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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