Direction finding based on iterative adaptive approach utilizing weighted ℓ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _2$$\end{document}-norm penalty for acoustic vector sensor array

It is well known that the iterative adaptive approach (IAA) is an effective direction-of-arrival (DOA) estimation method for large aperture array, high signal-to-noise ratio (SNR) and large source separation. However, its derivation is obtained by minimizing a weighted least square cost function without considering the sparsity of solution, it cannot work properly in low SNR, small aperture array and small source separation scenarios. In this paper, to address this problem, the weighted ℓ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _2$$\end{document}-norm based IAA, namely as WIAA, is proposed to provide accurate DOA utilizing acoustic vector sensor array (AVSA). First, to improve the sparsity of solution for IAA, the auxiliary cost function with respect to the signal, which is penalized by the ℓ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _{2}$$\end{document}-norm with a user parameter, is reconstructed based on the spatial sparsity of signal. Then, to obtain an analytical solution, the Majorization-minimization algorithm is used to turn the penalty term with a user parameter into a weighted ℓ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _2$$\end{document}-norm one. Finally, the sparse solution is quantified by the Frobenius norm properties. Several simulation and experimental results verify the superiority of the WIAA method compared to some other existing algorithms.