数字通信大作业.docx
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数字通信大作业.docx
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数字通信大作业
大作业2
一.题目:
线性均衡器设计研究
假设带限信道模型如下:
0.000+j0.000,0.0485+j0.0194,0.0573+j0.0253,
0.0786+j0.0282,0.0874+j0.0447,0.9222+j0.03031,
F=0.1427+j0.0349,0.0835+j0.0157,0.0621+j0.0078,
0.0359+j0.0049,0.0214+j0.0019
1.研究信道的幅度谱|F(ejwT)|(单位dB),画出频谱图。
2.设计K=1(2K+1=3)及K=10(2K+1=21)的MMSE均衡器。
3.设计K=1(2K+1=3)及K=10(2K+1=21)的ZF均衡器。
4.画出以上均衡器的频谱图,|C(ejwT)|及等效信道谱|F(ejwT)C(ejwT)|。
5.分析总结。
2.具体解决步骤如下:
1:
研究信道的幅度谱
(单位
),画出频谱图。
若要了解离散信号的频谱特征,首先要对离散信号进行傅里叶变换或者是Z变换。
在Z变换中,单位圆上的结果则对应傅里叶变换的结果,即
。
而要得到信道的频谱图,首先要对序列
进行Z变换,得到
。
MATLAB仿真程序:
f=[0.0000+j*0.0000,0.0485+j*0.0194,0.0573+j*0.0253,0.0786+j*0.0282,0.0874+j*0.0447,0.9222+j*0.0301,0.1427+j*0.0349,0.0835+j*0.0157,0.0621+j*0.0078,0.0359+j*0.0049,0.0214+j*0.0019];
f1=0;
forn=1:
11
f1=f(n)*f(n)+f1;
end
b=sqrt(f1);
f=f/b;
w=-3:
2*pi/255:
3;
T=1;
x=0;
form=1:
11
x=x+f(m)*exp(-j*m*w*T);
end
x=10*log10(abs(x));
figure;
plot(w*T,x);
xlabel('\omegaT');
ylabel('10log10|F(e^{j\omega})|(dB)');
title('信道的幅度谱');
gridon
运行的结果如下图:
2:
设计k=1(2k+1=3)及k=10(2k+1=21)的ZF(迫零)均衡器。
(1)根据算法
可以求出所需的抽头系数。
(2)3抽头ZF
clear;
clc;
fs=100;
N=1024;
n=0:
N-1;
t=n/fs;
F3=[0.9222+j*0.030310.0874+j*0.04470.0786+j*0.0282;
0.1427+j*0.03490.9222+j*0.030310.0874+j*0.0447;
0.0835+j*0.01570.1427+j*0.03490.9222+j*0.03031];
q3=[0;1;0];
M=inv(F3);%逆方阵
Cop3=M*q3;
H=[0.0000+j*0.00000.0485+j*0.01940.0573+j*0.02530.0786+j*0.02820.0847+j*0.04470.9222+j*0.030310.1427+j*0.03490.0835+j*0.01570.0621+j*0.00780.0359+j*0.00490.0214+j*0.0019];
ht=conv(H,Cop3);
y=fft(ht,N);%快速傅里叶变换
yy=abs(y);%取绝对值
x3=10*log10(yy);
f=n*fs/N;
plot(f,x3);
xlabel('频率');
ylabel('振幅');
(3)21抽头ZF
clear;
clc;
fs=100;
N=512;
n=0:
N-1;
%21抽头ZF
F21=toeplitz([0.9222+j*0.030310.1427+j*0.03490.0835+j*0.01570.0621+j*0.00780.0359+j*0.00490.0214+j*0.0019000000000000000],
[0.9222+j*0.030310.0874+j*0.04470.0786+j*0.02820.0573+j*0.02530.0485+j*0.01940.0000+j*0.0000000000000000000]);
q21=[0;0;0;0;0;0;0;0;0;0;1;0;0;0;0;0;0;0;0;0;0];
M=inv(F21);
Cop21=M*q21;
H=[0.0000+j*0.00000.0485+j*0.01940.0573+j*0.02530.0786+j*0.02820.0847+j*0.04470.9222+j*0.030310.1427+j*0.03490.0835+j*0.01570.0621+j*0.00780.0359+j*0.00490.0214+j*0.0019]
ht=conv(H,Cop21);%卷积
y=fft(ht([6:
26]),N);
yy=abs(y);
x21=10*log10(yy);
