Searching for Costas Arrays Using General Particle Swarm Optimization

Abstract

Costas arrays special permutation matrices have widespread applications in many fields such as signal processing and cryptography. However, so far the basic problem-the existence problem remains unsolved. To check the existence of costas arrays for a certain order, there are two kinds of methods: algebraic constructions and exhaustive search. But algebraic constructions do not work for lots of orders, and exhaustive search has exponential computational complexity. Here stochastic search is considered. Every ntimesn permutation matrix has 4n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> +4n two-dimensional discrete autocorrelation function values. If the maximum takes 1, the corresponding permutation matrix is a costas array. Then quest for costas arrays can be viewed as an optimization problem. The optimization objective is minimizing the maximal auto-correlation function value. Swarm intelligence techniques have been applied successfully to many optimization problems. Therefore, this paper tries to search for costas arrays with general particle swarm optimization (GPSO), and preliminarily finds that GPSO is effective for costas arrays for orders less than 18