分圆跳频序列的时频二维汉明相关性

Time-frequency two dimensional hamming correlation of cyclotomy frequency hopping sequences

跳频序列的汉明相关性是跳频通信抗干扰性的指标之一。以往跳频序列的汉明相关性由只包含时延变量的一维汉明相关函数表示。本文将分圆跳频序列的汉明相关性用包含时延和频移两个变量的二维汉明相关函数表示,既考虑时延又考虑频率偏移因素下分圆跳频序列的汉明相关性。本文将序列长度为奇素数,频隙集分别为有限整数环和有限整数环加无穷量的两类分圆跳频序列的时频二维汉明相关性用每个分圆类集大小表示出来,并且指出频隙集为有限整数环加无穷量的分圆跳频序列(集)具有最优时频二维汉明相关性。

Hamming correlation of frequency hopping sequence is one of the anti-interference indexes in frequency hopping communication.Previously,Hamming correlation of frequency hopping sequence is presented by one dimensional Hamming correlation function which contains only time delay variables.Hamming correlation of cyclotomy frequency hopping sequence by two dimensional Hamming correlation function containing two variables is presented,i.e.time delay and frequency shift.This Hamming correlation considers not only time delay but also frequency shift of cyclotomic frequency hopping sequence.In the paper,timefrequency two dimensional Hamming correlation of two classes cyclotomy frequency hopping sequences with odd period and two frequency gap sets are represented by the size of every cyclotomic class set.The above two frequency gap sets are respectively finite integer ring and finite integer ring plus infinity.It concludes that cyclotomy frequency hopping sequence(sets)on frequency gap sets with finite integer ring plus infinite quantity have optimal time-frequency two dimensional Hamming correlation.