f=n*fs/N;
plot(f,x21);
xlabel('频率');
ylabel('振幅');
3:
设计k=1(2k+1=3)及k=10(2k+1=21)的MMSE(最小均方误差)均衡器。
(1)3抽头均衡器
clear;
clc;
fs=100;N=1024;
n=0:
N-1;
a=[0.00000.04850.05730.07860.08740.92220.14270.08350.06210.03590.0214];
b=[0.00000.01940.02530.02820.04470.03030.03490.01570.00780.00490.0019];
x=a+j*b;
h1=conj(x(5));
h2=conj(x(6));
h3=conj(x(7));
q=[h1;h2;h3];
m=conv(conj(x),fliplr(x));%fliplr翻转矩阵
F=toeplitz([m(11)m(12)m(13)],[m(11)m(12)m(13)]);%托普利兹矩阵
F3=F;
Cop3=inv(F3)*q;
H=[0.0000+j*0.00000.0485+j*0.01940.0573+j*0.02530.0786+j*0.02820.0847+j*0.04470.9222+j*0.030310.1427+j*0.03490.0835+j*0.01570.0621+j*0.00780.0359+j*0.00490.0214+j*0.0019];
hr=conv(H,Cop3);
y=fft(Cop3,N);
yy=abs(y);
h=10*log10(yy);
y1=fft(hr,N);
yy1=abs(y1);
h1=10*log10(yy1);
f=n*fs/N;
plot(f,h);
holdon;
plot(f,h1);
xlabel('频率');
ylabel('振幅')
(2)21抽头均衡器
clear;
clc;
fs=100;N=1024;
n=0:
N-1;
N0=0;
a=[0.00000.04850.05730.07860.08740.92220.14270.08350.06210.03590.0214];
b=[0.00000.01940.02530.02820.04470.03030.03490.01570.00780.00490.0019];
x=a+j*b;
q=[0;0;0;0;0;conj(x(11));conj(x(10));conj(x(9));conj(x(8));conj(x(7));conj(x(6));conj(x(5));conj(x(4));conj(x(3));conj(x
(2));conj(x
(1));0;0;0;0;0];
m=conv(conj(x),fliplr(x));
F=toeplitz([m(11)m(10)m(9)m(8)m(7)m(6)m(5)m(4)m(3)m
(2)m
(1)0000000000],[m(11)m(10)m(9)m(8)m(7)m(6)m(5)m(4)m(3)m
(2)m
(1)0000000000]);
F21=F+N0*eye(21);
Cop21=inv(F21)*q;
H=[0.0000+j*0.00000.0485+j*0.01940.0573+j*0.02530.0786+j*0.02820.0847+j*0.04470.9222+j*0.030310.1427+j*0.03490.0835+j*0.01570.0621+j*0.00780.0359+j*0.00490.0214+j*0.0019];
hr=conv(H,Cop21);
y=fft(Cop21,N);
yy=abs(y);
h=10*log10(yy);
y1=fft(hr,N);
yy1=abs(y1);
h1=10*log10(yy1);
f=n*fs/N;
plot(f,h);
holdon;
plot(f,h1);
xlabel('频率');
ylabel('振幅')
3.等效信道谱
求等效信道谱:
由信道求出均衡器的系数,再将f卷积C3可以得到等效的系统,同样将f卷积c21可以得到另一个等效系统。
1、当c=3时,等效信道的幅度谱,MATLAB仿真程序:
clear;
clc;
F3=[0.9222+j*0.030310.0874+j*0.04470.0786+j*0.0282;
0.1427+j*0.03490.9222+j*0.030310.0874+j*0.0447;
0.0835+j*0.01570.1427+j*0.03490.9222+j*0.03031];
q3=[0;1;0];
c3=F3\q3;
c1=0;
fork=1:
3
c1=c3(k)*c3(k)+c1;
end
d=sqrt(c1);
c3=c3/d;
f=[0.0000+j*0.0000,0.0485+j*0.0194,0.0573+j*0.0253,0.0786+j*0.0282,0.0874+j*0.0447,0.9222+j*0.0301,0.1427+j*0.0349,0.0835+j*0.0157,0.0621+j*0.0078,0.0359+j*0.0049,0.0214+j*0.0019];
f1=0;
form=1:
11
f1=f(m)*f(m)+f1;
end
b=sqrt(f1);
f=f/b;
