New Constructions for Optimal Sets of Frequency-Hopping Sequences

Abstract

In this paper, two generic constructions of optimal frequency-hopping sequence (FHS) sets employing <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> -form functions with difference-balanced property are presented. They generalize the previous constructions of optimal FHS sets using <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> -sequences and produce new optimal FHS sets that cannot be produced by the earlier constructions. By choosing appropriate <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> -form functions with difference-balanced property, both constructions lead to FHSs with large linear complexity. In addition, one of the proposed constructions gives new optimal parameters of FHS sets.