## Introduction

Quadrature Amplitude Modulation(QAM): Theory and Matlab

QAM stands for Quadrature Amplitude Modulation. It is a method of combining two amplitude-modulated (AM) signals into a single channel, thereby doubling the effective bandwidth. In telecommunications and signal processing, QAM is a method of mapping an analog signal, such as an audio or video signal, onto a digital signal for transmission.

The digital signal consists of a series of symbols, each of which represents a unique combination of the two amplitude-modulated signals. This allows the transmission of multiple bits of data in each symbol, which increases the data rate compared to simple amplitude modulation. QAM is widely used in digital television and cable television systems, as well as in digital communications systems such as Wi-Fi, Ethernet, and cable modems.

## QAM Modulator and Demodulator

In the context of QAM, a modulator is a device that takes an input digital or analog signal and maps it onto a QAM signal for transmission over a communication channel. The modulator performs amplitude modulation on two carriers that are 90 degrees out of phase with each other, resulting in a signal that carries both amplitude and phase information.

A demodulator, on the other hand, is a device that takes the received QAM signal and recovers the original data or message. The demodulator performs the inverse operation of the modulator, converting the QAM signal back into its original digital or analog form. This typically involves separating the two carriers and demodulating them separately, then combining the resulting signals to recover the original data.

The performance of a QAM system depends on the accuracy of the modulator and demodulator, as well as the quality of the communication channel. To minimize errors, the modulator and demodulator must be designed to have good signal-to-noise ratios and to be able to handle any phase or amplitude distortions that may occur in the channel. Additionally, the system may use error correction codes or other techniques to further improve the accuracy of the transmitted data.

**QAM Modulator:**

Input signal —-> Binary data mapping —-> Amplitude modulation of two carriers —-> QAM signal

**QAM Demodulator:**

Received QAM signal —-> Multiplication with two carriers —-> Integration —-> Demodulated signal

## Software Requirement

Matlab Software or Online Matlab

## Matlab Code Version 1

```
Fd=1;Fs=1;
nsamp=1;
M=32;
k = log2(M);
n = 30000;
x = randi([0 1],n,1);
stem(x(1:40),'filled');
title('Random Bits');
xlabel('Bit Index');
ylabel('Binary Value');
xsym = bi2de(reshape(x,k,length(x)/k).');
figure;
stem(xsym(1:10));
title('Random Symbols');
xlabel('Symbol Index');
ylabel('Integer Value');
y=qammod(xsym,M);
title('modulated');
xlabel('Symbol Index');
ylabel('Integer Value');
ytx = y;
stem(y(1:10));
EbNo=10;
snr = EbNo + 10*log10(k) - 10*log10(nsamp);
pinput=std(ytx);
noise = (randn(1,n/k)+sqrt(-1)*randn(1,n/k))*(1/sqrt(2));
Noisestd = (pinput*10^(-snr/20));
ynoisy = ytx + (Noisestd*noise);
yrx=ynoisy;
figure;
plot(real(yrx(1:5e3)),imag(yrx(1:5e3)),'b*');
hold on;
plot(real(ytx(1:5e3)),imag(ytx(1:5e3)),'y.');
title('Signal Constellation');
legend('Received Signal', 'Transmitted Signal');
axis([-5 5 -5 5]);
hold off;
```

## QAM Code Version 1 Output

## Matlab Code Version 2

```
clc;
clear all;
close all;
M=8;
N=12;
msg = round(rand(N,1));
disp('BInary input at transmitter:');
disp(msg);
Tb=0.000001;
x= msg;
bits=[];
for n=1:1:length(x)
if x(n)== 1 ;
sig=ones(1,100);
else x(n)==0 ;
sig=zeros(1,100);
end
bits = [bits sig];
end
t1 = Tb/100:Tb/100:100*length(x)*(Tb/100);
subplot(3,1,1);
plot(t1,bits,'linewidth',2.5);
grid on;
axis([0 Tb*length(x) -0.5 1.5]);
xlabel('Time(sec)');
ylabel('Amplitude(volts)');
title('Digital input signal');
msg_reshape=reshape(x,log2(M),N/log2(M))';
disp('Information is reshaped to convert into symbol form');
disp(msg_reshape);
fprintf('\n\n');
size(msg_reshape);
for j=1 : 1 : N/log2(M)
for i=1 :1 :log2(M)
a(j,i)=num2str(msg_reshape(j,i));
end
end
as=bin2dec(a);
ast=as';
subplot(3,1,2);
stem(ast,'Linewidth',2.0);
title('Serial synbol for 8-QAM modulation');
xlabel('n(discrete time)');
ylabel('Magnitude');
disp('Symbol form of information for 8-QAM');
disp(ast);
fprintf('\n\n');
%Mapping for 8-QAM modulation
p=qammod(ast,M);
scatterplot(p),grid on;
title('8-QAM constellation diagram');
%QAM Modulation
RR = real(p);
II = imag(p);
sp = Tb*2;
sr=1/sp;
f=sr*2;
t=sp/100:sp/100:sp;
ss=length(t);
m=[];
for k=1:1:length(RR)
yr=RR(k)*cos(2*pi*f*t);
yim=II(k)*sin(2*pi*f*t);
y=yr+yim;
m=[m y];
end
tt = sp/100:sp/100:sp*length(RR);
figure(1);
subplot(3,1,3);
plot(tt,m);
xlabel('Time(Sec)');
ylabel('Amplitude(volts)');
title('8-QAM Modulated signal');
```

## Output Version 2

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