相位生成載波(PGC)調(diào)制與解調(diào)(包含MATLAB代碼)

PGC

ω0C，調(diào)制信號(hào)可以表示為（1）式：(t)Ccos(0IABcos[0(t)s(t)]ABcos[Ccos(0t)s

)Dcosωstψ(t)。將（2）式按Bessel（3）式[2]：IABJ(C)2(1)kJ(C)cos2k (t)2(1)k (C)cos(2k1)

2 0tcos

2 0tsin PGC

k

k

微分交叉相乘（differentialandcross—multiply，DCM）算法和反正切算法是兩種傳統(tǒng)的PGC1DCMPGC 1DCM輸入的干涉信號(hào)IS1Gcos0tS2Hcos20t進(jìn)I(t)BGJ1(C)sinsQ(t)BHJ2(C)coss

I(t、Q(t含有外界干擾，還不能直接提取待測信號(hào)，再通過微分交叉相乘（DCM）sin2?scos2?s1（7） V'B2GHJ(C)J(C)

VB2GHJ(C)J(C)(t)B2

t)

ψ(t)V通過高通濾波器濾除相位噪聲，就

B2GHJ(C)J(C)Dcos(

BκAκ DCM后，I(t)、Q(t)進(jìn)行相除得到（10）式[3]：I(t)GJ1(C)tan

s HJ2 (t)Dcos(t)(t)arctan(I(t)*HJ2

ψ(t)ψ(t)即可得到Vout=Dcosωst。1，從而使解調(diào)結(jié)果產(chǎn)生了非線性，同時(shí)帶來了嚴(yán)重的諧波失真以及總諧波失真。[1]C=2.37.PGC-Arctan算法來講，解調(diào)的結(jié)果是與J1(C）/J2(C)C=2.63時(shí)，J1(C）/J2(C)=1PGC-Arctan，C=2.63PGC-DCMPGC-AtctanC果隨著與C[4]根據(jù)文獻(xiàn)[4],fpassf0/2。D滿足(D1)s02MATLAB4MHz10K。f0=5000050KHzfn=10;10Hzs1，s2，s3，I3：調(diào)制信號(hào)50 待測信號(hào)20 信號(hào)20 調(diào)制后的信號(hào)210 3x2=I.*mod2;%2%x1%x2forj=1:N-fori=2:L-X(i)=X(i-1)+(x_d(i)+x_d(i-1))/2;fori=2:L-1解調(diào)后的信號(hào)解調(diào)后的信號(hào)10 4f0=5000050KHz調(diào)制信號(hào)50 待測信號(hào)20 信號(hào)20 調(diào)制后的信號(hào)210 5Number/2（Number=512解調(diào)后的信號(hào)解調(diào)后的信號(hào)10 6張愛玲，王愷晗，等.PGC解調(diào)算法的研究[J].光電技術(shù)應(yīng)用，2013，28GaoshengFang,TuanweiXu.Phase-sensitiveOpticalTimeDomainReflectometerBasedonPhaseGeneratedCarrierAlgorithm[J].JournalofLightwaveTechnology,2015.王燕.干涉型光纖傳感器及PGC解調(diào)技術(shù)研究[D].天津:天津理工大學(xué)cos(zcos)J(z)2(1)nJ(z)cos(2n sin(zcos)2(1)n cos(zsin)J0(z)2J2n(z)cos(2nsin(zsin)2J2n1(z)sin[(2n1)PGCDCM(MATLABclearall;closef0=50000;50KHzfs=1200;1.2KHzfn=1010Hzsubplot(4,1,3),plot(s3);title('(cs3');2x2=I.*mod22%x1%x2forj=1:N-fori=2:L-%積分fori=2:L-1plot(XX./max(XX),'r');holdon;PGC(MATLABclearall;closef0=50000;50KHzfs=1200;1.2KHzfn=1010Hzsubplot(4,1,3),plot(s3);title('(cs3');2x2=I.*mod22%x1%x2低通forplot(XX./max(XX),'r');holdon;File->GenerateMATLABcodelowpassfilter.mfunctionHd=%LOWPASSFILTERReturnsadiscrete-timefilter%%MATLAB%GeneratedbyMATLAB(R)7.13andtheSignalProcessingToolbox%%Generatedon:27-Oct-2016%%FIRWindowLowpassfilterdesignedusingtheFIR1%AllfrequencyvaluesareinHz.Fs=10000000;%SamplingFrequency = % =20000; %CutoffFrequencyflag='scale';%SamplingFlag%Createthewindowvectorforthedesignalgorithm.