Research Article
A Simple Formulation for the Distribution of the Scaled Largest Eigenvalue and Application to Spectrum Sensing
@INPROCEEDINGS{10.1007/978-3-319-40352-6_23, author={Hussein Kobeissi and Youssef Nasser and Amor Nafkha and Oussama Bazzi and Yves Lou\`{\i}t}, title={A Simple Formulation for the Distribution of the Scaled Largest Eigenvalue and Application to Spectrum Sensing}, proceedings={Cognitive Radio Oriented Wireless Networks. 11th International Conference, CROWNCOM 2016, Grenoble, France, May 30 - June 1, 2016, Proceedings}, proceedings_a={CROWNCOM}, year={2016}, month={6}, keywords={Scaled largest eigenvalue detector Spectrum sensing Wishart matrix}, doi={10.1007/978-3-319-40352-6_23} }- Hussein Kobeissi
Youssef Nasser
Amor Nafkha
Oussama Bazzi
Yves Louët
Year: 2016
A Simple Formulation for the Distribution of the Scaled Largest Eigenvalue and Application to Spectrum Sensing
CROWNCOM
Springer
DOI: 10.1007/978-3-319-40352-6_23
Abstract
Scaled Largest Eigenvalue (SLE) detector stands out as the best 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. We study the distribution of the SLE as a large number of samples are used in detection without constraint on the number of antennas. 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 as a normal random variable. Moreover, we derive the distribution of the SLE and deduce a simple yet accurate form of the probability of false alarm. Hence, this derivation yields a very simple form of the detection threshold. The analytical derivations are validated through extensive Monte Carlo simulations.