On the performance of Grassmann-covariance-matrix-based spectrum sensing for cognitive radio

Cognitive radio assures efficient utilization of spectral resources by encouraging opportunistic spectral access. Its inevitable task of spectrum sensing has been widely addressed in the literature through the covariance-matrix-computation-based approaches. Unlike these blind approaches, recently a Grassmann covariance matrix (GCM)-based approach has been devised that requires a priori signal covariance matrix. To alleviate this impractical limitation, this paper proposes a spectrum sensing approach based on the computation of a modified projection distance metric on the Grassmann manifold. Particularly, the test statistic is derived using two GCMs estimated from the received signal frame and the threshold is calculated using Gaussian noise statistics of the null hypothesis pertaining to the detection problem. Simulations on the signals received in Rayleigh environments show that the proposed approach renders better probability of detection (Pd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_d$$\end{document}) compared with Covariance Absolute Value (CAV), Akaike Information Criterion (AIC)-based and Maximum Minimum Eigenvalue (MME) approaches. Performance of the proposed approach is at par with the case when signal covariance matrix is known a priori. Experiments are conducted using ADALM PLUTO software-defined radio (SDR) measurements in the ultra-high-frequency (UHF) television (TV) band. Using these measured signals it is verified that the proposed approach renders Pd=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_d=1$$\end{document} at an SNR of –15 dB compared with the CAV, AIC and MME approaches, which render Pd=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_d=1$$\end{document} at an SNR of –5 dB.