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Content uploaded by Khaled Elleithy
Author content
All content in this area was uploaded by Khaled Elleithy
Content may be subject to copyright.
Content uploaded by Khaled Elleithy
Author content
All content in this area was uploaded by Khaled Elleithy
Content may be subject to copyright.
Content uploaded by Khaled Elleithy
Author content
All content in this area was uploaded by Khaled Elleithy
Content may be subject to copyright.
Improvement in the Spread Spectrum
System in DSSS, FHSS, AND CDMA
Gowrilakshmi Ponuratinam, Bhumika Patel, Syed S. Rizvi Khaled M. Elleithy
Computer Science and Engineering Department, University of Bridgeport, Bridgeport, CT 06605
{gponurat, bhumikpa, srizvi, elleithy}@bridgeport.edu
Abstract - In this paper, we introduce spread
spectrum links that can be used to overcome
intentional jamming. The problem of communicating
in the presence of jamming is very much akin to the
problem of communicating over fading channels.
Hence, by finding out how to defeat jamming by
spread spectrum will also reveal how to overcome
fading. Today, spread spectrum links are also used in
many civilian systems to overcome non-intentional
jamming (or interference), and the report is concluded
with an overview of current commercial spread
spectrum systems. In addition to the traditional
coherent spread-spectrum systems, the definition of an
ideal modified version is introduced and this model is
analyzed from an information theoretic viewpoint. The
project uses a simple point-to-point communication
system with fully synchronized transmitter and
receiver in a simple channel with white Gaussian
noise and arbitrary jamming signal. We prove that in
traditional systems the channel converges to a
Gaussian noisy channel in the limit in the case of
almost any jamming signal, and in our new ideal
modified system the channel converges to a white
Gaussian noisy channel in the limit in the case of any
jamming signal when the processing gain goes to
infinity.
I. INTRODUCTION
Spread-spectrum techniques are methods by
which energy generated in a particular
bandwidth is deliberately spread in the frequency
domain resulting in a signal with a wider
bandwidth.
Spread-spectrum telecommunications is a
signal structuring technique that employs direct
sequence, frequency hopping or a hybrid of
these, which can be used for multiple access
and/or multiple functions. This technique
decreases the potential interference to other
receivers while achieving privacy. Spread
spectrum generally makes use of a sequential
noise-like signal structure to spread the normally
narrowband information signal over a relatively
wideband (radio) band of frequencies. The
receiver correlates the received signals to
retrieve the original information signal.
Originally there were two motivations: either to
resist enemy efforts to jam the communications
(anti-jam, or AJ), or to hide the fact that
communication was even taking place,
sometimes called low probability of intercept
(LPI).
Frequency-hopping spread spectrum (FHSS)
is a method of transmitting radio signals by
rapidly switching a carrier among many
frequency channel, using a pseudorandom
sequence known to both transmitter and receiver.
Spread-spectrum signals are highly resistant to
narrowband interference. The process of re-
collecting a spread signal spreads out the
interfering signal, causing it to recede into the
background.
Code division multiple access (CDMA) is a
channel access method utilized by various radio
communication technologies. CDMA employs
spread-spectrum technology and a special coding
scheme (where each transmitter is assigned a
code) to allow multiple users to be multiplexed
over the same physical channel. By contrast,
time division multiple access (TDMA) divides
access by time, while frequency-division
multiple access (FDMA) divides it by frequency.
CDMA is a form of “spread-spectrum”
signaling, since the modulated coded signal has a
much higher data bandwidth than the data being
communicated.
A. Problem Identification
Let us study a simple example to illustrate the
basic concepts and ideas of spread spectrum. Let
the average received communication signal
power and received jamming signal power is
denoted by S and J, respectively. We ignore any
other interference, such as thermal noise, at this
stage. The basic question is “How can we
communicate reliably even when J>>
S?”Actually, we know the answer from basic
communication theory. We know that we can
communicate over a channel disturbed by
additive white Gaussian noise (an AWGN
channel). White noise has infinite power, but
since the power is spread over an infinite number
of signal space dimensions (or infinite
bandwidth), the power per signal space
dimension is finite. Hence, by concentrating the
transmitter power to a finite-dimensional signal
space, we can gain a power advantage over the
noise.
