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 c...

In this article we consider Wigner matrices (XN)N∈N with variance profiles which are of the form XN(i,j)=σ(i∕N,j∕N)ai,j∕ N where σ is a symmetric real positive function [0,1]2, either continuous or piecewise constant and ai,j independent, centered one above diagonal. We prove large deviation principle for largest eigenvalue those under condition that they have sharp sub-Gaussian tails some addi...

We study the probability that all eigenvalues of $n\times n$ Hermitian matrices, from Laguerre unitary ensemble with weight $x^{\gamma}\mathrm{e}^{-4nx},\;x\in[0,\infty),\;\gamma>-1$, lie in interval $[0,\alpha]$. By using previous results for finite $n$ obtained by ladder operator approach orthogonal polynomials, we derive large asymptotics largest eigenvalue distribution function $\alpha$ ran...

Let v ( k , λ ) be the maximum number of vertices a connected -regular graph with second largest eigenvalue at most . The Alon-Boppana Theorem implies that is finite when > 2 + 4 In this paper, we show for fixed ≥ 1 there exists constant C such ≤