%%% 16-QAM Modulator and Demodulator Implementation with an AWGN Channel %%%
clc;
clear;
close all;
%%%% Input Signal %%%%
% Input is a stream of binary digits of integers 0-15
dec=[0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1];
dl=length(dec);
%%%% Serial To Parallel and 2-to-4 Level Converter %%%%
sp=[];
o1=[];
o2=[];
clear i;
for i=1:4:64;
sp=[dec(1,i:i+3)]; % Serial to Parallel 4-bit Register
I=sp(1,1); % Separation of I and Q bits
Id=sp(1,2);
Q=sp(1,3);
Qd=sp(1,4);
if I==0 % Assigning Amplitude levels for I-channel
if Id==0
o1=[o1 -3]; % if input is 00, output is -3
else
o1=[o1 -1]; % if input is 01, output is -1
end
else
if Id==0
o1=[o1 1]; % if input is 10, output is 1
else
o1=[o1 3]; % if input is 11, output is 3
end
end
if Q==0 % Assigning Amplitude levels for Q-channel
if Qd==0
o2=[o2 -3]; % if input is 00, output is -3
else
o2=[o2 -1]; % if input is 01, output is -1
end
else
if Qd==0
o2=[o2 1]; % if input is 10, output is 1
else
o2=[o2 3]; % if input is 11, output is 3
end
end
clear sp, clear I, clear Id, clear Q, clear Qd;
end
%%%% Oscillator and Balanced Modulator %%%%
fc=500; % Carrier Frequency
fs=20000; % Sampling Frequency
t=1:100; % Duration of Signal
s=[];
clear i;
for i=1:1:16; % Modulation (multiplication with carrier signals cos and sin)
Ac=o1(i);
As=o2(i);
s1=Ac*cos(2*pi*(fc/fs)*t);
s2=As*sin(2*pi*(fc/fs)*t);
s=[s (s1+s2)];
end
figure(1)
plot(s) % 's' demotes the transmitted signal
title('16-QAM Modulated Signal','FontSize',14)
Xlim([0 1610])
%%%% AWGN Addition While Passing Through The Channel %%%%
r=awgn(s,10); % Transmitted Signal passes through AWGN Channel
figure(2) % Received Signal SNR is 10 db
plot(r) % received signal is denoted by 'r'
title('Transmitted Signal With Additive Noise After Passing Through The Channel','FontSize',14);
%%%% COHERENT DEMODULATION %%%%
ss1=[];
ss2=[];
rs1=2*cos(2*pi*(fc/fs)*t); % Sin and Cos generation by Local Oscillator
rs2=2*sin(2*pi*(fc/fs)*t);
clear i;
for i=1:100:1600; % Demodulation of Received Signal
ss1=[ss1 rs1.*r(1,i:i+99)]; % for I-channel
ss2=[ss2 rs2.*r(1,i:i+99)]; % for Q-channel
end
%%%% Low-Pass Filtering %%%%
wn=2*(fc/fs); % Cut-off Frequency is 500Hz
[b1,a1]=butter(1,wn,'low'); % ButterWorth filter of Order 1
[b2,a2]=butter(1,wn,'low');
fo1=filter(b1,a1,ss1); % Filtering
fo2=filter(b2,a2,ss2);
figure(3);
plot(fo1,'linewidth',1.5)
title('I-Channel After Passing Through Low Pass ButterWorth Filter of Order 2','FontSize',14);
figure(4);
plot(fo2,'linewidth',1.5)
title('Q-Channel After Passing Through Low Pass ButterWorth Filter of Order 2','FontSize',14);
%%%% Thresholding and Phase Detection %%%%
ro1=[];
ro2=[];
clear i;
for i=1:100:1600; % Calculating Average values over an interval of 100 bits for I-channel
ff1=fo1(1,i:i+99);
l1=length(ff1);
sum1=sum(ff1);
av1=sum1/l1;
ro1=[ro1 av1];
end
clear i;
for i=1:100:1600; % Calculating Average values over an interval of 100 bits for Q-channel
ff2=fo2(1,i:i+99);
l2=length(ff2);
sum2=sum(ff2);
av2=sum2/l2;