y=conv(c3,f);
w=-3:
2*pi/255:
3;
T=1;
z=0;
fork=1:
length(y)
z=z+y(k)*exp(-j*k*w*T);
end
z=10*log10(abs(z));
figure
plot(w*T,z);
xlabel('\omegaT');
ylabel('10log10|F(e^{j\omega})*C(e^{j\omega})|(dB)');
title('3抽头信道均衡的等效信道幅度谱');
gridon
运行的结果如下图:
2、当c=21时,等效信道的幅度谱,MATLAB仿真程序:
F21=[0.9222+j*0.02102110.0874+j*0.04470.0786+j*0.02820.05721+j*0.025210.0485+j*0.01940.0000+j*0.0000000000000000000;
0.1427+j*0.021490.9222+j*0.02102110.0874+j*0.04470.0786+j*0.02820.05721+j*0.025210.0485+j*0.01940.0000+j*0.000000000000000000;
0.08215+j*0.01570.1427+j*0.021490.9222+j*0.02102110.0874+j*0.04470.0786+j*0.02820.05721+j*0.025210.0485+j*0.01940.0000+j*0.00000000000000000;
0.0621+j*0.00780.08215+j*0.01570.1427+j*0.021490.9222+j*0.02102110.0874+j*0.04470.0786+j*0.02820.05721+j*0.025210.0485+j*0.01940.0000+j*0.0000000000000000;
0.02159+j*0.00490.0621+j*0.00780.08215+j*0.01570.1427+j*0.021490.9222+j*0.02102110.0874+j*0.04470.0786+j*0.02820.05721+j*0.025210.0485+j*0.01940.0000+j*0.000000000000000;
0.0214+j*0.00190.02159+j*0.00490.0621+j*0.00780.08215+j*0.01570.1427+j*0.021490.9222+j*0.02102110.0874+j*0.04470.0786+j*0.02820.05721+j*0.025210.0485+j*0.01940.0000+j*0.00000000000000;
00.0214+j*0.00190.02159+j*0.00490.0621+j*0.00780.08215+j*0.01570.1427+j*0.021490.9222+j*0.02102110.0874+j*0.04470.0786+j*0.02820.05721+j*0.025210.0485+j*0.01940.0000+j*0.0000000000000;
000.0214+j*0.00190.02159+j*0.00490.0621+j*0.00780.08215+j*0.01570.1427+j*0.021490.9222+j*0.02102110.0874+j*0.04470.0786+j*0.02820.05721+j*0.025210.0485+j*0.01940.0000+j*0.000000000000;
0000.0214+j*0.00190.02159+j*0.00490.0621+j*0.00780.08215+j*0.01570.1427+j*0.021490.9222+j*0.02102110.0874+j*0.04470.0786+j*0.02820.05721+j*0.025210.0485+j*0.01940.0000+j*0.00000000000;
00000.0214+j*0.00190.02159+j*0.00490.0621+j*0.00780.08215+j*0.01570.1427+j*0.021490.9222+j*0.02102110.0874+j*0.04470.0786+j*0.02820.05721+j*0.025210.0485+j*0.01940.0000+j*0.0000000000;
000000.0214+j*0.00190.02159+j*0.00490.0621+j*0.00780.08215+j*0.01570.1427+j*0.021490.9222+j*0.02102110.0874+j*0.04470.0786+j*0.02820.05721+j*0.025210.0485+j*0.01940.0000+j*0.000000000;
0000000.0214+j*0.00190.02159+j*0.00490.0621+j*0.00780.08215+j*0.01570.1427+j*0.021490.9222+j*0.02102110.0874+j*0.04470.0786+j*0.02820.05721+j*0.025210.0485+j*0.01940.0000+j*0.00000000;
