一类周期为素数倍数的跳频序列族

摘要

跳频技术具有抗干扰、抗截获、码分多址和频带共享等优点，在军事无线电通信、民用移动通信、现代雷达和声纳等电子系统中具有重要的应用。其中跳频序列是跳频系统中不可或缺的一部分。本文基于有限域上的分圆法和中国剩余定理，首先构造了一类周期为素数倍数的跳频序列族，随后利用分圆数的性质导出了此序列族的汉明相关值。研究结果表明，该序列族不仅关于 Peng-Fan 界是最优的，而且每个序列关于 Lempel-Greenberger 界也是最优（或次最优）的。另外，已有的基于分圆法的最优跳频序列构造是本文的特例。%Frequency-hopping spread spectrum (FHSS)systems,with properties of anti-jamming,anti-intercept,code division multiple access (CDMA),channel sharing,etc,are usually applied in military radio communication,mobile communication,modern radar and sonar echolocation systems.Frequency-hopping sequences (FHS)is an integral part of FHSS systems.Based on the cyclo-tomy over the finite field and the Chinese remainder theorem,a class of FHSs set with a multiple of prime number length is con-structed and the Hamming correlations of the new set are derived by some basic properties of the cyclotomic numbers.The results show that the proposed set is optimal with respect to the Peng-Fan bound and each FHS of the set is optimal or near optimal with re-spect to the Lempel-Greenberger bound.Furthermore,the previous constructions of optimal FHS sets based on cyclotomy are special cases of this paper.