Clock Synchronization

In this chapter we have seen that a popular implementation of the
optimal receiver makes use of matched filters and samplers at the matched filter output.
In all these cases we assumed that the receiver has complete knowledge of the
sampling instant and can sample perfectly at this time. Systems that achieve this type

A simple implementation of clock synchronization employs an early-late gate.

Summary

Matlab Coding

 1 % MATLAB script for Illustrative Problem 7.14
 
.
 2 echo on
 3 alpha=0.4;
 4 T=1/4800;
 5 t=[-3*T:1.001*T/100:3*T];
 6 x=sinc(t./T).*(cos(pi*alpha*t./T)./(1-4*alpha^2*t.^2/T^2));
 7 pause % Press any key to see a plot of x(t).
 8 plot(t,x)

 9 y=xcorr(x);
10 ty=[t-3*T,t(2:length(t))+3*T];
11 pause % Press any key to see a plot of the autocorrelation of x(t).
 
12 plot(ty,y);

13 d=60;                   % Early and late advance and delay
14 ee=0.01;                % Precision
15 e=1;                    % Step size
16 n=700;                  % The incorrect sampling time
17 while abs(abs(y(n+d))-abs(y(n-d)))>=ee
18     if abs(y(n+d))-abs(y(n-d))>0
19         n=n+e;
20     elseif abs(y(n+d))-abs(y(n-d))<0
21         n=n-e;
22     end
23     echo off ;
24 end
25 echo on ;
26 pause % Press any key to see the corrected sampling time
27 n　　

n =

600

28 n=500;                  % Another incorrect sampling time
29 while abs(abs(y(n+d))-abs(y(n-d)))>=ee
30     if abs(y(n+d))-abs(y(n-d))>0
31         n=n+e;
32     elseif abs(y(n+d))-abs(y(n-d))<0
33         n=n-e;
34     end 
35     echo off ;
36 end
37 echo on ;
38 pause % Press any key to see the corrected sampling time
39 n

n =

600

In both cases the early-late gate corrects the sampling time to the optimum 600.

Reference,

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