electroscience

7/28/2019 electroscience

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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


ISBN: 978-960-6766-79-4 33 ISSN 1790-5117



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.


ISBN: 978-960-6766-79-4 34 ISSN 1790-5117



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


ISBN: 978-960-6766-79-4 35 ISSN 1790-5117



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.


ISBN: 978-960-6766-79-4 36 ISSN 1790-5117

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