gold序列实验报告

1、Gold序列实验报告一、实验过程及分析1 m序列&Gold序列的产生（1）选取本原多项式，产生m序列。fbconnection_m=1 0 1 0 0 1 1;mseq=m_sequence(fbconnection_m);（2）由本原多项式生成的m序列为m序列优选对，以此优选对来产生Gold序列。fbconnection_op_1=0 0 1 0 0 0 1;fbconnection_op_2=1 1 1 0 0 0 1;goldseq=gold_seq(fbconnection_op_1,fbconnection_op_2);2 m序列的相关特性图1 m序列自相关函数图 2 m序列互相关函

2、数3 Gold序列的相关特性图3 Gold序列自相关函数图4 Gold序列互相关函数图2-5 m序列&Gold序列最小，最大相关值4 m序列&Gold序列相关特性比较图6 m序列&Gold序列自相关函数比较图7 m序列&Gold序列互相关函数比较gold序列在时延不为0是三值的，这一点不如m序列，在时延为0处具有与m序列相同的峰值特性。显然，m序列的自相关特性比Gold序列的自相关特性要好。Gold序列具有更小的互相关峰值，显然Gold序列的互相关特性比m序列的互相关特性性能要好。5 m序列优选对m序列优选对也是gold序列族中的gold序列，所以其互相关函数与gold序列一致。图8 m序列优

3、选对的互相关函数6 任选6个Gold序列，观察其自相关函数图9 任选6个Gold序列的自相关函数7 任选6对Gold序列，观察其互相关函数图 10 任选6对Gold序列的互相关函数任意两个Gold序列互相关函数幅度小于或等于17，符合Gold理论。源码(1) PN_Correlation.m% =% PN_Correlation.m% Correlation analysis of PN sequence% Author: jzh (04011646 seu)% Date: 2014.12.29% =% cleanclose all;clear all;clc;% optimum pairsf

4、bconnection_op_1=0 0 1 0 0 0 1;fbconnection_op_2=1 1 1 0 0 0 1;% any m sequence for testfbconnection_m=1 0 1 0 0 1 1;% gold sequencemseq_op_1=m_sequence(fbconnection_op_1);mseq_op_2=m_sequence(fbconnection_op_2);goldseq=gold_seq(fbconnection_op_1,fbconnection_op_2);% m sequencemseq=m_sequence(fbconn

5、ection_m);% mappingmseq_op_1(mseq_op_1=0)=-1;mseq_op_2(mseq_op_2=0)=-1;goldseq(goldseq=0)=-1;mseq(mseq=0)=-1;m_auto=ccorr(mseq);% any two m sequences except optimum pairsm_cross=ccorr(mseq,mseq_op_1);gold_auto=ccorr(goldseq(1,:);gold_cross=ccorr(goldseq(1,:),goldseq(2,:);m_op_cross=ccorr(mseq_op_1,m

6、seq_op_2);m_auto_max = max(m_auto)m_auto_min = min(m_auto)gold_auto_max = max(gold_auto)m_cross_amplitude_max = max(abs(m_cross)gold_cross_amplitude_max = max(abs(gold_cross)N=length(mseq); % sequence lengthabscissa=-N+1:N-1; % abscissa axisfigure(1);plot(abscissa,m_auto);xlabel(k); ylabel(R(k);lege

7、nd(autocorrelation function of m sequence);title(autocorrelation function of m sequence);figure(2);plot(abscissa,m_cross);xlabel(k); ylabel(R(k);legend(cross-correlation function of m sequence);title(cross-correlation function of m sequence);figure(3);plot(abscissa,gold_auto);xlabel(k); ylabel(R(k);

8、legend(autocorrelation function of gold sequence);title(autocorrelation function of gold sequence);figure(4);plot(abscissa,gold_cross);xlabel(k); ylabel(R(k);legend(cross-correlation function of gold sequence);title(cross-correlation function of gold sequence);figure(5);subplot(1,2,1);plot(abscissa,

