仿真高斯白噪声信道下QPSK的EbN0与误比特率之间的关系讲课讲稿.doc

仿真高斯白噪声信道下QPSK的EbN0与误比特率之间的关系

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QPSK调制与解调在MATLAB平台上的实现
QPSK即四进制移向键控（Quaternary Phase Shift Keying），它利用载波的四种不同相位来表示数字信息，由于每一种载波相位代表两个比特信息，因此每个四进制码元可以用两个二进制码元的组合来表示。两个二进制码元中的前一个码元用a表示，后一个码元用b表示。
QPSK信号可以看作两个载波正交2PSK信号的合成，下图表示QPSK正交调制器。

由QPSK信号的调制可知，对它的解调可以采用与2PSK信号类似的解调方法进行解调。解调原理图如下所示，同相支路和正交支路分别采用相干解调方式解调，得到和，经过抽样判决和并/串交换器，将上下支路得到的并行数据恢复成串行数据。

% 调相法
clear all
close all

t=[-1:0.01:7-0.01];
tt=length(t);
x1=ones(1,800);
for i=1:tt
if (t(i)>=-1 & t(i)<=1) | (t(i)>=5& t(i)<=7);
x1(i)=1;

else x1(i)=-1;
end
end

t1=[0:0.01:8-0.01];
t2=0:0.01:7-0.01;
t3=-1:0.01:7.1-0.01;
t4=0:0.01:8.1-0.01;

tt1=length(t1);
x2=ones(1,800);
for i=1:tt1
if (t1(i)>=0 & t1(i)<=2) | (t1(i)>=4& t1(i)<=8);
x2(i)=1;

else x2(i)=-1;
end
end

f=0:0.1:1;
xrc=0.5+0.5*cos(pi*f);

y1=conv(x1,xrc)/5.5;
y2=conv(x2,xrc)/5.5;

n0=randn(size(t2));

f1=1;
i=x1.*cos(2*pi*f1*t);
q=x2.*sin(2*pi*f1*t1);
I=i(101:800);
Q=q(1:700);

QPSK=sqrt(1/2).*I+sqrt(1/2).*Q;
QPSK_n=(sqrt(1/2).*I+sqrt(1/2).*Q)+n0;

n1=randn(size(t2));
i_rc=y1.*cos(2*pi*f1*t3);
q_rc=y2.*sin(2*pi*f1*t4);

I_rc=i_rc(101:800);
Q_rc=q_rc(1:700);
QPSK_rc=(sqrt(1/2).*I_rc+sqrt(1/2).*Q_rc);
QPSK_rc_n1=QPSK_rc+n1;

figure(1)
subplot(4,1,1);plot(t3,i_rc);axis([-1 8 -1 1]);ylabel('a序列');
subplot(4,1,2);plot(t4,q_rc);axis([-1 8 -1 1]);ylabel('b序列');
subplot(4,1,3);plot(t2,QPSK_rc);axis([-1 8 -1 1]);ylabel('合成序列');
subplot(4,1,4);plot(t2,QPSK_rc_n1);axis([-1 8 -1 1]);ylabel('加入噪声');

效果图：

% 设定 T=1,加入高斯噪声
clear all
close all

% 调制
bit_in = randint(1e3, 1, [0 1]);

bit_I = bit_in(1:2:1e3);
bit_Q = bit_in(2:2:1e3);

data_I = -2*bit_I+1;
data_Q = -2*bit_Q+1;

data_I1=repmat(data_I',20,1);
data_Q1=repmat(data_Q',20,1);

for i=1:1e4
data_I2(i)=data_I1(i);
data_Q2(i)=data_Q1(i);
end;

f=0:0.1:1;
xrc=0.5+0.5*cos(pi*f);

data_I2_rc=conv(data_I2,xrc)/5.5;
data_Q2_rc=conv(data_Q2,xrc)/5.5;

f1=1;
t1=0:0.1:1e3+0.9;

n0=rand(size(t1));
I_rc=data_I2_rc.*cos(2*pi*f1*t1);
Q_rc=data_Q2_rc.*sin(2*pi*f1*t1);
QPSK_rc=(sqrt(1/2).*I_rc+sqrt(1/2).*Q_rc);
QPSK_rc_n0=QPSK_rc+n0;

% 解调
I_demo=QPSK_rc_n0.*cos(2*pi*f1*t1);
Q_demo=QPSK_rc_n0.*sin(2*pi*f1*t1);

% 低通滤波
I_recover=conv(I_demo,xrc);
Q_recover=conv(Q_demo,xrc);

I=I_recover(11:10010);
Q=Q_recover(11:10010);
t2=0:0.05:1e3-0.05;
t3=0:0.1:1e3-0.1;

% 抽样判决
data_recover=[];
for i=1:20:10000
data_recover=[data_recover I(i:1:i+19) Q(i:1:i+19)];
end;

bit_recover=[];
for i=1:20:20000
if sum(data_recover(i:i+19))>0
data_recover_a(i:i+19)=1;
bit_recover=[bit_recover 1];
else
data_recover_a(i:i+19)=-1;
bit_recover=[bit_recover -1];
end
end

error=0;

dd = -2*bit_in+1;
ddd=[dd'];
ddd1=repmat(ddd,20,1);
for i=1:2e4
ddd2(i)=ddd1(i);
end
for i=1:1e3
if bit_recover(i)~=ddd(i)
error=error+1;
end
end

p=error/1000;

figure(1)
subplot(2,1,1);plot(t2,ddd2);axis([0 100 -2 2]);title('原序列');
subplot(2,1,2);plot(t2,data_recover_a);axis([0 100 -2 2]);title('解调后序列');