The same idea is used in a jamming
situation. However, we must make the choice of
signal space dimensions used for transmission a
secret for the jammer. Otherwise, the jammer can
concentrate its power to the same dimensions,
and nothing is gained. This implies that we need
to hide the transmitted signal in a space with
many more dimensions than what is needed for
the transmitted signal.
The different types of jamming problems
identified in the Spread Spectrum are as follows:
i) DS-SS and Broadband Continuous Noise
Jamming.
ii) DS-SS and Narrowband Jamming.
iii) Plus Jamming.
iv) Broadband Jamming.
v) Partial- Band Noise Jamming.
II. RELATED WORK
As explained in the problem identification, the
definition of Jamming and the cause and effect
of Jamming, the dimensionality of a signal space
depends on duration and bandwidth of the
signals in the space. If the spread spectrum
bandwidth is Wss. i.e. the transmitted signal must
reside in a frequency band of width Wss Hz. If
the data rate is Rb = 1/Tb, then the transmission
of a packet of P information bits will take
approximately Tp seconds, where
Tp= PTb= P/ Rb
The set of all signals that are time-limited to
Tp seconds and band limited to Wss Hz spans a
signal space of (approximately) Np = 2WssTp
dimensions. Hence, the number of dimensions
available for the transmission of one information
bit is
Nd= Np/P= 2(Wss/ Rb)
A characteristic of a spread spectrum system is
that ratio Wss/Rb is very large. The larger the
ratio the more resistant to jamming the system
can be made. The number Wss/Rb is often called
the processing gain. If the jammer has no idea
which subset of the Nd dimensions that is used
for the transmission, it may decide to spread its
power equally over all dimensions. The spectral
height of the jamming signal, see Figure 1 is
denoted NJ/2, where
J = 2 Wss (NJ/2) = Wss (NJ)
This type of jamming is called broadband and
now we will assume that the noise is Gaussian.
The broadband noise jamming is benign. To
quantify the effect of jamming, consider the
effect on a binary phase-shift keying. The bit
error probability is
Pb = Q (√ 2 Eb/NJ)
Where Eb = STb = S/Rb is the received energy
per information bit and Q(x) = 1/√2∏ ∫ e−t2/2
dt.
The error probability is decreasing
exponentially with Eb/NJ, since Eb/NJ= S
Wss/J Rb. We can reach any bit error probability
for any jammer-to-signal power ratio, J/S, by
making the processing gain large enough.
However, we should remember that we have
Figure 1: Power spectral density of a broadband noise
jammer
.
Figure 2: Modulator for DS-
SS with BPSK modulation and
rectangular chip waveforms.
reached this conclusion under idealized
circumstances. For instance, if the jamming
causes the synchronization or front-end
electronics or processing to fail, then this will
effectively disrupt the communication.
III. PROPOSED SOLUTION FOR DIRECT
SEQUENCE SPREAD SPECTRUM
Consider an ordinary un-coded BPSK. The
transmitted signal would be
s (t) =√2Eb cos (2πfct)
summation with upper bound ∞ and lower bound
n= -∞ for b[n]p (t − nTb). Where Eb is the
energy per information bit, fc is the carrier
frequency, b[n] ∈ {±1} is the nth information
bit, p(t) is the unit-energy pulse shape, and the
data rate is Rb = 1/Tb. The bandwidth of s(t) is
determined by the pulse shape and data rate. For
the special case of rectangular chip pulses, we
can rewrite the transmitted signal as:
s (t) = √ 2Eb/Tb cos (2∏fc t) b (t) c (t)
where the data signal b (t) is defined as
b (t) = summation with upper bound ∞
and lower bound n= -∞ (b[n]Π Tb (t − nTb)),
and the scrambling waveform be defined as
c (t) = summation with upper bound ∞
and lower bound m= -∞(c[m]Π Tc (t − mTc)
From the figures given below, when we take
up and rectangular chip pulse the bit probability
error is minimized if the received signal is equal
to the transmitted signal plus white Gaussian
noise. Hence, if the jammer waveform is
Gaussian noise that is spectrally white over the
system bandwidth and if we ignore any other
interference the bit error probability is Pb=
Q (√ 2Eb/Nj). Assuming that the channel also
adds white Gaussian noise with power spectral
density No/2, and then the resulting bit error
probability is Pb= Q (√2 (Eb/Nj+No)).Note that
the processing gain only affects NJ=J Rb/Wss.
