Construction And Property Of Frequency Hopping Sequences Based On Cyclotomy

In recent decades,the Frequency Hopping(FH) communication as a important and common mean in spread-spectrum communication system has been developed more rapid-ly, with amount of demand of military and civilian communication.It has become a impor-tant subject,for its wide application distinctive property and high-end technology.Frequency Hopping sequence(FHS) is key in the FH communication as its core issue.So to design FH-S is hot in the academic field.Among designs,the design of FHC based on cyclotomy has some feature,such as new,simple and practical.We will begin new study and design with two recent FHSs based on the generalized cyclotomy firstly in the thesis. One which we will give detailed introduction has optimal Maximum Hamming correlation(MHC) whose length is L= pi(p2-1),based on Chinese Remainder Theorem and discrete logarithm ,and that constructed fromDx= rx< rM>,0≤x≤M-1, the cyclotomic classes of order M inF(p2),where pi,p2 are prime number, gcd(pi,pn2-1)= 1,p2n-1=MN,and r is a primitive element of F(p2).The other has near-optimal MHC based on Chinese Remainder Theorem.:firstly,we need construct a cyclic subgroup of ZL of order M,based on the primitive elementrx of pxnx,every factor of a odd integer L= p1n1pn2…pknk,then follow,the generalized cyclotomic classes Dx,0≤x≤x≤L-1M of Z*L are constructed,and map into the integer residue ring ZL-1/M which will be the frequency alphabet following,where px,0≤x≤k are all primes,and Mis a common factor ofpx-1,0≤x≤k.Uniform distri-bution of frequencise is not only necessary for good performance of FHS also a sufficient condition of FHS with optimal AHC. So we will prove frequency hopping sequence with optimal AHC been constructed on basis of the first method, and with uniformly distribut-ed frequency property. Maximum Hamming correlation and average hamming correlation are two different measures for performance evaluation of FHS. MHC measures the worst case of frequency hopping sequence set namely maximum interference, and AHC indicates the average interference.So in the second method, this thesis constructs frequency hopping sequence set with near-optimal MHC but optimal AHC with length being a prime L> 3 and use frequency gap of uniform distribution to prove the optimal AHC property.