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Fast Fourier Transform of Frequency Hopping Spread Spectrum in Noisy
Environment
ABID YAHYA
Collaborative MicroElectronic Design Excellence Center
Universiti Sains Malaysia, Engineering Campus
OTHMAN SIDEK
Collaborative MicroElectronic Design Excellence Center
Universiti Sains Malaysia, Engineer ing Campus
MOHD FADZLI MOHD SALLEH
School of Electric and Electronic, University Science Malaysia
14300 Nebong Tebal, Pulau Penang, Malaysia
Abstract: - Frequency hopping spread spectrum (FHSS) systems have traditionally been applied in low data rate
applications where the received signal can be considered narrow band. In this paper we have discussed a synchronouscoherently detected FHSS/BPSK system. Pseudonoise sequence generator has been implemented to select the
frequencies for transmission or reception. We have investigated the spectral characteristics of both spread and non-
spread BPSK waveforms. We have analyzed and simulated these systems with several variations by taking the Fast
Fourier Transform (FFT) of FHSS with original binary sequence and with noisy signal. The simulated results have
shown that a signal lingering at a predefined frequency for a short period of time limits the possibility of interference
from another signal source generating radiated power at a specific hop frequency.
Key-Words: - Frequency hopping spread spectrum, Correlation, Pseudonoise, Fourier transform
1 IntroductionDigital communication has become an essential part of
the lifestyle in most parts of the world. The desire toaccess information and media around the globe, in the
comfort of the home or the office, has lead to an
exponential increase in the use of the Internet and other
data services. The demand for such services has inspired
telecom operators of large-scale wireless systems to seek
new revenue by extending their service selection from
the traditional voice service to provide data services on
an anywhere-anytime basis.
The performance of a communications system depends
on system designer and environmental parameters. The
relationship between these parameters and performance
metrics of interest is usually complex and a small
change in design parameter tends to impact all
performance metrics of interest. In order to achieve the
specific performance levels, emphasis has been given onthe design parameters. The three-way divide between
narrowband, direct sequence spread spectrum, and
frequency hop spread spectrum is an example of a
situation where such a choice must be made.
Development of the first spread spectrum (SS) systems
began at least six decades ago [1-3]. During the world
war II SS devices were already in action. The early
systems were designed to provide low detectability or
protection from jamming or interface. Most of the
applications of SS techniques previously were in the
fields of military applications such as radar and communication systems. Recently SS technique
6th WSEAS International Conference on APPLIED ELECTROMAGNETICS, WIRELESS andOPTICAL COMMUNICATIONS (ELECTROSCIENCE '08), Trondheim, Norway, July 2-4, 2008
ISBN: 978-960-6766-79-4 32 ISSN 1790-5117
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becomes very popular in many civilian applications. In
the field of communications the SS technique is used in
mobile networks communication and wireless local area
network (WLAN).
A SS system is one in which the transmitted signal is
spread over a wide frequency band, much wider, in fact,
than the minimum bandwidth required to transmit the
information being sent.
2 Frequency hopping spread spectrum
(FHSS)
Frequency hopping spread spectrum (FHSS) transmits
short radio bursts on one frequency then randomly hops
to another for the next short burst. The carrier signal
changes frequency in a pattern known to both transmitter
and receiver. The transmission source and destinationmust be synchronized, so they are on the same frequency
simultaneously.
Each user in FHSS follows a different and unique
sequence of hops. The hop sequence is designed so as to
minimize the likelihood that any given hop will land on
the same frequency. At the same time as another user
(design of spreading sequence). The code division is
performed by varying the frequency hopping sequence
from user to user. The code sequences do not guarantee
that collisions will not occur [4-7]. The code sequence
limits the amount of mutual interference to a definable
level.
Frequency hopping spread spectrum Implements
frequency division multiplexing (FDM) and time
division multiplexing (TDM) the pattern of channel
usage is called hopping sequence. The time spend on a
channel with a certain frequency is called dwell time.
Frequency hopping spread spectrum has two types:
• Slow hopping:
Transmitter uses one frequency for several bits periods
i.e. frequency changes at a rate that is lower than thesymbol rate.
• Fast hopping:
Transmitter changes the frequency several times during
the transmission of a single bit i.e. frequency changes at
a rate that is higher than the symbol rate.
Spread spectrum technology has been used to ensure
security of the transmitted data for that purpose pseudo-
noise-sequence (PN) has been using on transmitter as
well receiver end. The block diagram of FHSS with PN
code generator is shown in the Fig.1. A transmitted signal is modulated and spread out so that the signal is
hidden within the noise level. At the receiver end, the
signal is demodulated, received, and decoded to the
same form that it was transmitted. Within a signal
generation code, a data pulse waveform has been taken,
which has been code modulated by multiplying the data
stream with a pseudo-noise-sequence. The code
modulation has spread the signal by the code pulse
waveform. The PN code must be on both the transmitter
and receiver sides so that the original data pulse can be
recovered. A pseudo-random code generator drives a
frequency synthesizer, which synthesizes the desired
hopping frequency. A mixer provides the upconversion
to the desired band and the power amplifier drives the
antenna which sends the desired data stream through the
air.
