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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).

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UNIVERSITY OF TECHNOLOGY

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