17-03-2014, 08:34 PM
Abstract
In this paper we studied the chaotic property that
can arise in transmission technique that mostly use in
high-speed bidirectional wireless data transfer and
mobile data transfer. The spectrum of OFDM carrier
in frequency domain is a sinc function, which is
Fourier transform of the rectangular pulse. The
transmission sensitivity that caused from small change
in an initial condition of a system could be explained
by a divergent rate of the Lyapunov exponent of
OFDM spectrum. The corresponding bifurcation
diagram of the Lyapunov exponent is presented. The
chaotic behavior of the function was also discussed.
1. Introduction
An efficient modulation technique that widely use
in many high speed data transmission today like
WiMAX, UMTS and Power line communications and
many areas is Orthogonal Frequency Division
Multiplexing or OFDM. The technique has been in
commercial usage since the 1980s. In 1990, it is use as
a transmission technique in Digital Audio Broadcast
project. This technique is the standard for ADSL,
VDSL, HIPERLAN 2 and extension of IEEE 802.11
standard at 5 GHz. More recently, IEEE 802.16 has
standardized OFDM for both fixed and mobile
WiMAX. [7] The transmission technique is based on
inverse Fast Fourier transforms that proposed by
Weinstein, Ebert and others. [7]
OFDM was firstly proposed in the 1960s. It has
taken many years for this technology to move from
research to industry. The concept of this technique is
based on orthogonal property of the carriers signal. A
single stream of data is branched into parallel stream
each of data stream is coded and modulated onto a
subcarrier. The FDM scheme has been widely accepted
for many decades. In FDM the carriers are all
independent of each other. There is a guard period in
between them and without an overlapping. In FDM
technique each carrier carries data meant for a different
user or application. An example of FDM is FM radio.
The technique is not a purpose of wide band systems
because the technique is wastes too much bandwidth.
This is where OFDM plays an important role. In
OFDM technique, subcarriers are overlap and they are
orthogonal because the peak of one subcarrier occurs
when other subcarriers are at zero, which achieved
using Inverse Fast Fourier Transform (IFFT). [3] The
signal at the receiver is demodulated in parallel from a
Fast Fourier Transform block. Each of subcarrier is
still modulated independently.
In this paper we studied the chaotic property that
can arise in transmission technique that mostly use in
high-speed bidirectional wireless data transfer and
mobile data transfer. The spectrum of OFDM carrier
in frequency domain is a sinc function, which is
Fourier transform of the rectangular pulse. The
transmission sensitivity that caused from small change
in an initial condition of a system could be explained
by a divergent rate of the Lyapunov exponent of
OFDM spectrum. The corresponding bifurcation
diagram of the Lyapunov exponent is presented. The
chaotic behavior of the function was also discussed.
1. Introduction
An efficient modulation technique that widely use
in many high speed data transmission today like
WiMAX, UMTS and Power line communications and
many areas is Orthogonal Frequency Division
Multiplexing or OFDM. The technique has been in
commercial usage since the 1980s. In 1990, it is use as
a transmission technique in Digital Audio Broadcast
project. This technique is the standard for ADSL,
VDSL, HIPERLAN 2 and extension of IEEE 802.11
standard at 5 GHz. More recently, IEEE 802.16 has
standardized OFDM for both fixed and mobile
WiMAX. [7] The transmission technique is based on
inverse Fast Fourier transforms that proposed by
Weinstein, Ebert and others. [7]
OFDM was firstly proposed in the 1960s. It has
taken many years for this technology to move from
research to industry. The concept of this technique is
based on orthogonal property of the carriers signal. A
single stream of data is branched into parallel stream
each of data stream is coded and modulated onto a
subcarrier. The FDM scheme has been widely accepted
for many decades. In FDM the carriers are all
independent of each other. There is a guard period in
between them and without an overlapping. In FDM
technique each carrier carries data meant for a different
user or application. An example of FDM is FM radio.
The technique is not a purpose of wide band systems
because the technique is wastes too much bandwidth.
This is where OFDM plays an important role. In
OFDM technique, subcarriers are overlap and they are
orthogonal because the peak of one subcarrier occurs
when other subcarriers are at zero, which achieved
using Inverse Fast Fourier Transform (IFFT). [3] The
signal at the receiver is demodulated in parallel from a
Fast Fourier Transform block. Each of subcarrier is
still modulated independently.