A Simple formulation for the Distribution of the Scaled Largest Eigenvalue and application to Spectrum Sensing

Hussein Kobeissi (1) , Amor Nafkha (1) , Youssef Nasser (2) , Oussama Bazzi (3) , Yves Louët (1)

1 IETR - Institut d'Électronique et des Technologies du numéRique
2 ECE Department
3 Department of Physics and Electronics

"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 num- ber of samples are used in detection without constraint on the number of antennas. By the exploitation of the distributions of the largest eigen- value 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."

Domains: Engineering Sciences [physics]; Signal and Image processing

Hussein Kobeissi, Amor Nafkha, Youssef Nasser, Oussama Bazzi, Yves Louët. A Simple formulation for the Distribution of the Scaled Largest Eigenvalue and application to Spectrum Sensing . 11th EAI International Conference on Cognitive Radio Oriented Wireless Networks, Jun 2016, Grenoble, France. ⟨hal-01318205⟩