Bit Error rate of QAM

PONDICHERRY UNIVERSITY
DEPARTMENT OF ELECTRONICS
AND COMMUNICATION
ENGINEERING
QUADRATURE AMPLITUDE MODULATION (QAM)
GUIDED BY:
PROF. DR. P. SAMUNDISWARY
PRESENTED BY
AWANISH KUMAR
(21304006)

CONTENTS
❖ OBJECTIVE
❖ INTRODUCTION
❖ QUADRATURE AMPLITUDE MODULATION
❖ QAM WORKING Principle
❖ BLOCK DIAGRAM
❖ CONSTELLATION DIAGRAM
❖ ADVANTAGES AND DISADVANTAGES
❖ CODE
❖ CONCLUSION

OBJECTIVE
The main objective of the system is achieved through the analysis
of Bit Error Rate performance of M-QAM modulation techniques
over Gaussian fading channel.
Due to the faded environment the results which obtained clearly
indicate that out of three QAM which considered in the analysis
16-QAM gave better results on Gaussian and Rayleigh fading
channel.
The performance of Bit error rate will improve by using effective
suitable channel coding techniques over faded environment.

INTRODUCTION
Quadrature Amplitude Modulation or QAM is a form of modulation
which is widely used for modulating data signals onto a carrier used
for radio communications. It is widely used because it offers
advantages over other forms of data modulation such as PSK,
although many forms of data modulation operate along side each
other.
Quadrature Amplitude Modulation, QAM is a signal in which two
carriers shifted in phase by 90 degrees are modulated and the
resultant output consists of both amplitude and phase variations. In
view of the fact that both amplitude and phase variations are present
it may also be considered as a mixture of amplitude and phase
modulation.

What is QAM, quadrature amplitude modulation
•Quadrature Amplitude Modulation, QAM is a signal in which two
carriers shifted in phase by 90 degrees (i.e. sine and cosine) are
modulated and combined. As a result of their 90° phase
difference they are in quadrature and this gives rise to the name.
Often one signal is called the In-phase or “I” signal, and the other
is the quadrature or “Q” signal.
•The resultant overall signal consisting of the combination of both
I and Q carriers contains of both amplitude and phase variations.
In view of the fact that both amplitude and phase variations are
present it may also be considered as a mixture of amplitude and
phase modulation.

QAM Working Principle
QAM Modulator
•In the QAM transmitter, the above
section i.e., product modulator1 and
local oscillator are called the
in-phase channel and product
modulator2 and local oscillator are
called a quadrature channel. Both
output signals of the in-phase
channel and quadrature channel are
summed so the resultant output will
be QAM.”

➢ QAM Demodulator
At the receiver level, the QAM
signal is forwarded from the
upper channel of receiver and
lower channel, and the
resultant signals of product
modulators are forwarded from
LPF1 and LPF2.
These LPF’s are fixed to the
cut off frequencies of input 1
and input 2 signals. Then the
filtered outputs are the
recovered original signals.

● One signal is called the in-phase “I”
signal, and the other is called the
quadrature “Q” signal. Mathematically,
one of the carrier signals can be
represented by a sine wave (i.e. sin(wt))
and the other can be represented by a
cosine wave (i.e.cos(wt) ).
● The two modulated carrier signals are
transmitted together at the source and
at the destination, these two carrier
signals are demodulated (i.e. separated)
independently. To demodulate the signal
coherent detection method is used.

CONSTELLATION DIAGRAM
• The constellation diagram is useful for
QAM. In QAM, the constellation points are
usually arranged in a square grid with
equal vertical and horizontal spacing.
• In digital telecommunication the data is
usually binary, so the number of points in
the grid is typically a power of 2 (2, 4, 8,
…), corresponding to the number of bits
per symbol. The simplest and most
commonly used QAM constellations
consist of points arranged in a square, i.e.
16-QAM, 64-QAM and 256-QAM (even
powers of two)

The BER of M-ary QAM signals
•Eb and N0 are the energy and
noise power per bit.
•for M = 16, 64, 256, and 1024

Advantages of QAM
•One of the best advantages of QAM – supports a high data rate.
So, the number of bits can be carried by the carrier signal.
Because of these advantages it preferable in wireless
communication networks.
•QAM’s noise immunity is very high. Due to this noise
interference is very less.
•It has a low probability of error value.
•QAM expertly uses channel bandwidth.

Disadvantages of QAM
● In QAM, amplitude changes are susceptible to noise.
● It is not necessary to use of linear amplifier in a radio transmitter
when a phase or frequency modulated.
● It is possible to transmit more bits per symbol but in higher-order
QAM formats the constellation points are closely spaced which is
more susceptible to noise and produces errors in the data.
● Also in higher-order QAM formats, there is a difficulty for the
receiver to decode the signal appropriately. In other words, there is
reduced noise immunity.
● So the higher-order QAM formats are only used when there is a high
signal to noise ratio

● QAM technique is widely used in the radio communications field
because of the increase of the bit data rate.
● QAM is used in applications ranging from short-range wireless
communications to long-distance telephone systems.
● QAM is used in microwave and telecommunication systems to
transmit the information.
● The 64 QAM and 256 QAM are used in digital cable television and
cable modem.
● QAM is used in optical fiber systems to increase bit rates. It is
used in many communication systems like Wi-Fi, Digital Video
Broadcast (DVB), and WiMAX.
APPLICATIONS OF QAM

CODE (16-QAM)
clc;
clear;
M = 16;
K = log2(M);
N = 30000; % number of symbols
alpha16qam = [-3 -1 1 3]; % 16-QAM alphabets
Es_N0_dB = [0:20]; % multiple Es/N0 values
ipHat = zeros(1,N);
for ii = 1:length(Es_N0_dB)
ip = randsrc(1,N,alpha16qam) +
j*randsrc(1,N,alpha16qam);
s = (1/sqrt(10))*ip; % normalization of energy to 1
n = 1/sqrt(2)*[randn(1,N) + j*randn(1,N)]; % white
guassian noise, 0dB variance
y = s + 10^(-Es_N0_dB(ii)/20)*n; % additive white
gaussian noise
% demodulation

y_re = real(y); % real part
y_im = imag(y); % imaginary part
ipHat_re(find(y_re< -2/sqrt(10))) = -3;
ipHat_re(find(y_re > 2/sqrt(10))) = 3;
ipHat_re(find(y_re>-2/sqrt(10) & y_re<=0)) = -1;
ipHat_re(find(y_re>0 & y_re<=2/sqrt(10))) = 1;
ipHat_im(find(y_im< -2/sqrt(10))) = -3;
ipHat_im(find(y_im > 2/sqrt(10))) = 3;
ipHat_im(find(y_im>-2/sqrt(10) & y_im<=0)) = -1;
ipHat_im(find(y_im>0 & y_im<=2/sqrt(10))) = 1;
ipHat = ipHat_re + j*ipHat_im;
nErr(ii) = size(find([ip- ipHat]),2); % couting the
number of errors
end

simBer = nErr/N;
theoryBer = 3/2*erfc(sqrt(0.1*(10.^(Es_N0_dB/10))));
close all
figure
semilogy(Es_N0_dB,theoryBer,'b.-','LineWidth',2);
hold on
semilogy(Es_N0_dB,simBer,'mx-','Linewidth',2);
axis([0 20 10^-5 1])
grid on
legend('theory', 'simulation');
xlabel('Es/No, dB')
ylabel('Symbol Error Rate')
title('Symbol error probability curve for 16-QAM
modulation')

Bit Error Rate plot for 16QAM modulation

CONCLUSION
From the simulation we can conclude (expected from the theory)
that as Eb/N0 increased (so SNR increased), BER reduced.
Interference typically increases when we are moving to a higher
order QAM constellation (more constellation points, higher data
rate and mode)

REFERENCES
● J. G. Proakis, Digital Communications, New York, NY, McGrawHill,
2001.
● B. Sklar, Digital Communications - Fundamentals and Applications,
Prentice Hall, New Jersey, 2001.

Bit Error rate of QAM

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