Design of no-hit-zone frequency-hopping sequence sets with optimal Hamming autocorrelation

Abstract

No-hit-zone frequency-hopping sequence (NHZ-FHS) is a core element for quasi-synchronous frequency-hopping multiple access (QS-FHMA) systems. In this paper we construct new optimal NHZ-FHS sets with respect to the bound by Ye and Fan by interleaving techniques.We first give three constructions for optimal NHZ-FHS sets of length 2N for any positive integer N ≥ 3 according to whether the size of NHZ is even or odd. We also construct optimal NHZ-FHS sets of length kN for any positive integers k and N with 2 ≤ k ≪ N by generalizing one of the proposed constructions for NHZ-FHS sets of length 2N. All the FHSs from our constructions are non-repeating FHSs which are optimal with respect to the Lempel-Greenberger bound. Since the NHZ size and set size can be freely selected in our constructions, they may be applied to various situations in QS-FHMA systems.