Fig.1 Structure of the transmitter and receiver of FHSS
system
3 Pseudonoise
In practice, it is unrealistic to generate identical copies
of white noise and as a result deterministic waveforms
with cross correlation properties similar to white noise
are used to implement this technique. Maximal-length
(m-length) pseudo-random or pseudonoise binary
sequences (PN sequences) are a popular choice since
they appear to be random (having auto correlationapproaching and impulse) over a finite range but are
actually deterministic and periodic. Furthermore, they
are relatively easy to generate using linear feed back
shift registers and digital logic [8].
3.1 Correlation Properties
Correlation is a measure of similarity between any two
variables. Although in this paper wave form correlation
is done, these correlations can be separated into
functions that are specific to the waveform pulse shape,
and the discrete correlations between sequences. The
waveform correlation properties solely determine fromthe discrete sequence correlations once pulse shape is
6th WSEAS International Conference on APPLIED ELECTROMAGNETICS, WIRELESS andOPTICAL COMMUNICATIONS (ELECTROSCIENCE '08), Trondheim, Norway, July 2-4, 2008
ISBN: 978-960-6766-79-4 33 ISSN 1790-5117
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given.
Crosscorrelation measures the extent of similarity
between two sequences, and Autocorrelation measures
the same for a sequence with itself, both correlations are
a function of time delay, or shift.
• The autocorrelation values for side lobes are
minimal to reduce multipath interference.
• The Crosscorrelation values between the
sequences are low to minimize the multiple
access interference.
At the core of the sliding correlator technique (also
known as the swept time delay cross correlation
technique) are the cross correlation properties of linear
systems. It is known from linear system theory that if
white noise is applied to the input of a linear
system, and the output is cross correlated with adelayed replica of the input,
( ) p t
( )w t
( p t )τ − , then the resulting
cross correlation coefficient is proportional to the
impulse response of the system evaluated at the
delay time [9]. Under the assumption that the channel is
a linear time-invariant system this technique can be used
to measure the channel impulse response.
(h t )
Assume white noise with auto correlation function( ) p t
( ) pp R τ given by (2) is the input to a channel with
impulse response , then the output of the
channel is given by the convolution of and or
( )h t ( )w t
( )h t ( ) p t
( ) ( ) ( )w t h p t d ζ ζ ζ = −∫ (1)
[ ( ) ( )] ( ) pp E p t p t Rτ τ − = (2)
The cross correlation of the output and a delayed
version of the input
( )w t
( ) p t τ − is given by
( ) [ ( ) ( )]wp R E w t p t τ τ = − (3)
Using (1) in (3) the cross correlation can be expressed as
( ) [ ( ) ( )] ( ) ( ) ( )wp R E w t p t E h p t d p t τ τ ζ ζ ζ ⎡
= − = − × −⎣∫ τ ⎤⎦ (4)
( ) [ ( ) ( )]h E p t p t d ζ ζ τ ζ = − −∫ (5)
Using a change of variables ( )m t ζ = − in (5) yields
( ) ( ) [ ( ) ( ( ))]wp R h E p m p m d τ ζ τ ζ ζ = −∫ −
d
(6)
Using the definition of the auto correlation of two
signals, this can be written as
( ) ( ) ( )wp pp R h Rτ ζ τ ζ ζ = −∫ (7)
Equation (7) shows the convolution of the channel
impulse response with the auto correlation of whitenoise.
4 Results and DiscussionThere are numbers of transformations that can be
applied, among which the Fourier transform (FT) are
probably by far the most popular. The Fourier transformlies in its ability to analyze a signal in the time domain
for its frequency content. The transform works by first
translating a function in the time domain into a function
in the frequency domain. The signal can then be
analyzed for its frequency content because the Fourier
coefficients of the transformed function represent the
contribution of each sine and cosine function at each
frequency.
Simulation has been carried out by using Matlab first of
all data sequence has been generated by using rand
function. Noise had been added to the original bitsequence as shown in Fig.2.When we plot time-domain
signals as shown in Fig.3, we have obtained a time-
amplitude representation of the signal. This
representation is not always the best representation of
the signal for most signal processing related
applications. In many cases, the most distinguished
information is hidden in the frequency content of the
signal. The frequency spectrum of a signal is basically
the frequency components (spectral components) of that
signal. The frequency spectrum of a signal shows what
frequencies exist in the signal. If the FT of a signal in
time domain is taken, the frequency-amplituderepresentation of that signal is obtained.
We have a plot modulated BPSK and FHSS as shown in
Fig.4 and Fig.5 respectively, with one axis being the
frequency and the other being the amplitude. These plots
tell us how much of each frequency exists in our signal
and from these results it clearly depicted that FHSS
overcomes the other ordinary modulation.
