CCS

Carrier Synchronization

Synchronization is a methods to generate sinusoids with the same frequency and phase of the carrier at the demodulator.

A carrier synchronization system consists of a local oscillator whose phase is controlled
to be in synch with the carrier signal. This is achieved by employing a PLL. A phaselocked
loop is a nonlinear feedback-control system for controlling the phase of the
local oscillator. In the following discussion, for simplicity we consider only binary PSK modulation systems.

 

 

 

 

 

 

Note, a simple first-order loop filter results in a PLL that can track jumps in the input phase.

Matlab Coding

% MATLAB script for Illustrative Problem 7.13.
echo on
num=[0.01 1];
den=[1 1.01 1];
[a,b,c,d]=tf2ss(num,den);
dt=0.01;
u=ones(1,2000);
x=zeros(2,2001);
for i=1:2000
    x(:,i+1)=x(:,i)+dt.*a*x(:,i)+dt.*b*u(i);
    y(i)=c*x(:,i);
    echo off;
end
echo on;
t=[0:dt:20];
plot(t(1:2000),y)

Simulation Result

As we can see from simulation, the output of the PLL eventually follows the input;
however, the speed by which it follows the input depends on the loop filter parameters
and K, the VCO proportionality constant.

Reference,

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