Hence, the bandwidth expansion does not help at
all to combat the white channel noise. However
by replacing the repetition code with a better
channel code, we can combat both the jamming
and the channel noise more efficiency.
Figure3: Demodulator for DS-SS with BPSK modulation with an arbitrary chip waveform p (t)
Figure 4: Demodulator for DS-SS with BPSK modulation with rectangular chip waveform
From figure 2 and 4, DS-SS is more effective
against narrowband jamming and interference.
Suppose the jamming signal is a pure cosine at
carrier frequency fc with the power J and phase
ϴ, .i.e. j (t) = √2J cos (2∏ fc t +ϴ) contribution
from the jammer to the input to the integrator
block figure 2 is
j (t)√2J cos (2∏ fc t +ϴ)=
√Jc(t) 2cos(2πfct + θ) cos(2πfct)
=√Jc(t)[cos(θ) + cos(4πfct + θ)]
= √Jc(t) cos(θ) + √Jc(t) cos(4πfct + θ).
Figure 5: Bit error probability for DS-SS with BPSK modulation over an AWGN channel with Eb/No=8.4
dB
and with broadband noise jamming of varying power
Figure 6: Despreading operation in the presence of narrowband jamming.
The second term in the equation above will have
its power centered on twice the carrier frequency
and since the integrator is a low-pass filter. The
first term has its power centered on DC and is
spread over the entire system bandwidth. The
integrator is a low-pass filter with a cut-off
frequency of approximately 1/Tb Hz only a
fraction of the jammer power will remain after
the integrator. The same arguments can be made
for a more general narrowband jamming signal.
The receiver will spread the power of the
jamming signal over a span approx. the entire
system bandwidth, and the integrator will
lowpass filter the spread jamming signal. So,
only a small amount of the jamming power will
effect the decision on the information bits.
Finally the desired signal component will be
dispread by the receiver.
B. Pulse Jamming
A broadband pulsed noise jammer transmits
noise whose power is spread over the entire
system bandwidth. However, the transmission is
only on for a fraction ρ of the time (i.e., ρ is the
duty cycle of the jammer transmission and 0 < ρ
≤ 1). This allows the jammer to transmit with a
power of J/ρ when it is transmitting (remember
that J is the average received jammer power),
and the equivalent spectral height of the noise is
NJ/2ρ. To make a simple analysis of the impact
of a pulsed jammer we start by assuming that the
jammer affects an integer number of information
bits. That is, during the transmission of a certain
information bit, the jammer is either on (with
probability ρ) or off (with probability 1 − ρ).
Furthermore, if we assume that the jammer
waveforms is Gaussian noise and ignore all other
noise and interference, the bit error probability
for a DS-SS system with BPSK modulation is
Pb =ρ Q(√(2Eb/Nj ) ρ
For a fixed value Eb/Nj, the worst case jammer
duty cycle can be found by:
ρwc = { 0.769/(Eb/Nj); Eb/Nj>0.769
1; Eb/Nj< 0.769 and the corresponding bit error
probability is:
Pb = { 0.083/(Eb/Nj); Eb/Nj>0.769
Q (√Eb/Nj); Eb/Nj< 0.769
The above is explained in figure 7, if the jammer
uses the worst-case duty cycle, then the bit error
probability is only decaying as 1/ (Eb/NJ) rather
than exponentially in Eb/NJ. As seen from the
figure, to reach Pb = 10−4 we have to spend
almost 21 dB more signal power compared to
case for a broadband continuous noise jammer.
