%%% QPSK PLL
clear all;
close all;
% loop parameters
% digital bandwidth, theta_0 = w_0*T/2
% damping factor, eta = sqrt(2)/2
theta_0=2*pi/1000;
eta = 1;
k_i=(4*theta_0*theta_0)/(1+2*eta*theta_0+theta_0*theta_0);
k_p=(4*eta*theta_0)/(1+2*eta*theta_0+theta_0*theta_0);
% at the transimitter
n_dat=5000;
x1=(floor(2*rand(1,n_dat))-0.5)/0.5+j*((floor(2*rand(1,n_dat))-0.5)/0.5);
x2=reshape([x1;zeros(3,n_dat)],1,4*n_dat);
h=rcosine(1,4,'sqrt',0.5,6);
h=h/max(h);
x3=filter(h,1,x2);
% Channel
x3_ch = x3.*exp(j*0.3);
plot(x3_ch(1:4:4*n_dat),'rx') %% rotate the constellation
hold off
axis('square')
grid on
% Receiver
phi_2_save=zeros(1,4*n_dat);
int_1_save=zeros(1,4*n_dat);
int_2_save=zeros(1,4*n_dat);
dphi_sv=zeros(1,4*n_dat);
int_1=0;
int_2=0;
SCL=h*h';
gg = h/SCL;
reg1 = zeros(1,length(gg)); % MF reg
reg2 = zeros(1,4);
for n = 1:4*n_dat
prod(n) = x3_ch(n)*exp(-j*int_2); % compute one input, high rate
reg1 = [prod(n) reg1(1:length(gg)-1)];
MF_out(n) = reg1*gg';
if (mod(n,4)==1)
det_out(ceil(n/4)) = conj(MF_out(n))*(sign(real(MF_out(n)))+j*sign(imag(MF_out(n)))); % slicer output (Angle difference)
ATN(ceil(n/4)) = -atan(imag(det_out(ceil(n/4)))/real(det_out(ceil(n/4))));
% loop filter
int_1 = int_1 + k_i*ATN(ceil(n/4));
int_1_save(ceil(n/4)) = int_1;
dphi = k_p*ATN(ceil(n/4))+int_1;
dphi_sv(ceil(n/4)) = dphi;
% hold for 4 samples
reg2 = dphi.*ones(1,4);
% dss
phi_2_save(n) = int_2;
int_2 = int_2 + reg2(1);
end
if(mod(n,4)==2)
phi_2_save(n) = int_2;
int_2 = int_2 + reg2(2);
end
if(mod(n,4)==3)
phi_2_save(n) = int_2;
int_2 = int_2 + reg2(3);
end
if(mod(n,4)==0)
phi_2_save(n) = int_2;
int_2 = int_2 + reg2(4);
end
end
x4 = filter(h/SCL,1,x3_ch); % if no PLL
output = MF_out(1:4:4*n_dat); % final output
figure
subplot(221)
plot(x3_ch(1:4:4*n_dat),'rx')
title('Received Signal Constellation')
grid on
axis('square')
subplot(222)
plot(x4(1:4:4*n_dat),'rx')
grid on
axis('square') % constellation if without PLL
title('Matched Filter Ouput without PLL')
subplot(223)
plot(output(1:1000),'rx') % first 100 samples of the output
grid on
axis('square')
title('First 500 Samples from MF with PLL')
subplot(224)
plot(output(2000:5000),'rx') % 2000th - 5000th sample of the output
grid on
axis('square')
title('The Rest Ouput from MF')
figure
subplot(2,1,2)
plot(phi_2_save(1:3000))
grid on
axis([-20 2500 -0.1 0.45])
title('Output of The Phase Accumulator')
subplot(2,1,1)
plot(dphi_sv(1:200))
grid on
axis([-5 200 -0.025 0.025])
title('Output of The Loop Filter')