00000000.0214+j*0.00190.02159+j*0.00490.0621+j*0.00780.08215+j*0.01570.1427+j*0.021490.9222+j*0.02102110.0874+j*0.04470.0786+j*0.02820.05721+j*0.025210.0485+j*0.01940.0000+j*0.0000000;
000000000.0214+j*0.00190.02159+j*0.00490.0621+j*0.00780.08215+j*0.01570.1427+j*0.021490.9222+j*0.02102110.0874+j*0.04470.0786+j*0.02820.05721+j*0.025210.0485+j*0.01940.0000+j*0.000000;
0000000000.0214+j*0.00190.02159+j*0.00490.0621+j*0.00780.08215+j*0.01570.1427+j*0.021490.9222+j*0.02102110.0874+j*0.04470.0786+j*0.02820.05721+j*0.025210.0485+j*0.01940.0000+j*0.00000;
00000000000.0214+j*0.00190.02159+j*0.00490.0621+j*0.00780.08215+j*0.01570.1427+j*0.021490.9222+j*0.02102110.0874+j*0.04470.0786+j*0.02820.05721+j*0.025210.0485+j*0.01940.0000+j*0.0000;
000000000000.0214+j*0.00190.02159+j*0.00490.0621+j*0.00780.08215+j*0.01570.1427+j*0.021490.9222+j*0.02102110.0874+j*0.04470.0786+j*0.02820.05721+j*0.025210.0485+j*0.0194;
0000000000000.0214+j*0.00190.02159+j*0.00490.0621+j*0.00780.08215+j*0.01570.1427+j*0.021490.9222+j*0.02102110.0874+j*0.04470.0786+j*0.02820.05721+j*0.02521;
00000000000000.0214+j*0.00190.02159+j*0.00490.0621+j*0.00780.08215+j*0.01570.1427+j*0.021490.9222+j*0.02102110.0874+j*0.04470.0786+j*0.0282;
000000000000000.0214+j*0.00190.02159+j*0.00490.0621+j*0.00780.08215+j*0.01570.1427+j*0.021490.9222+j*0.02102110.0874+j*0.0447;
0000000000000000.0214+j*0.00190.02159+j*0.00490.0621+j*0.00780.08215+j*0.01570.1427+j*0.021490.9222+j*0.0210211];
q21=[0;0;0;0;0;0;0;0;0;0;1;0;0;0;0;0;0;0;0;0;0];
c21=F21\q21;
c1=0;
fork=1:
21;
c1=c21(k)*conj(c21(k))+c1;%conj求复共轭
end
d=sqrt(c1);
c21=c21/d;
f=[0.0000+j*0.0000,0.0485+j*0.0194,0.0573+j*0.0253,0.0786+j*0.0282,0.0874+j*0.0447,0.9222+j*0.0301,0.1427+j*0.0349,0.0835+j*0.0157,0.0621+j*0.0078,0.0359+j*0.0049,0.0214+j*0.0019];
f1=0;
form=1:
11
f1=f(m)*f(m)+f1;
end
b=sqrt(f1);
f=f/b;
y=conv(c21,f);
w=-1:
2*pi/255:
1;
T=1;
z=0;
fork=1:
length(y)
z=z+y(k)*exp(-j*k*w*T);
end
y=10*log10(abs(z));
figure
plot(w*T,y)
xlabel('\omegaT');
ylabel('10log10|F(e^{j\omega})*C(e^{j\omega})|(dB)');
title('21抽头等效信道均衡的幅度谱');
gridon
运行的结果如下图:
四:
结论
1.对于同种均衡器下不同抽头数的比较发现:
抽头数越大,计算精度越高。
2.对于不同均衡器的比较发现:
在相同信噪比的条件下MMSE均衡器相较与迫零均衡器而言能更加有效的改善码间干扰,提高基带传输的有效性。
但是在克服严重的码间干扰方面具有很大的局限性。
3.对于不同系数下的等效信道谱比较得知:
抽头数越大,信道谱越平缓,波动性越小,精确度越高。
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