9、m_auto);xlabel(k); ylabel(R(k);title(autocorrelation function of m sequence);subplot(1,2,2);plot(abscissa,gold_auto);xlabel(k); ylabel(R(k);title(autocorrelation function of gold sequence);figure(6);subplot(1,2,1);plot(abscissa,m_cross);xlabel(k); ylabel(R(k);title(cross-correlation function of m se

10、quence);subplot(1,2,2);plot(abscissa,gold_cross);xlabel(k); ylabel(R(k);title(cross-correlation function of gold sequence);figure(7);plot(abscissa,m_op_cross);xlabel(k); ylabel(R(k);legend(cross-correlation function of m sequence optimum pairs);title(cross-correlation function of m sequence optimum

11、pairs);% test autocorrelation of any gold sequencefor test_time = 1:6 ii = ceil(rand()*(N+2); figure(); temp_gold_auto = ccorr(goldseq(ii,:); plot(abscissa,temp_gold_auto); xlabel(k); ylabel(R(k); legend(strcat( seq number = ,num2str(ii); title(autocorrelation function of a random gold sequence);end

12、% test cross-correlation of any 2 gold sequencefor test_time = 1:6 ii = ceil(rand()*(N+2); jj=ceil(rand()*(N+2); while jj = ii jj=ceil(rand()*(N+2); end figure(); temp_gold_cross = ccorr(goldseq(ii,:),goldseq(jj,:); plot(abscissa,temp_gold_cross); xlabel(k); ylabel(R(k); legend(strcat( seq1 number=,

13、num2str(ii), seq2 number=,num2str(jj); title(strcat(cross-correlation function of 2 random gold sequence:,. cross correlation amplitude MAX = ,. num2str(max(abs(temp_gold_cross);end(2) m_sequence.m% =% m_sequence.m% generating m sequence% Author: jzh (04011646 seu)% Date: 2014.12.29% =function mseq

14、= m_sequence(fbconnection)% = m_sequence =% generating m sequence% Input:% fbconnection: feedback connection responding to primitive polynomial% Output:% msequ: generation of m sequence, 1-by-N% =n = length(fbconnection);N = 2n-1; % length of m sequenceregister = zeros(1,n-1) 1; % initial state of s

15、hift register% preallocatingnewregister = zeros(1,n);mseq = zeros(1,N);mseq(1)=register(n);for ii=2:N % feedback newregister(1) = mod(sum(fbconnection.*register),2); % shift for jj=2:n newregister(jj)=register(jj-1); end register=newregister; % update mseq(ii)=register(n); % output m sequenceend(3)

16、gold_seq.m% =% gold_seq.m% generating gold sequence family% Author: jzh (04011646 seu)% Date: 2014.12.29% =function goldseq = gold_seq(fbconnection1,fbconnection2)% = gold_seq =% generating gold sequence family% Input:% fbconnection1: feedback connection 1 % fbconnection2: feedback connection 2% Not

17、e: fbconnection1 & fbconnection2 are optimum pairs% Output:% goldseq: generation of gold sequence family, (N+2)-by-N% =mseq1 = m_sequence(fbconnection1);mseq2 = m_sequence(fbconnection2);N=2length(fbconnection1) - 1;goldseq = zeros(N+2,N); % preallocating% different shift amount of two m sequencefor

18、 shift_amount = 0:N-1 shift_mseq2 = mseq2(shift_amount+1:N) mseq2(1:shift_amount); goldseq(shift_amount+1,:) = mod(mseq1+shift_mseq2,2);endgoldseq(N+1,:)=mseq1;goldseq(N+2,:)=mseq2;(4) ccorr.m% =% ccorr.m% calculate cross-correlation function% Author: jzh (04011646 seu)% Date: 2014.12.29% =function r = ccorr(seq1,seq