Two-Dimensional Hamming Correlation Theory Bound And Construction Of Wide-Gap Frequency Hopping Sequence Set

Frequency hopping communication technology is widely used in modern communication field because of its good anti-jamming characteristics and multi-access networking performance.In the practical application of frequency hopping communication system,time shift and frequency shift will occur in the process of signal transmission.Therefore,it is necessary to study the time-frequency two-dimensional hamming correlation characteristics of frequency hopping sequence set.Wide-gap frequency hopping sequences have outstanding performance in suppressing narrowband interference and broadband blocking interference.Therefore,it is of great significance to study wide-interval frequency hopping sequences.This paper mainly studies the partial hamming correlation and average hamming correlation of wide-gap frequency hopping sequence set in time-frequency two-dimensional low hit zone,and proposes a method to construct wide-gap frequency hopping sequence set in time-frequency two-dimensional low hit zone.Firstly,the periodic partial hamming correlation function of the wide-gap frequency hopping sequence set is given,and the theoretical bound satisfied by the periodic partial hamming auto-correlation and cross-correlation function of the wide-gap frequency hopping sequence set is proved.For the wide-gap frequency hopping sequence set in the time-frequency two-dimensional low hit zone,the theoretical bound satisfied by the periodic partial hamming auto-correlation and cross-correlation function of the time-frequency two-dimensional low hit zone is proved.Compared with the Hamming correlation theory bound which only considers the time shift,the theory bound proposed in this paper is broader,and the application scope is wider,including the theory bound which only considers the time shift.Secondly,the average periodic hamming correlation bounds of wide-gap frequency hopping sequences and the average periodic hamming correlation bounds of wide-gap frequency hopping sequences in time-frequency two-dimensional low hit zone are derived.The average periodic partial hamming correlation theory bound of wide-gap frequency hopping sequence and the average periodic partial hamming correlation theory bound of wide-gap frequency hopping sequence in low hit zone are deduced by mathematical method.Compared with the Hamming correlation theory bound which only considers the time shift,the theory bound proposed in this paper is broader,and the application scope is wider,including the theory bound which only considers the time shift.Finally,the necessary and sufficient conditions for the optimal frequency hopping sequence set satisfying the theoretical bound of average periodic hamming correlation in time-frequency two-dimensional low hit zone are analyzed.Then,the construction methods of two kinds of time-frequency two-dimensional low hit zone wide-gap frequency hopping sequence sets are proposed,and the average periodic hamming correlation characteristics in the time-frequency two-dimensional low hit zone are analyzed.Finally,two construction examples are given and the average periodic hamming correlation value in the time-frequency two-dimensional low hit zone is analyzed.