On the Performance Analysis and Evaluation of Scaled Largest Eigenvalue in Spectrum Sensing: A Simple Form Approach

Hussein Kobeissi; Amor Nafkha; Youssef Nasser; Oussama Bazzi; Yves Louët

Research Article

On the Performance Analysis and Evaluation of Scaled Largest Eigenvalue in Spectrum Sensing: A Simple Form Approach

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@ARTICLE{10.4108/eai.23-2-2017.152193,
    author={Hussein Kobeissi and Amor Nafkha and Youssef Nasser and Oussama Bazzi and Yves Lou\`{\i}t},
    title={On the Performance Analysis and Evaluation of Scaled Largest Eigenvalue in Spectrum Sensing: A Simple Form Approach},
    journal={EAI Endorsed Transactions on Cognitive Communications},
    volume={3},
    number={10},
    publisher={EAI},
    journal_a={COGCOM},
    year={2017},
    month={2},
    keywords={Scaled largest eigenvalue detector, Spectrum sensing, Wishart matrix},
    doi={10.4108/eai.23-2-2017.152193}
}

Hussein Kobeissi
Amor Nafkha
Youssef Nasser
Oussama Bazzi
Yves Louët
Year: 2017
On the Performance Analysis and Evaluation of Scaled Largest Eigenvalue in Spectrum Sensing: A Simple Form Approach
COGCOM
EAI
DOI: 10.4108/eai.23-2-2017.152193

Hussein Kobeissi¹^,*, Amor Nafkha², Youssef Nasser³, Oussama Bazzi⁴, Yves Louët²

1: SCEE/IETR, CentraleSupélec - Campus de Rennes, Rennes, France. Department of Physics and Electronics, Faculty of Science 1, Lebanese University, Beirut, Lebanon.
2: SCEE/IETR, CentraleSupélec - Campus de Rennes, Rennes, France.
3: ECE Department, AUB, Bliss Street, Beirut, Lebanon.
4: Department of Physics and Electronics, Faculty of Science 1, Lebanese University, Beirut, Lebanon.

*Contact email: hussein.kobeissi.87@gmail.com

Abstract

Scaled Largest Eigenvalue (SLE) detector stands out as the optimal single-primary-user detector in uncertain noisy environments. In this paper, we consider a multi-antenna cognitive radio system in which we aim at detecting the presence/absence of a Primary User (PU) using the SLE detector. By the exploitation of the distributions of the largest eigenvalue and the trace of the receiver sample covariance matrix, we show that the SLE could be modeled using the standard Gaussian function. Moreover, we derive the distribution of the SLE and deduce a simple yet accurate form of the probability of false alarm and the probability of detection. Hence, this derivation yields a very simple form of the detection threshold. Correlation coeÿcient between the largest eigenvalue and the trace is also considered as we derive a simple analytical expression. These analytical derivations are validated through extensive Monte Carlo simulations

Keywords: Scaled largest eigenvalue detector, Spectrum sensing, Wishart matrix

Received: 2017-02-20
Accepted: 2016-06-01
Published: 2017-02-23
Publisher: EAI

: http://dx.doi.org/10.4108/eai.23-2-2017.152193

Copyright © 2017 H. Kobeissi et al., licensed to EAI. This is an open access article distributed under the terms of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/), which permits unlimited use, distribution and reproduction in any medium so long as the original work is properly cited.