Direction of arrival (DOA) estimation with extended optimum co-prime sensor array (EOCSA)

In this study we propose a novel sparse antenna array and suitable beamforming algorithm in order to decrease the number of antennas in large-scale antenna systems (LSASs) and achieving the performance of a dense antenna array. To design a sparse array we use the familiar array geometry that is called co-prime sensor array (CSA), which has been recently introduced as an effective sparse configuration in direction of arrival (DOA) estimation and beamforming applications. The prototype CSA can achieve narrow beam widths using far fewer sensors than a fully populated uniform linear array (Full ULA), but at a cost of the appearance of grating lobes. Grating lobe manifests itself as leakage in the spectral domain, distorting other weak spectral responses. To mitigate this issue, we use a new processing method based on digital beamforming at sub-array level. Moreover, we developed a novel sparse array geometry, so-called Extended Optimum CSA (EOCSA), for DOA estimation of received signal. The EOCSA would be very useful in many practical applications where the number of sensors is limited. The performance of the proposed beamfoming method in EOCSA with N=O(N1+N2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N=O(N_1+N_2)$$\end{document} sensors is compared to a Full ULA with M=O(N1N2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M=O(N_1N_2)$$\end{document} physical sensors. The results illustrate the EOSCA ability to reaches the same power pattern of a Full ULA using relatively few sensors. Analytical and simulated results demonstrate that the power pattern obtained by the proposed beamforming processor in the EOCSA, in terms of side lobe level (SSL), peak side lobe level (PSL) and integrated side lobe level (ISL), is better than the previous arrays and processors.