CCS

Use of a Cyclic Prefix to Eliminate Channel Dispersion

In this section, we consider a method to mitigate channel dispersion.

 

 

 

Matlab Coding

 https://www.cnblogs.com/zzyzz/p/13702307.html

% MATLAB script for Illustrative Problem 8.4

echo on
clear;
K=10;N=2*K;T=100;m=4;
a=rand(1,36);
a=sign(a-0.5); 
b=reshape(a,9,4);

% Generate the 16QAM points
XXX=2*b(:,1)+b(:,2)+1i*(2*b(:,3)+b(:,4));
XX=XXX';
X=[0 XX 0 conj(XX(9:-1:1))];
xt=zeros(1,101);
for t=0:100
    for k=0:N-1
        xt(1,t+1)=xt(1,t+1)+1/sqrt(N)*X(k+1)*exp(1i*2*pi*k*t/T);
        echo off
    end
end
echo on
xn=zeros(1,N+m);
for n=0:N-1
    for k=0:N-1
        xn(n+m+1)=xn(n+1)+1/sqrt(N)*X(k+1)*exp(1i*2*pi*n*k/N);
        echo off
    end
end
   xn0 = xn;
xn(1:m)=xn(N-m+1:N);    % Cycle Shift
echo on

pause % press any key to see a plot of x(t)
plot([0:100],abs(xt))
% Check the difference between xn and samples of x(t)
for n=0:N-1
    d(n+1)=xt(T/N*n+1)-xn(1+n+m);
    echo off
end
echo on
e=norm(d);
Y=zeros(1,10);
for k=1:9
    for n=0:N-1
        Y(1,k+1)=Y(1,k+1)+1/sqrt(N)*xn(n+m+1)*exp(-1i*2*pi*k*n/N);
        echo off
    end
end
echo on
dd=Y(1:10)-X(1:10);
ee=norm(dd);


Simulation Result

>> xn0

xn0 =

Columns 1 through 6

0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.6708 - 0.2236i -0.7071 - 0.0054i

Columns 7 through 12

-0.6741 + 0.2134i -0.5752 + 0.4113i -1.0908 + 0.3453i -0.9307 + 0.6655i -0.6795 + 0.9205i -0.3618 + 1.0854i

Columns 13 through 18

-0.6795 + 0.9205i -0.3618 + 1.0854i -0.0087 + 1.1441i 0.3453 + 1.0908i -0.0054 + 0.7071i 0.2134 + 0.6741i

Columns 19 through 24

0.4113 + 0.5752i 0.5689 + 0.4200i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i

>> xn

xn =

Columns 1 through 6

-0.0054 + 0.7071i 0.2134 + 0.6741i 0.4113 + 0.5752i 0.5689 + 0.4200i -0.6708 - 0.2236i -0.7071 - 0.0054i

Columns 7 through 12

-0.6741 + 0.2134i -0.5752 + 0.4113i -1.0908 + 0.3453i -0.9307 + 0.6655i -0.6795 + 0.9205i -0.3618 + 1.0854i

Columns 13 through 18

-0.6795 + 0.9205i -0.3618 + 1.0854i -0.0087 + 1.1441i 0.3453 + 1.0908i -0.0054 + 0.7071i 0.2134 + 0.6741i

Columns 19 through 24

0.4113 + 0.5752i 0.5689 + 0.4200i -0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i

>> e

e =

11.6719

>> ee

ee =

8.1777

Reference,

　　1. <<Contemporary Communication System using MATLAB>> - John G. Proakis