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信道频谱及线性均衡器设计.docx

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信道频谱及线性均衡器设计.docx

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信道频谱及线性均衡器设计.docx

信道频谱及线性均衡器设计

基于下图所示的信道模型

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]

一，研究信道的幅度谱

（单位

）,画出频谱图。

二，设计k=1（2k+1=3）及k=10（2k+1=21）的迫零均衡器。

三，画出以上均衡器的频谱图

以及等效信道谱

。

四，采用蒙特卡洛方法，仿真研究无均衡器，采用了3个抽头均衡器和21抽头均衡器情况下系统的符号错误率，系统采用QPSK调制。

一，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

。

（1）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：

二，设计k=1（2k+1=3）及k=10（2k+1=21）的迫零均衡器。

（1）根据算法

可以求出所需的抽头系数。

（2）MATLAB仿真程序

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

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）*c21（k）+c1;

end

d=sqrt（c1）;

c21=c21/d

运行的结果如下

c3=

-0.0834-0.0377i

0.9867-0.0071i

-0.1469-0.0266i

c21=

-0.0005-0.0004i

-0.0010-0.0014i

0.0010+0.0000i

0.0030+0.0016i

0.0074+0.0043i

0.0115+0.0097i

-0.0435-0.0120i

-0.0402-0.0122i

-0.0604-0.0129i

-0.0627-0.0323i

0.9837-0.0054i

-0.1321-0.0081i

-0.0569-0.0047i

-0.0427-0.0004i

-0.0009+0.0001i

-0.0131+0.0002i

0.0091+0.0012i

0.0021+0.0002i

0.0008-0.0001i

-0.0006-0.0001i

-0.0000-0.0001i

三、求c=3和c=21时均衡器的频谱图及等效信道谱。

（1）k=1时，求3抽头的系数的幅度谱，MATLAB仿真程序：

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）*conj（c3（k））+c1;

end

d=sqrt（c1）;

c3=c3/d;

w=-3:

2*pi/255:

3;

T=1;

x3=0;

fork=1:

3

x3=x3+c3（k）*exp（-j*k*w*T）;

end

x3=10*log10（abs（x3））;

figure;

plot（w*T,x3）;

xlabel（'\omegaT'）;

ylabel（'10log10|C（e^{j\omega}）|（dB）'）;

title（'3抽头均衡器的幅度谱'）;

gridon

运行的结果如下图：

（2）k=10时，求21抽头的系数的幅度谱，MATLAB仿真程序：