C. FHSS Analysis
Figure 7: Bit error probability for BPSK-modulated DS-SS with pulsed noise jamming with duty cycle ρ
The larger the system bandwidth, the shorter
the pulses must be. Hence, for DS spread
spectrum, Wss is limited to few hundred MHz
due to hardware constraints. This implies that the
processing gain is also limited. Moreover, the
system bandwidth must be contiguous. Both
these limitations can be avoided by using a
frequency-hopped spread spectrum (FH-SS)
system. The baseband signal denoted by
s (t)= x(t)√2cos(2πfkt +θk), k Th ≤ t < (k + 1)Th
where 1/Th is the frequency hopping rate and fk
and θk is the carrier frequency and phase after
the kth hop.
D. Broadband Jamming
The most benign form of jamming is
broadband non-pulsed noise jamming. For
uncoded binary FSK with non-coherent
detection, the resulting bit error probability is:
Pb =1/2 ℮ power –Eb/2Nj
where Nj=J/Wss.
A jammer that uses partial-band noise jamming
will concentrate its power to a bandwidth ρWss,
where ρ is the frequency domain duty cycle (0 <
ρ ≤ 1). The jammer signal is Gaussian noise with
a flat power spectral density over the jammed
bandwidth, i.e., in the jammed band the power
spectral density is J/2Wss ρ= Nj/2 ρ. If we
assume that the jammed bandwidth is placed
such that all signal alternatives used for a certain
symbol are either jammed or not jammed, then
the probability that a certain symbol will be
jammed is ρ. The resulting bit error probability
for BFSK with non-coherent detection is then
Pb = (1 − ρ) × 0 + ρ1/2exp (-Eb ρ/2Nj)
= ρ/2exp (-Eb ρ/2Nj). The worst duty cycle
would be ρwc={ 2/(Eb/Nj);Eb/Nj>2 &
1;Eb/Nj<=2, the worst bit error probability will
be Pb,wc = {1/(eEb/Nj; Eb/Nj>2 & ρ/2exp(-Eb
ρ/2Nj) ;Eb/Nj<=2
IV. CONCLUSION
The Spread Spectrum System has a diverse
application over non-military work like
underwater communication, wireless local loop
system, wireless local area networks, cellular
system, satellite communication and ultra
wideband systems. Spread Spectrum is also used
in wired application in e.g. power-line
communication and has been proposed for
communication over cable- TV network and
optical fiber system. Finally, spread spectrum
techniques have been found to be useful in
ranging e.g., radar, and navigation (GPS).
REFERENCE
1) google.com-Chalmers “Introduction to Spread
Spectrum System”, ERIK STRO¨ M, TONY
OTTOSSON, ARNE SVENSSON Department
of Signals and Systems CHALMERS
UNIVERSITY OF TECHNOLOGY
2) Robert A. Scholtz. “The origins of spread
spectrum communications.” IEEE Transactions
on Communications, vol. 30, no. 5, pp. 822–854,
May 1982. (Part I).
3) Robert A. Scholtz. “Notes on spread-spectrum
history.” IEEE Transactions on
Communications, vol. 31, no. 1
4) Marvin K. Simon, Jim K. Omura, Robert A.
Scholtz, and Barry K. Levitt. Spread Spectrum
Communications Handbook. McGraw-Hill,
revised edition, edition, 1994.
5) Robert C. Dixon. Spread Spectrum Systems
with Commercial Applications. John Wiley and
Sons, third edition, 1994.
6) Denny Radford. “Spread spectrum data leap
through AC power wiring.” IEEE Spectrum, vol.
33, no. 11, pp. 48–53.
