Optimal No-Hit-Zone Sequences With Wide-Gap for Improved FHMA Systems Under Follower Jamming

Abstract

Frequency hopping multiple access (FHMA) techniques applied to critical wireless applications often encounter the effects of multiple-access interference (MAI) and follower jamming. The generalized orthogonal FH, which includes no-hit-zone (NHZ) and low-hit-zone (LHZ) FH sequence (FHS), has emerged as a highly promising hopping pattern in quasi-synchronous FHMA systems due to its ability to minimize MAI, but is unable to resist follower jamming attacks. In this paper, we firstly introduce the wide-gap property into an improved NHZ-FHS (i.e., WG-NHZ-FHS), where the frequencies at adjacent time-slots are hopped across a relatively wide gap of bandwidth, so as to address the issues of the MAI and the follower jamming. A general method to generate optimal WG-NHZ-FHS sets satisfying the theoretical bound is proposed. Subsequently, to present the merits of such a hopping pattern, the numerical error-rate performance of the WG-NHZ-FHS set imposed in a quasi-synchronous FHMA system under a follower jamming attacker is derived by using the characteristic function method; in addition, the obtained numerical result is extended to the case of WG-LHZ-FHS as the comparison benchmark. Finally, the numerical analysis and the system simulation results reveal that, compared to the previous types of FHSs, the proposed WG-NHZ-FHS set provides the lower error-rate and higher reliability for critical FHMA applications thanks to its inherent advantages of the MAI-free and the follower jamming suppression.