The Construction And Analysis Of Frequency Hopping Sequence Set With Optimal Average Hamming Correlation

The study of frequency-hopping spread spectrum system originated from military radio communication.Frequency-hopping spread spectrum system has many advantages,such as strong concealment,anti-interference and anti-fading ability.With the innovation of technology,frequency-hopping spread spectrum system is more widely used.Frequency-hopping system is a class of extended spectrum system which can be extended by the continuous hopping of carrier signal between different frequencies.The switching of carriers between different frequencies ensures the frequency-hopping spread spectrum system can not be disturbed,so it ensures the safety and reliability of the system.The research of frequency-hopping system can not be separated from the research of frequency-hopping sequence.Frequency-hopping sequence greatly affects the quality of the whole communication system.Therefore,finding out the frequency-hopping sequence set with good performance is an important part to study the whole frequency hopping spread spectrum system.If the performance of frequency hopping sequence is poor,even if the hardware of frequency-hopping spread spectrum system is excellent,it is also difficult to achieve the ideal anti-interference ability which can meet the requirement of the frequency-hopping system.The study of frequency-hopping sequence generally includes two research directions: one is to find the mutual constraint relationship between the parameters of frequency-hopping sequence,the other is to design the optimal frequency-hopping sequence which is optimal or nearly optimal respect to the theoretical bound.The current research on the theoretical bound of frequency-hopping sequences has achieved a wealth of theoretical results.The research is mainly divided into two types,one is the maximum Hamming correlation theoretical bound that studies the "worst" case,and the other is the "average" case The average Hamming correlation value is a measure of the average error of a frequency-hopping spread spectrum system.With the maximum Hamming correlation and the average Hamming correlation value can more objectively evaluate the frequency-hopping sequence set.So,the frequency-hopping sequence which is optimal respect to the average Hamming correlation theoretical bound is also very important.In this thesis,firstly,based on the generalized cyclotomy,a set of optimal frequency-hopping sequences respect to maximum Hamming correlation bound is proposed.Subsequently,an optimal average hamming correlation frequency-hopping sequence set is obtained based on the generalized cyclotomy.Based on the Chinese Remainder theorem,the set of optimal average hamming correlation frequency hopping sequence has been extended to construct a class of frequency-hopping sequence sets with flexible parameter,and the new frequency-hopping sequence set is the optimal average hamming correlation frequency-hopping sequence set.The main contents of this thesis are :(1)Based on the generalized cyclotomy and the Chinese Remainder theorem,A construction is given to obtain a better set of frequency hopping sequences with more composite length.We discussed the result and the results of the construction are optimal respect to the maximum hamming correlation theoretical bound.(2)Based on the generalized cyclotomy,a frequency hopping sequence set with a sequence length v-1 is given,where v is the result of the product of different prime power.And we pay some attention to the hamming correlation and discussed it.The result sequence set of the construction respect to Peng-Niu-Tang bound is optimal.(3)Based on the Chinese Remainder theorem,a construction is given to obtain a frequency hopping sequence set with flexible parameter,and the result sequence set of the structure is optimal for Peng-Niu-Tang bounds.Then two types of known extension constructs are analyzed,the extended sequence set is proved to be the optimal average hamming correlation frequency-hopping sequence set by selecting the optimal average hamming correlation frequency-hopping sequence set as the basic sequence set.