ro2=[ro2 av2];
end
%%%% Amplitude Detection and Generation of Demodulated Data %%%%
oo1=round(ro1);
oo2=round(ro2);
op=[];
clear i;
% Re-assigning bits with respect to amplitude levels
for i=1:16; % Demodulation by Amplitude Detection
if oo1(i)==-3;
op=[op 0 0]; % if amplitude of I-channel is -3, output is 00
if oo2(i)==-3;
op=[op 0 0]; % if amplitude of Q-channel is -3 output is 00
else if oo2(i)==-1;
op=[op 0 1]; % if amplitude of Q-channel is -1 output is 01
else if oo2(i)==1;
op=[op 1 0]; % if amplitude of Q-channel is 1 output is 10
else
op=[op 1 1]; % if amplitude of Q-channel is 3 output is 11
end
end
end
else if oo1(i)==-1; % if amplitude of I-channel is -1, output is 01
op=[op 0 1];
if oo2(i)==-3;
op=[op 0 0]; % if amplitude of Q-channel is -3 output is 00
else if oo2(i)==-1;
op=[op 0 1]; % if amplitude of Q-channel is -1 output is 01
else if oo2(i)==1;
op=[op 1 0]; % if amplitude of Q-channel is 1 output is 10
else
op=[op 1 1]; % if amplitude of Q-channel is 3 output is 11
end
end
end
else if oo1(i)==1;
op=[op 1 0]; % if amplitude of I-channel is 1, output is 10
if oo2(i)==-3;
op=[op 0 0]; % if amplitude of Q-channel is -3 output is 00
else if oo2(i)==-1;
op=[op 0 1]; % if amplitude of Q-channel is -1 output is 01
else if oo2(i)==1;
op=[op 1 0]; % if amplitude of Q-channel is 1 output is 10
else
op=[op 1 1]; % if amplitude of Q-channel is 3 output is 11
end
end
end
else
op=[op 1 1]; % if amplitude of I-channel is 3, output is 11
if oo2(i)==-3;
op=[op 0 0]; % if amplitude of Q-channel is -3 output is 00
else if oo2(i)==-1;
op=[op 0 1]; % if amplitude of Q-channel is -1 output is 01
else if oo2(i)==1;
op=[op 1 0]; % if amplitude of Q-channel is 1 output is 10
else
op=[op 1 1]; % if amplitude of Q-channel is 3 output is 11
end
end
end
end
end
end
end
figure(5);
subplot(2,1,1);
plot(dec,'linewidth',2)
title('Input Data Stream','FontSize',14);
Xlim([0 65])
Ylim([-0.5 1.5])
subplot(2,1,2);
plot(op,'linewidth',2)
title('Demodulated Output Data (Same As Input)','FontSize',14);
Ylim([-0.5 1.5])
Xlim([0 65])
%%%% Generation of Constellation Diagram For Transmitted Data and Received Data%%%%
xo1=o1;
yo2=o2;
xoo1=ro1;
yoo2=ro2;
figure(6);
plot(xo1,yo2,'hk','linewidth',4); % plot of original symbols
hold on
plot(xoo1,yoo2,'Or','linewidth',4); % plot of received symbols
legend('= Transmitted Data','= Received Data');
x=line([-5 5],[-2 -2],'linewidth',4); % Horizontal Lines on Constellation Diagram
text(-1.9,3.7,'x=-2','FontSize',14)
x1=line([-5 5],[0 0],'linewidth',4);
text(0.1,3.7,'x=0','FontSize',14)
x2=line([-5 5],[2 2],'linewidth',4);
text(2.1,3.7,'x=2','FontSize',14)
y=line([-2 -2],[-15 15],'linewidth',4); % Vertical Lines on Constellation Diagram
text(-3.9,-1.8,'y=-2','FontSize',14)
y1=line([0 0],[-15 15],'linewidth',4);
text(-3.9,0.2,'y=0','FontSize',14)
y2=line([2 2],[-15 15],'linewidth',4);
text(-3.9,2.2,'y=2','FontSize',14)
title('Constellation Diagram for Transmitted and Received Data','FontSize',14);
Xlim([-4 4])
Ylim([-4 4])