In direct spread spectrum the wide modulation is applied
to a fixed frequency carrier signal for transmission. The
spreading code directly spreads the information, and
independent of the RF modulator. While in FH the
information is left unchanged and directly modulates a
carrier of varying frequency which has been plotted in
Fig.6. This is showing the graphical display of tabulated
frequency. The simulated results have shown that a
signal lingering at a predefined frequency for a short
period of time limits the possibility of interference from
another signal source generating radiated power at a
specific hop frequency.
6th WSEAS International Conference on APPLIED ELECTROMAGNETICS, WIRELESS andOPTICAL COMMUNICATIONS (ELECTROSCIENCE '08), Trondheim, Norway, July 2-4, 2008
ISBN: 978-960-6766-79-4 34 ISSN 1790-5117
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0 500 1000 1500 2000 2500
-1
0
1
Original Bi t Sequence
0 500 1000 1500 2000 2500
-1
0
1
Noisy signal
Fig.2 Binary data stream with and without noise
0 500 1000 1500 2000 2500
-1
0
1
BPSK Modul ation of orignal Si gnal
0 500 1000 1500 2000 2500
-1
0
1
BPSK Modulation of Noisy Signal
Fig.3 BPSK modulation of original and noisy signal
0 500 1000 1500 2000
0
0.5
1
1.5
2
FFT of BPSK Modulated Orignal Signal
0 500 1000 1500 2000
0
0.5
1
1.5
2
FFT of BPSK Modulated Noisy Signal
Fig.4 BPSK modulation of original and noisy signal
0 500 1000 1500 2000
0
1
2
3
4
FHSS of Orginal signal
0 500 1000 1500 2000
0
1
2
3
4
FHSS of Noisey signal
Fig.5 Structure of the transmitter and receiver of FFH
system
-1 -0.5 0 0.5 1 1.5 2 2.5 30
50
100
150
200
250
300
350
400
450
500
Fig.6 Histogram of FHSS system
5 ConclusionThe performance of a communications system depends
on system designer and environmental parameters. The
relationship between these parameters and performance
metrics of interest is usually complex and a small
change in design parameter tends to impact all performance metrics of interest. In order to achieve the
specific performance levels, emphasis has been given on
the design parameters. There are numbers of
transformations that can be applied, among which the
Fourier transform (FT) are probably by far the most
popular. We have investigated the spectral
characteristics of both spread and non-spread BPSK
waveforms. We have analyzed and simulated these
systems with several variations by taking the Fast
Fourier Transform (FFT) of FHSS with original binary
sequence and with noisy signal. The simulated results
have shown that a signal lingering at a predefined
frequency for a short period of time limits the possibility
6th WSEAS International Conference on APPLIED ELECTROMAGNETICS, WIRELESS andOPTICAL COMMUNICATIONS (ELECTROSCIENCE '08), Trondheim, Norway, July 2-4, 2008
ISBN: 978-960-6766-79-4 35 ISSN 1790-5117
7/28/2019 electroscience
http://slidepdf.com/reader/full/electroscience 5/5
of interference from another signal source generating
radiated power at a specific hop frequency.
References:
[1] R. A. Scholz, “The origins of spread-spectrum
communications," IEEE Trans. On Comm., vol. COM-
30, pp. 822{854, May 1982.
[2] R. C. Dixon, “Spread spectrum techniques," IEEE
Press, New York, Tech. Rep., 1976.
[3] R. A. Dillard and G. M. Dillard, Detectability of
Spread-Spectrum Signals. Boston. London: Artch
House, 1989.
[4] S. Haykin, Communication systems, 4th ed. New
York: Wiley, 2001.
[5] W. E. Kock, Radar, Sonar, and Holography. New
York: Academic Press, 1973.[6] M. I. Skolnik, Introduction to radar systems, 3rd ed.
New York: McGraw-Hill, 2001.
[7] A. W. Rihaczek, Principles of High-Resolution
Radar . Boston. London: Artch House, 1996.
[8]. Anderson, C., “Design and Implementation of an
Ultrabroadband Millimeter-Wavelentgh Vector Sliding
Correlator Channel Sounder and In-Building Multipath
Measurements at 2.5 & 60 GHz,” Masters Thesis,
Virginia Polytechnic Institute and State University,
http://scholar.lib.vt.edu/theses/index.html, May 2002.
[9] J. D. Parsons, D. A. Demery, A. M. D. Turkamani,
“Sounding Techniques for Wideband Mobile RadioChannels: A Review,” IEE Proceedings, vol. 138, no. 5,
pp. 437-446, October 1992.
6th WSEAS International Conference on APPLIED ELECTROMAGNETICS, WIRELESS andOPTICAL COMMUNICATIONS (ELECTROSCIENCE '08), Trondheim, Norway, July 2-4, 2008
ISBN: 978-960-6766-79-4 36 ISSN 1790-5117