Stochastic constructions of equiangular tight frames

Abstract

Equiangular tight frames have applications in communications, signal processing, and coding theory. Previous work demonstrates that few real equiangular tight frames exist for most pairs (n,d). This work compares three stochastic solutions to the frame design problem, specifically, the problem of designing real equiangular tight frames by minimizing the subspace minor angle sum-squared error. Numerical experiments show that particle swarm optimization outperforms genetic algorithms and the cross-entropy method for equiangular tight frame constructions for pairs (d+1,d) with d less than nine and specific pairs (n,d) where an equiangular tight frame is known to exist.