Localization of mixed near-field and far-field multi-band sources based on sparse representation

In this paper, a novel source localization algorithm using a uniform linear array is proposed for scenarios where both the near-field (NF) and far-field multi-band sources may exist simultaneously. The proposed method is performed in two stages. In the first stage, we firstly exploit some spatial correlations of each frequency output component to construct a virtual array output and represent the virtual array output on a corresponding overcomplete basis or dictionary which is only related to the direction-of-arrivals (DOAs) of sources. And then we can establish a multiple-dictionary sparse representation model. Finally, we estimate DOAs of the incident sources by solving the weighted ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _1$$\end{document}-norm minimization problem. In the second stage, every frequency output component is firstly represented on a corresponding mixed overcomplete basis with the estimated DOAs, and then a multiple-dictionary sparse representation model is created. At last, the ranges of the NF sources are estimated using the weighted ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _1$$\end{document}-norm minimization, and the types of sources are also distinguished. The proposed algorithm avoids parameter pair-matching and two-dimensional search, and does not require a prior knowledge of source number. Simulation results indicate that the proposed algorithm can provide an improved localization accuracy and locate more sources than the existing techniques for the case of multi-band sources.