CONTENT

UNIT TITLE PAGE

NO. NO.
CONTENT i

SYLLABUS iv

TWO MARKS 1- 18
1 INTRODUCTION 19 - 52
1.1 Origins of Spread Spectrum Communications 19

1.2 Spread Spectrum System Criteria 20

1.3 Reasons For Use of Spread Spectrum Systems 20

1.4 Advantages of Spread-Spectrum Technology 20
1.4.1 Avoiding Interception 20

1.4.2 Privacy of Transmission 21

1.4.3 Resistance to Fading 21

1.4.4 Accurate Low Power Position Finding 21

1.4.5 Low Transmit Power Density Function Per 22

Hertz
1.4.6 Interference Rejection Capability 22

1.4.7 Improved Multiple Access Scheme 22

1.5 Types of Techniques Used For Spread Spectrum 22

1.5.1 Frequency Hop Spread Spectrum 23

1.5.2 Direct Sequence Spread Spectrum 25

1.5.3 Advantages and Disadvantages of Spread 28

Spectrum Techniques
1.5.4 Time Hopping 29

1.5.5 Hybrid System 30

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 1.6 Jamming Considerations 31

1.6.1 The Jamming Game 31

1.6.2 Jammer Waveforms 31
1.6.3 Tools of the Communicator 32
1.6.4 Anti-Jam Margin 34
1.6.5 Broadband Noise Jamming 35
1.6.6 Partial-Band Noise Jamming 36
1.6.7 Multiple-Tone Jamming 38
1.6.8 Pulse Jamming 39
1.6.9 Repeat-Back Jamming 41
1.7 Binary Pseudo-Random Sequences 42

1.8 Maximal-Length Sequences 44

1.8.1 Decimation Of M-Sequences 47

1.8.2 Preferred Pairs of M-Sequences 48

1.9 Gold Codes Sequence 49

1.9.1 Properties of Gold Codes 50

1.9.2 Applications of Gold Codes 50

1.10 Kasami Sequences 51

1.10.1 Generating A Small Set of Kasami Sequences 51

1.10.2 Generating A Large Set of Kasami Sequence 52

2 DIRECT SEQUENCE SPREAD SPECTRUM SYSTEM 53 - 67

2.1 Coherent Direct Sequence Systems 53

2.2 Model of A DS/BPSK System 54

2.3 Chernoff Bound 57

2.4 Uncoded Direct Sequence Spread Binary Phase 58

Shift Keying

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 2.5 Under Constant Power Broad Band Jammer 61
2.6 Coded Direct Sequence Spread Binary Phase Shift 63
Keying

3 FREQUENCY HOPPING SPREAD SPECTRUM SYSTEM 68 - 74

3.1 Non-Coherent Frequency Hopping Systems 68
3.2 Uncoded FH/BFSH Performance Under Constant 69
Power Broadband Jammer
3.3 Code FH/BFSK Performance For Practical Band 71
Multitone Jammer
3.4 Performance of FH/MDPSK In The Presence of 72
Partial Band Multitone Jammer

4 SYNCHRONIZATION OF SS RECEIVERS 75 - 83
4.1 Introduction 75
4.2 Acquisition 75
4.2.1 Correlator Structures 76
4.3 Serial Search 78
4.4 Sequential Estimation 80
4.5 Tracking 81

5 APPLICATIONS 84 - 101
5.1 Application of Spread Spectrum in Satellite 84
Commmunication
5.1.1 Direct Sequence Spread Spectrum 89
5.1.2 Frequency Hopping Spread Spectrum 90
5.2 Antijam Communications 92
5.3 Low-Probability Of Intercept 94
5.4 Mobile Communications 95
5.4.1 Code Division Multiple Access 95
5.4.2 Capacity of Cellular Cdma 99
REFERENCES 102
QUESTION BANK 103
PREVIOUS YEAR UNIVERSITY QUESTION PAPERS 108

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 EC E74 - SPREAD SPECTRUM COMMUNICATION

UNIT-I
Introduction: Origins of SS communications – Advantages of Spectrum spreading –
Types of techniques used for spread spectrum – Processing gain and other fundamental
parameters – Jamming methods – Linear Feedback shift register sequence generation –
M sequence and their statistical properties. Introduction to Non-linear sequences – Gold
codes - Kasami sequences & chaotic sequences.

UNIT-II
Direct Sequence Spread Spectrum System: Coherent direct sequence systems –
Model of a DS/BPSK system, Chernoff bound – Performance of encoded DS/BPSK –
Constant power and pulse jammer. Coded DS/BPSK Performance for known and
unknown channel states.

UNIT-III
Frequency Hopping SS System: Non-coherent FH system model – Uncoded
FH/BFSK performance under constant power broadband jammer – Partial band noise
jammer – Multitone jammer. Coded FH/BFSK performance for partial and multitone
jammer. Performance of FH/MDPSK in the presence of partial band mutitone jamming.

