The Research Of Bound And Design On Hamming Correlation Of Frequency Hopping Sequences

Frequency hopping communication is one of the most commonly used communication technology in spread spectrum.Because of its great anti-jamming and randomness,frequency hopping communication plays a very important role in the military and civilian fields(such as underwater communication,radar,Bluetooth,and global mobile communication systems).In a multiple-access spread spectrum communication system,when many users work in the same frequency band,then their carrier frequency jump to the same frequency slot in a certain frequency hopping time slot,a collision will be occurred,causing multiple access interference between users,may cause bit errors in the demodulation output of the receiver.The degree of the interference is directly related to the Hamming correlation performance of the frequency hopping sequences.Hamming correlation functions have different classifications: periodic Hamming correlation frequency hopping sequences,aperiodic Hamming correlation frequency hopping sequences,conventional Hamming correlation frequency hopping sequences and partial Hamming correlation hopping sequences.In recent years,studies on the different Hamming correlations of frequency hopping sequences have become the focus of scholars at home and abroad.The One-Coincidence(OC)frequency hopping sequence is a new class of frequency hopping sequence proposed by Ahmad Adib Shaar in 1984.It is a set of non-repetitive sequences.For any two sequences in the sequence set,at any time slot,the maximum Hamming correlation is 1.The OC frequency hopping sequence can effectively reduce the multiple access interference in the multiple access system application and ensure the integrity of the transmitted information in the communication process.In this paper,we study the theoretical bound of the aperiodic partial Hamming correlation of frequency hopping sequences and constructions with optimal period Hamming correlation of OC frequency hopping sequence sets.In this paper,firstly,we deduced the theoretical bound of aperiodic partial Hamming correlation of frequency hopping sequence.Then analyze the constraint relationships on the theoretical bound of the aperiodic Hamming correlation and the period partial Hamming correlation.Based on the structural characteristics of frequency hopping sequence,the theoretical bound on the aperiodic partial Hamming correlation of the frequency hopping sequence is deduced.The constraint inequality between the frequency slot size,the sequence family size,the sequence period length,the correlation window length,and the maximum aperiodic partial Hamming correlation parameters are given.Secondly,three methods for constructing OC frequency hopping sequence with different parameters are given.Analyze the existing method of constructions on OC frequency hopping sequence,based on the theory of power residue and interleaving techniques,using the Chinese Remainder Theorem and finite field theory,three kinds of constructions on OC frequency hopping sequence set with different parameters are given.Firstly,frequency hopping sequences set with length n N is constructed,and frequency hopping sequences set with length(l-1)N is constructed using primitive elements of a given prime number.Then,combining the two constructions,the OC frequency hopping sequences set is expanded into another optimal OC frequency hopping sequences set with complex length.The constructed three kinds of sequence sets all satisfy the Peng-Fan bound optimality.With these three constructions and OC frequency hopping sequences,more new optimal OC frequency hopping sequences sets that meet the Peng-Fan and Lempel-Greenberger bounds can be constructed,and the hopping sequence set for a given frequency hopping spread spectrum system can be constructed.The choices provide more flexibility.Finally,compared and analyzed the parameters of this paper and the parameters of the existing OC frequency hopping sequences.