Abstract:
We investigate the spectral norms of symmetric N × N matrices from two pseudo-random ensembles. The first is the pseudo-Wigner ensemble introduced in “Pseudo-Wigner Matri...Show MoreMetadata
Abstract:
We investigate the spectral norms of symmetric N × N matrices from two pseudo-random ensembles. The first is the pseudo-Wigner ensemble introduced in “Pseudo-Wigner Matrices” by Soloveychik, Xiang and Tarokh and the second is its sample covariance-type analog defined in this work. Both ensembles are defined through the concept of r-independence by controlling the amount of randomness in the underlying matrices, and can be constructed from dual BCH codes. We show that when the measure of randomness r grows as Np, where p ϵ (0,1] and ε > 0, the norm of the matrices is almost surely within o(log1 + εN/Nmin[ρ, 2/3]) distance from 1. Numerical simulations verifying the obtained results are provided.
Published in: 2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
Date of Conference: 03-06 October 2017
Date Added to IEEE Xplore: 18 January 2018
ISBN Information: