International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 5 – Sep 2014
OFDM using Chaotic Sequence for Adaptive
Modulation
Apurva Dubey#1, Prof. Gaurav Gupta*2, Vratika Mehta#3
1
Student ME(DC), Electronics & Communication, Mahakal Institute of Technology, Ujjain, India
Associate Professor, Electronics & Communication, Mahakal Institute of Technology, Ujjain, India
3
Student ME(DC), Electronics & Communication, Patel Group of Institute , Indore, India
2
Abstract- In a present scenario more and more people
started using the communication equipments, the
demand for high data rate increased quickly. So here
we are using OFDM systems that provide large data
rates with sufficient robustness to radio channel
impairments. In this we have used chaotic
communication in OFDM system for secure
communication and to improve system performance.
Also the adaptive modulation has been applied to the
sequence due to dynamic characteristics of the medium.
The different fading channels i.e. Rayleigh and Rician
in the presence of additive white Gaussian noise
(AWGN) to analyze the BER & SNR of the different
chaotic sequences. The performance of the modulation
technique is evaluated when the system is subjected to
noise and interference in the channel.
Index Terms—Chaotic Sequence, OFDM, Adaptive
Modulation, Fading channel
I. INTRODUCTION
The main feature of the next-generation wireless
systems will be the convergence of multi-media
services such as speech, audio, video, image, and
data. This implies that a future wireless terminal, by
guaranteeing high speed data, will be able to connect
to different networks in order to support various
services. As in present scenario the rapid increase in
the number of wireless mobile terminal subscribers,
which currently exceeds 3 billion users, highlights
the importance of wireless communications in this
new millennium. [3] In this paper we will see the
digital techniques used for wireless, as Digital band
pass modulation techniques can be broadly classified
into two categories. The first is single-carrier
modulation, where data is transmitted by using a
single radio frequency (RF) carrier. The other is
multicarrier modulation, where data is transmitted by
simultaneously modulating multiple RF carrier .But
here we are concerned with a particular type of multicarrier modulation known as orthogonal frequency
division multiplexing (OFDM). [1]
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A. BASIC OF OFDM
OFDM has gained popularity in a number of
applications including digital subscriber loops,
wireless local area networks. It is also a strong
contender for fourth generation cellular land mobile
radio systems. OFDM is attractive because it admits
relatively easy solutions to some difficult challenges
that are encountered when using single-carrier
modulation schemes on wireless channels. Simplified
frequency domain equalization is often touted as a
primary advantage of OFDM over single-carrier
modulation
with
conventional
time-domain
equalization. It is a special case of multicarrier
transmission was a single stream is transmitted over a
number of subcarrier.
B. BLOCK DIAGRAM OF OFDM SYSTEM
At the transmitter, the user information bit
sequence is first subjected to channel encoding to
reduce the probability of error at the receiver due to
the channel effects. Usually, convolution encoding is
preferred. Then the bits are mapped to symbols.
Usually, the bits are mapped into the symbols of
either 16-QAM or QPSK. The symbol sequence is
converted to parallel format and IFFT (OFDM
modulation) is applied and the sequence is once again
converted to the serial format. Guard time is provided
between the OFDM symbols and the guard time is
filled with the cyclic extension of the OFDM symbol.
Windowing is applied to the OFDM symbols to make
the fall-off rate of the spectrum steeper. The resulting
sequence is converted to an analog signal using a
DAC and passed on to the RF modulation stage. The
resulting RF modulated signal is, then, transmitted to
the receiver using the transmit antennas. Here,
directional beam forming can be achieved using
antenna array, which allows for efficient spectrum
reuse by providing spatial diversity. At the receiver,
first RF demodulation is performed. Then, the signal
is digitized using an ADC and timing and frequency
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International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 5 – Sep 2014
synchronization are performed. Synchronization will
be dealt with in the later sections. The guard time is
removed from each OFDM symbol and the sequence
is converted to parallel format and FFT (OFDM
demodulation) is applied. The output is then
serialized and symbol de-mapping is done to get back
the coded bit sequence. Channel decoding is, then,
done to get the user bit sequence.
Fig.1 Basic block diagram of OFDM
C. Orthogonality
Conceptually, OFDM is a specialized FDM,
the additional constraint being: all the carrier signals
are orthogonal to each other. In OFDM, the subcarrier frequencies are chosen so that the sub-carriers
are orthogonal to each other, meaning that cross
talk between the sub-channels is eliminated and intercarrier guard bands are not required. This greatly
simplifies the design of both the transmitter and
the receiver; unlike conventional FDM, a separate
filter for each sub-channel is not required.
The orthogonality requires that the sub-carrier
spacing is
Hertz, where TU seconds is the
useful symbol duration (the receiver side window
size), and k is a positive integer, typically equal to 1.
Therefore, with N sub-carriers, the total passband
bandwidth will be B ≈ N·Δf (Hz).
D. OFDM
Orthogonal
frequency-division
multiplexing
(OFDM) is a method of encoding digital data on
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multiple carrier frequencies. OFDM has developed
into a popular scheme for wideband digital
communication,
whether wireless or
over copper wires, used in applications such as digital
television and audio broadcasting, DSL Internet
access, wireless networks, powerline networks,
and 4G mobile communications.
OFDM is a frequency-division multiplexing (FDM)
scheme
used
as
a
digital
multicarrier modulation method. A large number of
closely spaced orthogonal sub-carrier signals are used
to carry data[1] on several parallel data streams or
channels. Each sub-carrier is modulated with a
conventional modulation scheme (such as quadrature
amplitude modulation or phase-shift keying) at a
low symbol rate, maintaining total data rates similar
to conventional single-carrier modulation schemes in
the same bandwidth.
The primary advantage of OFDM over single-carrier
schemes
is
its
ability
to
cope
with
severe channel conditions
(for
example, attenuation of high frequencies in a long
copper wire, narrowband interference and frequency-
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International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 5 – Sep 2014
selective fading due to multipath) without complex
equalization
filters.
Channel equalization is
simplified because OFDM may be viewed as using
many slowly modulated narrowband signals rather
than one rapidly modulated wideband signal. The low
symbol rate makes the use of a guard
interval between symbols affordable, making it
possible to eliminate inter symbol interference (ISI)
and utilize echoes and time-spreading (on analogue
TV these are visible as ghosting and blurring,
respectively) to achieve a diversity gain, i.e. a signalto-noise ratio improvement. This mechanism also
facilitates
the
design
of single
frequency
networks (SFNs), where several adjacent transmitters
send the same signal simultaneously at the same
frequency, as the signals from multiple distant
transmitters may be combined constructively, rather
than interfering as would typically occur in a
traditional
single-carrier
system.
Recently, chaotic sequences have been adopted
instead of random ones and very interesting results
have been shown in many applications such as secure
transmission [9], natural phenomena modeling [10],
neural networks [11]–[13], and nonlinear circuits
[14]. Also in [16], chaotic time series were used in
DNA computing procedures. The choice of chaotic
sequences is justified theoretically by their
unpredictability, i.e., by their spread-spectrum
characteristic.
Definition of a chaotic map
Let A be a set. A function f: A→A is called chaotic
on A if:
1) f has sensitive dependence on initial conditions.
2) f is topologically transitive.
3) Periodic points are dense in A.
Properties of a chaotic function
1) Unpredictability
A function f: A→A has sensitive dependence on
initial conditions if there exists δ> 0 such that, for
any x ∈ A and any neighbourhood N of x, there exists
y ∈ N and n ≥ 0 such that | f n(x)-f n(y)| > δ.
Intuition: For each point x there is at least one point y
in any neighbourhood of it, which will eventually
separate from x by a distance of at least δ after a
certain number n of iterations of the function.
2) Indecomposability
Fig. 2 Basic OFDM frequency Spectrum
E. CHAOTIC SEQUENCE
The word Chaos implies a state of disorder
and irregularity. It describes many physical
phenomena with complex behaviour by simple laws.
The dynamical systems mean systems that develop in
time in a non-trivial manner. Deterministic chaos is
an irregular motion generated by nonlinear dynamical
systems whose laws determine the time evolution of
a state of the system from knowledge of its previous
history.
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A function f : A→A is said to be topologically
transitive if for any pair of open sets B, C ⊂ A there
exists k > 0 such that f k(B) ∩C≠ ∅.
Intuition: Points belonging to an arbitrarily small
neighbourhood will eventually move to any other
neighbourhood after a certain number of iterations
3) Element of regularity
The point x is a fixed point for if f (x) =x. The point x
is a periodic point of period n if f n(x) =x. The least
positive integer n for which f n(x) =x is called the
prime period of x.
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International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 5 – Sep 2014
Intuition: There are points in set A that are finally
mapped onto them after a number of iterations. When
these points are dense in set A, an element of
regularity is introduced.
