Simplified Bounds on FHSs Set and Its Strictly Optimal Construction

Abstract

Frequency-hopping sequences (FHSs) with favorite partial Hamming correlation properties are intensively needed in many synchronization and multiple-access systems. Strictly optimal FHS sets are a kind of FHS sets which has optimal Hamming correlation for any correlation window. In this paper, firstly we present simplified representations of the generalized Lempel–Greenberger bound on the partial Hamming autocorrelation of an FHS and the generalized Peng-Fan bound on the partial Hamming correlation of an FHS set, respectively. Secondly, we propose a direct construction of strictly optimal FHS sets, which interprets the previous construction proposed by Cai, Zhou, Yang and Tang. By choosing appropriate parameters and bijections, we present more flexible constructions of strictly optimal FHS sets.