field narrowband signals, we proposed a new robust approach for DOA estimation based on array covariance matrix sparse representation. Our proposed method is not only capable of significantly increasing the degrees of freedom of linear arrays, but it also reducing computational complexity and make it robustly to solving the the sparse inverse problem or recover sparse coefficients. Also, we discuss how to utilize the asymptotic statistical properties of second order statistics of observed signals and gives the optimal choice of regularization parameter.2. For DOA estimation of broadband signals, a new method based on wideband covari-ance matrix using multiple-dictionary joint sparse representation is proposed.The covariance of wideband signals at every discrete frequency point is represented by its overcomplete dictionary, and then the multiple-dictionary joint sparse multi-ple measurement vectors (MMV) model is obtained. The DOAs are estimated by solving the multiple dictionary joint sparse inverse problem with the joint-sparse constraint of recovering MMV’s sparse representation coefficients. For uniform lin-ear array (ULA) the joint sparsity of multiple-dictionary joint sparse MMV model makes this proposed approach can breakthrough the classical spatial sampling the-orem, so we can increase the element spacing exceeding half-wavelength spacing which leads to a significant improvement in the resolution limit without spatial ambiguity or aliasing. In addition, the proposed method has the capability of estimating both uncorrelated and coherent wideband signals because of its inde-pendence with the rank of wideband covariance matrix.3. For short-time stationary signals [also called quasi-stationary (QS) signals], we pro-pose a underdetermined DOA estimation method based on the array covariance matrix sparse representation. We address the DOA estimation by sparsely repre-senting the left singular vectors of the array covariance matrix of QS signals to be formed a MMV model,which is capable of significantly increasing the degrees of freedom of linear arrays and improve the resolution of spatial spectrum.