Application of semi-circle law and Wigner spiked-model in GPS jamming confronting

Detection and reduction of global positioning system (GPS) jamming threats are inevitable considering importance of satellite navigation in different applications such as fixed and moving platforms. Different methods utilizing statistical/spectral signal processing, time/frequency transforms and antenna array have been introduced. In this paper, a new method based on random matrix theory is proposed for detection and reduction of GPS jamming threat. By using the concept of Wigner matrix and introducing spiked matrix model, our proposed method is based on Karhunen–Loeve transform (KLT) by distinguishing eigen-values through systematic (analytic) thresholding. The authentic (cleaned) signal is reconstructed by projecting received signal on the eigen-functions domain where jamming components can be better removed. The objective is to detect the presence of jamming in the early stage of jamming attack (early warning) and then trying to reduce the jamming effect (mitigation). Different parameters including acquisition metric, position deviation, cross ambiguity function and run-time have been evaluated in simulation part to provide a good preview. According to the simulation results, the proposed method has better performance in comparison with some reference algorithms in terms of detection and false alarm probabilities and acquired satellites. At least 2.5 dB improvement in detection is achieved for the proposed algorithm. The run-time is reduced about 30% compared with wavelet packet coefficients transforms. Also, the overhead computational complexity for covariance matrix estimation (Om3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O\left( {m^{3} } \right)$$\end{document}) is reduced compared to conventional covariance matrix estimation-based eigen-decomposition methods.