The Bounds And Coustructions Of Time-frequency Two Didemional Wide-gap Frequency Hopping Sequences

Frequency hopping communication technology is very important in modern spread spectrum communication,because of its good anti-interference and anti-multiple access capabilities.The anti-interference in the communication system is determined by the design of the frequency hopping sequence set,so the design of the frequency hopping sequence set is very important for the frequency hopping communication system.In addition to the time shift,the frequency hopping sequence set will also have a Doppler frequency shift during the communication process.Therefore,the time-frequency two-dimensional study is extremely important for the frequency hopping sequence set.In the frequency hopping communication system,when the sequence stays on one frequency for a long time,it will cause interference between the sequences,and then the wide gap frequency hopping communication is proposed.In a wide gap frequency hopping communication system,because two adjacent frequencies in the sequence must be different and there is a minimum gap,it has a more obvious effect on reducing the interference caused by the auto correlation caused by multiple access transmission and Doppler shift.The research results of this thesis are as follows:Firstly,the bounds of time-frequency two-dimensional Hamming correlation of wide-gap frequency hopping sequence set is derived.Hamming correlation bounds of Time-frequency two-dimensional with wide-gap frequency hopping sequence set.According to the relationship between the maximum and minimum values of the and function about the time-frequency two-dimensional Hamming correlation all frequency hopping sequences in the frequency hopping sequence set,the calculated time-frequency two-dimensional wide gap frequency hopping is proved by mathematical deduction Sequence set Hamming related theoretical bounds.Secondly,the Hamming correlation bounds of time-frequency two-dimensional low collision zone with wide interval frequency hopping sequence set is derived.The method proves that the wide gap frequency hopping sequence set time-frequency two-dimensional low hit zone Hamming related theoretical bounds.Finally,a time-frequency two-dimensional wide-interval frequency hopping sequence set is constructed.Using the Cartesian product method,the time-frequency two-dimensional wide gap frequency hopping sequence set and the time-frequency two-dimensional low hit zone wide gap frequency hopping sequence set when the maximum Hamming correlation theory reaches a certain value are constructed respectively.Through the application of the above-mentioned theoretical bounds,it is explored whether the constructed frequency hopping sequence set is optimal.The difference between the time-frequency two-dimensional wide gap frequency hopping sequence set constructed by the Cartesian product method and the time-frequency two-dimensional low hit zone wide gap frequency hopping sequence set is compared and analyzed.