Constructions of equiangular tight frames with Genetic Algorithms

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), where the frame ¿_n,d is a d × n matrix with d ¿ n. This work proposes a genetic algorithm as a solution 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 the proposed method is successful for pairs (n,d) with d less than nine.