F. FADING CHANNELS
Most wireless channels are affected by fading in
addition to added noise and interference. Fading is
due to multipath propagation between the transmit
and receive antennas. In its simplest form, the time
delays between these multipath components are small
compared with the symbol time of the modulation,
resulting in so-called flat fading. The effect is that the
signals arriving at the receive antenna experience
different carrier phases causing the power of the
received signal (the sum of all the multipath
components) to depend on the carrier phases of the
multipath components. A flat fading channel is often
modeled as an AWGN channel with an exponentially
distributed instantaneous SNR and a uniformly
distributed carrier phase of the received signal. This
particular fading channel is referred to as a Rayleighfading channel since the received amplitude is
Rayleigh distributed.
Rayleigh fading is a statistical model for the strong
influence of a propagation environment on a radio
signal, used by wireless communication devices
[Anderson & Salz, 1965]. Rayleigh fading models
consider that the magnitude of a signal that has
passed through a transmission channel or medium
will vary often and in a random manner, or fade,
according to a Rayleigh distribution- the radial
component of the addition of two uncorrelated
Gaussian random variables.
For wireless communications, the envelope of the
received carrier signal is Rayleigh distributed; such a
type of fading is called Rayleigh fading [Arnold &
Bodtmann, 1984]. This can be caused by multipath
with or without the Doppler Effect. Rayleigh fading
is observed as a sensible model for tropospheric and
ionospheric signal propagation as well as the effect of
heavily built-up urban ambience on radio signals.
Rayleigh fading is most applied in situations when
there is less or no dominant propagation along a line
of sight between the transmitter and receiver.
Presence of a dominant line of sight indicates that
Rayleigh fading is a reasonable model when there are
many objects in the environment that scatter the radio
signal before it finally reaches the receiver.
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According to the central limit theorem, if there is
sufficiently too much scattering, the impulse response
of the channel can be modelled well as a Gaussian
process, not bothering about the distribution of the
individual components [Aulin & Sundberg, 1981].
Absence of a dominant component to scatter clearly
indicates that the process will have zero mean and
phase evenly distributed between 0 and 2π radians.
The envelope of the channel response will therefore
be known as a Rayleigh distributed one.
In troposphere and ionosphere signal propagation
regions, many particles in the layers of the
atmosphere act as scatterers and this kind of
disturbed environment may also approximate
Rayleigh fading. If the environment is such that, in
addition to the effects of scattering, prevalence of a
strongly dominant signal is seen at the receiver
means, then such a situation may be better modelled
as Rician fading [3GPP, 2003]. One must always
remember that the Rayleigh fading channel is a
small-scale effect. There will be certain properties of
the environment such as path loss and shadowing
upon which the fading may be superimposed. The
rapidity of the channel fading will be affected by how
fast the receiver and/or transmitter are in mobility.
Constant motion causes Doppler shift in the received
signal components.
G. ADAPTIVE MODULATION
A major disadvantage with fixed modulation
(nonadaptive) on channels with varying signal-tonoise ratio (SNR) is that the bit-error-rate (BER)
probability performance is changing with the channel
quality. Most applications require a certain maximum
BER and there is normally no reason for providing a
smaller BER than required. An adaptive modulation
scheme, on the contrary, can be designed to have a
BER which is constant for all channel SNRs. The
spectral efficiency of the fixed modulation is
constant,
while it, in general, will increase with increasing
channel SNRs for the adaptive scheme. This in effect
means that the average spectral efficiency of the
adaptive scheme is improved, while at the same time
the BER is better suited to the requirement of the
application. Thus, the adaptive link becomes much
more efficient for data transmission.
Adaptive modulation is a method to improve the
spectral efficiency of a radio link for a given
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International Journal of Engineering Trends and Technology (IJETT) – Volume 15 Number 5 – Sep 2014
maximum required quality (error probability). The
idea of adapting the modulation and coding to the
channel conditions is not at all new; it has been
mentioned in numerous papers at least since the
1970s.1 It is, however, not until much later that
optimum schemes for this purpose became available.
Many papers on good schemes started to appear in
the middle of the 1990s.
Currently, single user simulation is used; however it
can be increased for multiple user scenarios.
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IV. CONCLUSION
In this work, performance comparison of chaotic
communication based OFDM system is done. The
use of chaotic communication system can increase
the security prospective of the system due to it
bifurcation behavior when varying the initial
condition. The proposed scheme has been verified in
AWGN channel along with Rayleigh Fading channel
and Rician Fading channel. It has been observed that
BER performance of the system is improved with
adaptive modulation .The adaptive modulation
improves the system performance greatly using
BPSK, QPSK and QAM modulation as per their
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Rician, Rayleigh.
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noted. The proposed system is used with 2-order
chaotic communication structure. It can further
extend for 3-order chaotic communication structure.
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