Frequency Hopping Sequence Time-frequency Two-dimensional Part Hamming Corelation Theoryand Corelation Analysis

Frequency-hopping spread-spectrum communications have good anti-jamming and high security factors,and are widely used in a variety of communications systems.The size of the Hamming correlation value of the frequency hopping sequence codes in the frequency hopping spread spectrum communication system is one of the important indexes for evaluating the performance of the system.In the high-speed movement of the communication terminal,the frequency hopping sequence codes both have a time delay and a frequency shift.This paper mainly studies the time-frequency two-dimensional Hamming correlation of the frequency hopping sequence(set)and the time-frequency two-dimensional partial Hamming correlation of the hopping sequence set.First,the Hamming correlation theory of time-frequency two-dimensional frequency hopping sequences in the low hit zone is extended to the Hamming-related theoretical bounds of general time-frequency two-dimensional frequency hopping sequences.The concept of the general time-frequency two-dimensional frequency hopping sequence optimal Hamming relevance is given.Secondly,using the segmentation method in combinatorial mathematics,the Hamming correlation function of one-dimensional cyclotomic frequency hopping sequence is extended to include two variables of time delay and frequency shift,taking into account both time delay and frequency offset.A two-dimensional Hamming correlation function is used to obtain the calculation formula of the time-frequency two-dimensional Hamming correlation function for the two types of cyclotomic frequency hopping sequences(sets)whose frequency gap sets are respectively an integer residual class ring and an integer remainder class ring plus infinite.It is pointed out that the frequency hopping sequences(sets)have an optimal time-frequency two-dimensional Hamming correlation which the frequency gap set is an integer residual class ring plus an infinite.Finally,in practical applications,under the given the constraints of the hardware conditions of the frequency hopping communication system,and in order to reduce theimpact on the anti-jamming and anti-interception of the communication system,the concept of time-frequency two-dimensional partial Hamming correlation of the frequency hopping sequence is given.This paper studies not only the time-frequency two-dimensional Hamming correlation of frequency hopping sequence sets,but also the time-frequency two-dimensional average part Hamming correlation,and the time-frequency two-dimensional partial Hamming correlation of the frequency hopping sequence set in the low hit zone and time-frequency two-dimensional average partial Hamming correlation in low hit zone.