Construction And Performance Analysis Of The Quartic Frequency Hopping Sequences Over Finite Field

The frequency hopping (FH) communication is one of spreading spectrum communication models. It's hopping carries frequencies are controlled by pseudonoise (PN) sequences. The FH communication is widely applied in modern military and civil communications because of its advantages such as anti-jamming, anti-fade, anti-capturing, channel sharing properties, and multi-access net-working etc.The FH sequences design is one of the key points of the FH communication system. The properties of FH sequences including frequencies number, sequences families number, Hamming auto-correction, Hamming cross-correction, frequencies gap and frequencies proportional etc, have a direct influence on FH communication system's abilities of anti-jamming, anti-fade, anti-capturing, and multi-access networking etc. The function of FH sequences is constructing FH pattern to control carries frequencies or play a role as address code in multi-access networking.Based on FH sequences's importances to FH communication systems, in this paper, around FH sequences's theory and the theoretical bound of designing sequences, we construct FH sequences families based on polynomials over finite fields and analyze their Hamming correlation performance.This paper first analyzes and summaries the FH sequences' functions, properties, theoretical bound and the main design types of FH frequencies. A method to construct polynomials of degree n FH sequences families over finite fields was introduced, we analyze and compare the Hamming correlation performance of special cases of polynomial FH sequences families. Generalised quartic FH sequences families were designed and give their Hamming correlation performance, derive their full collision probability and the formula of the average Hamming correlation. Then, analyze Hamming correlation performance of generalised quartic FH sequences families which all constant sequences have been deleted and derive their average Hamming correlation value too. Extend quartic FH sequences families's construction method alos were gived and analyze their averge Hamming correlation. We draw a conclusion that generalised quartic FH sequences families and extend quartic FH sequences families are all optimal averge Hamming correlation set. At last, compare generalised quartic FH sequences to extend quartic FH sequences, we can find that generalised quartic FH sequences families's sequence numbers are larged than extend quartic FH sequences families, but generalised quartic FH sequences families's average Hamming correlation performance is worse than extend quartic FH sequences families.