效果图：

% 设定 T=1, 不加噪声
clear all
close all

% 调制
bit_in = randint(1e3, 1, [0 1]);
bit_I = bit_in(1:2:1e3);
bit_Q = bit_in(2:2:1e3);

data_I = -2*bit_I+1;
data_Q = -2*bit_Q+1;

data_I1=repmat(data_I',20,1);
data_Q1=repmat(data_Q',20,1);

for i=1:1e4
data_I2(i)=data_I1(i);
data_Q2(i)=data_Q1(i);
end;

t=0:0.1:1e3-0.1;

f=0:0.1:1;
xrc=0.5+0.5*cos(pi*f);

data_I2_rc=conv(data_I2,xrc)/5.5;
data_Q2_rc=conv(data_Q2,xrc)/5.5;

f1=1;
t1=0:0.1:1e3+0.9;

I_rc=data_I2_rc.*cos(2*pi*f1*t1);
Q_rc=data_Q2_rc.*sin(2*pi*f1*t1);
QPSK_rc=(sqrt(1/2).*I_rc+sqrt(1/2).*Q_rc);

% 解调
I_demo=QPSK_rc.*cos(2*pi*f1*t1);
Q_demo=QPSK_rc.*sin(2*pi*f1*t1);

I_recover=conv(I_demo,xrc);
Q_recover=conv(Q_demo,xrc);
I=I_recover(11:10010);
Q=Q_recover(11:10010);
t2=0:0.05:1e3-0.05;
t3=0:0.1:1e3-0.1;

data_recover=[];
for i=1:20:10000
data_recover=[data_recover I(i:1:i+19) Q(i:1:i+19)];
end;

ddd = -2*bit_in+1;
ddd1=repmat(ddd',10,1);
for i=1:1e4
ddd2(i)=ddd1(i);
end

figure(1)
subplot(4,1,1);plot(t3,I);axis([0 20 -6 6]);
subplot(4,1,2);plot(t3,Q);axis([0 20 -6 6]);
subplot(4,1,3);plot(t2,data_recover);axis([0 20 -6 6]);
subplot(4,1,4);plot(t,ddd2);axis([0 20 -6 6]);

效果图：

% QPSK误码率分析
SNRindB1=0:2:10;
SNRindB2=0:0.1:10;
for i=1:length(SNRindB1)
[pb,ps]=cm_sm32(SNRindB1(i));
smld_bit_err_prb(i)=pb;
smld_symbol_err_prb(i)=ps;
end;
for i=1:length(SNRindB2)
SNR=exp(SNRindB2(i)*log(10)/10);
theo_err_prb(i)=Qfunct(sqrt(2*SNR));
end;
title('QPSK误码率分析');
semilogy(SNRindB1,smld_bit_err_prb,'*');
axis([0 10 10e-8 1]);
hold on;
% semilogy(SNRindB1,smld_symbol_err_prb,'o');
semilogy(SNRindB2,theo_err_prb);
legend('仿真比特误码率','理论比特误码率');
hold off;

function[y]=Qfunct(x)
y=(1/2)*erfc(x/sqrt(2));

function[pb,ps]=cm_sm32(SNRindB)
N=10000;
E=1;
SNR=10^(SNRindB/10);
sgma=sqrt(E/SNR)/2;
s00=[1 0];
s01=[0 1];
s11=[-1 0];
s10=[0 -1];
for i=1:N
temp=rand;
if (temp<0.25)
dsource1(i)=0;
dsource2(i)=0;
elseif (temp<0.5)
dsource1(i)=0;
dsource2(i)=1;
elseif (temp<0.75)
dsource1(i)=1;
dsource2(i)=0;
else
dsource1(i)=1;
dsource2(i)=1;
end;
end;
numofsymbolerror=0;
numofbiterror=0;
for i=1:N
n=sgma*randn(size(s00));
if((dsource1(i)==0)&(dsource2(i)==0))
r=s00+n;
elseif((dsource1(i)==0)&(dsource2(i)==1))
r=s01+n;
elseif((dsource1(i)==1)&(dsource2(i)==0))
r=s10+n;
else
r=s11+n;
end;
c00=dot(r,s00);
c01=dot(r,s01);
c10=dot(r,s10);
c11=dot(r,s11);
c_max=max([c00 c01 c10 c11]);
if (c00==c_max)
decis1=0;decis2=0;
elseif(c01==c_max)
decis1=0;decis2=1;
elseif(c10==c_max)
decis1=1;decis2=0;
else
decis1=1;decis2=1;
end;
symbolerror=0;
if(decis1~=dsource1(i))
numofbiterror=numofbiterror+1;
symbolerror=1;
end;
if(decis2~=dsource2(i))
numofbiterror=numofbiterror+1;
symbolerror=1;
end;
if(symbolerror==1)
numofsymbolerror=numofsymbolerror+1;
end;
end;
ps=numofsymbolerror/N;
pb=numofbiterror/(2*N);

效果图：

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