gold序列實驗報告

...wd......wd......wd...Gold序列實驗報告一、實驗過程及分析1m序列&Gold序列的產(chǎn)生〔1〕選取本原多項式，產(chǎn)生m序列。fbconnection_m=[1010011];mseq=m_sequence(fbconnection_m);〔2〕由本原多項式生成的m序列為m序列優(yōu)選對，以此優(yōu)選對來產(chǎn)生Gold序列。fbconnection_op_1=[0010001];fbconnection_op_2=[1110001];goldseq=gold_seq(fbconnection_op_1,fbconnection_op_2);2m序列的相關特性圖1m序列自相關函數(shù)圖2m序列互相關函數(shù)3Gold序列的相關特性圖3Gold序列自相關函數(shù)圖4Gold序列互相關函數(shù)圖2-5m序列&Gold序列最小，最大相關值4m序列&Gold序列相關特性比擬圖6m序列&Gold序列自相關函數(shù)比擬圖7m序列&Gold序列互相關函數(shù)比擬gold序列在時延不為0是三值的，這一點不如m序列，在時延為0處具有與m序列一樣的峰值特性。顯然，m序列的自相關特性比Gold序列的自相關特性要好。Gold序列具有更小的互相關峰值，顯然Gold序列的互相關特性比m序列的互相關特性性能要好。5m序列優(yōu)選對m序列優(yōu)選對也是gold序列族中的gold序列，所以其互相關函數(shù)與gold序列一致。圖8m序列優(yōu)選對的互相關函數(shù)6任選6個Gold序列，觀察其自相關函數(shù)圖9任選6個Gold序列的自相關函數(shù)7任選6對Gold序列，觀察其互相關函數(shù)圖10任選6對Gold序列的互相關函數(shù)任意兩個Gold序列互相關函數(shù)幅度小于或等于17，符合Gold理論。源碼(1)PN_Correlation.m%=======================================%PN_Correlation.m%CorrelationanalysisofPNsequence%%Author:jzh(04011646seu)%Date:2014.12.29%=======================================%cleancloseall;clearall;clc;%optimumpairsfbconnection_op_1=[0010001];fbconnection_op_2=[1110001];%anymsequencefortestfbconnection_m=[1010011];%goldsequencemseq_op_1=m_sequence(fbconnection_op_1);mseq_op_2=m_sequence(fbconnection_op_2);goldseq=gold_seq(fbconnection_op_1,fbconnection_op_2);%msequencemseq=m_sequence(fbconnection_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);%anytwomsequencesexceptoptimumpairsm_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,mseq_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);%sequencelengthabscissa=-N+1:N-1;%abscissaaxisfigure(1);plot(abscissa,m_auto);xlabel('k');ylabel('R(k)');legend('autocorrelationfunctionofmsequence');title('autocorrelationfunctionofmsequence');figure(2);plot(abscissa,m_cross);xlabel('k');ylabel('R(k)');legend('cross-correlationfunctionofmsequence');title('cross-correlationfunctionofmsequence');figure(3);plot(abscissa,gold_auto);xlabel('k');ylabel('R(k)');legend('autocorrelationfunctionofgoldsequence');title('autocorrelationfunctionofgoldsequence');figure(4);plot(abscissa,gold_cross);xlabel('k');ylabel('R(k)');legend('cross-correlationfunctionofgoldsequence');title('cross-correlationfunctionofgoldsequence');figure(5);subplot(1,2,1);plot(abscissa,m_auto);xlabel('k');ylabel('R(k)');title('autocorrelationfunctionofmsequence');subplot(1,2,2);plot(abscissa,gold_auto);xlabel('k');ylabel('R(k)');title('autocorrelationfunctionofgoldsequence');figure(6);subplot(1,2,1);plot(abscissa,m_cross);xlabel('k');ylabel('R(k)');title('cross-correlationfunctionofmsequence');subplot(1,2,2);plot(abscissa,gold_cross);xlabel('k');ylabel('R(k)');title('cross-correlationfunctionofgoldsequence');figure(7);plot(abscissa,m_op_cross);xlabel('k');ylabel('R(k)');legend('cross-correlationfunctionofmsequenceoptimumpairs');title('cross-correlationfunctionofmsequenceoptimumpairs');%testautocorrelationofanygoldsequencefortest_time=1:6ii=ceil(rand()*(N+2));figure();temp_gold_auto=ccorr(goldseq(ii,:));plot(abscissa,temp_gold_auto);xlabel('k');ylabel('R(k)');legend(strcat('seqnumber=',num2str(ii)));title('autocorrelationfunctionofarandomgoldsequence');end%testcross-correlationofany2goldsequencefortest_time=1:6ii=ceil(rand()*(N+2));jj=ceil(rand()*(N+2));whilejj==iijj=ceil(rand()*(N+2));endfigure();temp_gold_cross=ccorr(goldseq(ii,:),goldseq(jj,:));plot(abscissa,temp_gold_cross);xlabel('k');ylabel('R(k)');legend(strcat('seq1number=',num2str(ii),',seq2number=',num2str(jj)));title(strcat('cross-correlationfunctionof2randomgoldsequence:',...'crosscorrelationamplitudeMAX=',...num2str(max(abs(temp_gold_cross)))));end(2)m_sequence.m%==============================%m_sequence.m%generatingmsequence%%Author:jzh(04011646seu)%Date:2014.12.29%==============================functionmseq=m_sequence(fbconnection)%==============================m_sequence==============================%generatingmsequence%%Input:%fbconnection:feedbackconnectionrespondingtoprimitivepolynomial%Output:%msequ:generationofmsequence,1-by-N%========================================================================n=length(fbconnection);N=2^n-1;%lengthofmsequenceregister=[zeros(1,n-1)1];%initialstateofshiftregister%preallocatingnewregister=zeros(1,n);mseq=zeros(1,N);mseq(1)=register(n);forii=2:N%feedbacknewregister(1)=mod(sum(fbconnection.*register),2);%shiftforjj=2:nnewregister(jj)=register(jj-1);endregister=newregister;%updatemseq(ii)=register(n);%outputmsequenceend(3)gold_seq.m%==================================%gold_seq.m%generatinggoldsequencefamily%%Author:jzh(04011646seu)%Date:2014.12.29%==================================functiongoldseq=gold_seq(fbconnection1,fbconnection2)%===============================gold_seq===============================%generatinggoldsequencefamily%%Input:%fbconnection1:feedbackconnection1%fbconnection2:feedbackconnection2%Note:fbconnection1&fbconnection2areoptimumpairs%Output:%goldseq:generationofgoldsequencefamily,(N+2)-by-N%========================================================================mseq1=m_sequence(fbconnection1);mseq2=m_sequence(fbconnection2);N=2^length(fbconnection1)-1;goldseq=zeros(N+2,N);%preallocating%differentshiftamountoftwomsequenceforshift_amount=0:N-1shift_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%calculatecross-correlationfunction%%Author:jzh(04011646seu)%Date:2014.12.29%=======================================functionr=ccorr(seq1,seq2)%================================ccorr==========================