UNIT-IV
Synchronization of SS Receivers: Acquisition and tracking in DS SS receivers & FH
SS receivers – Sequential estimation – Matched filter techniques of acquisition and
tracking – Delay locked loop – Tau-Dither loop.

UNIT-V
Applications: Space systems – Satellite communication. Anti jam military
communication – Low probability of intercept communication – Mobile
communications.

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UNIT-I
INTRODUCTION

1. Define spread spectrum

Spread-spectrum techniques are methods by which a signal (e.g. an
electrical, electromagnetic, or acoustic signal) generated in a particular
bandwidth is deliberately spread in the frequency domain, resulting in a
signal with a wider bandwidth. These techniques are used for
establishment of secure communications, increasing resistance to
natural interference and jamming, to prevent detection, and to limit
power flux density (e.g. in satellite downlinks).

2. Mention the Spread Spectrum System Criteria

The following two criteria must be satisfied:

The transmitted signal must occupy a bandwidth much greater than
the bandwidth of the modulating signal (i.e. the input signal to the
system).

The bandwidth occupied by the transmitted signal must be
determined by a prescribed waveform and not by the modulating
frequency (i.e. carrier frequency)

3. Give the reasons for use of spread spectrum systems.

There are three major reasons for the use of spread spectrum
techniques in communication systems today.

They aid privacy of the transmission, since the spectral density of
the spread spectrum may be less than the noise spectral density of
the receiver.

The despreading process in the receiver will spread the spectra of
unwanted narrowband signals, thus improving interference
rejection.

The effect on a spread spectrum receiver, that receives a spread
spectrum from a different spread spectrum system using the same
frequency bands but implementing a different spreading pattern,
approximates to noise in the receiver.

4. Give the necessary bandwidth equation for error-free transmission

information at very low SNR.

NC
Bw ≈
S
where C is the capacity of a communication channel in bits per hertz, Bw
is the bandwidth in hertz, S is the signal power, and N is the noise power.

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5. What are the three ways to spread the bandwidth of the signal?

Direct sequence: The digital data is directly coded at a much higher

frequency. The code is generated pseudo-randomly, the receiver knows
how to generate the same code, and correlates the received signal with
that code to extract the data.

Frequency hopping: The signal is rapidly switched between different

frequencies within the hopping bandwidth pseudo-randomly, and the
receiver knows beforehand where to find the signal at any given time.

Time hopping: The signal is transmitted in short bursts pseudo-

randomly, and the receiver knows beforehand when to expect the burst.

6. Define DS-SS.
Direct-sequence spread spectrum (DS-SS) is a spread spectrum
modulation technique in which the transmitted signal takes up more
bandwidth than the information signal that is being modulated. The
name 'spread spectrum' comes from the fact that the carrier signals
occur over the full bandwidth (spectrum) of a device's transmitting
frequency.

7. What are the benefits of DSSS?

Resistance to intended or unintended jamming

Sharing of a single channel among multiple users

Reduced signal/background-noise level hampers interception

Determination of relative timing between transmitter and receiver

8. What are the applications of DS-SS?

The United States GPS and European Galileo satellite navigation

systems

DS-CDMA (Direct-Sequence Code Division Multiple Access) is a
multiple access scheme based on DSSS, by spreading the signals
from/to different users with different codes. It is the most widely
used type of CDMA.

Cordless phones operating in the 900 MHz, 2.4 GHz and 5.8 GHz
bands

9. What is despreading?
The resulting signal in the transmitter resembles white noise, like an
audio recording of "static". However, this noise-like signal can be used to
exactly reconstruct the original data at the receiving end, by multiplying
it by the same pseudorandom sequence (because 1 × 1 = 1, and −1 × −1
= 1). This process, known as "de-spreading", mathematically constitutes
a correlation of the transmitted PN sequence with the PN sequence that

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the receiver believes the transmitter is using. For de-spreading to work

correctly, transmit and receive sequences must be synchronized.

10. Define jamming.

Jamming is the (usually deliberate) transmission of radio signals that
disrupt communications by decreasing the signal to noise ratio.
Unintentional jamming occurs when an operator transmits on a busy
frequency without first checking whether it is in use, or without being
able to hear stations using the frequency. Another form of unintentional
jamming occurs when equipment accidentally radiates a signal

11. What are the assumptions to develop a jam-resistant

communication system?
The goals of the communicator are to develop a jam-resistant
communication system under the following assumptions:

Complete invulnerability is not possible;

Jammer has a priori knowledge of system parameters, such as
frequency bands, timing & traffic so on.

The jammer has no a priori knowledge of the PN spreading or
hopping codes.

12. What are the usual design goals for an anti-jam communication
system?
Design goal for an anti-jam (AJ) communication system is to force a
jammer to expend its resources

Over a wide-frequency band,

For a maximum time, and

For a diversity of sites.

13. What are the most prevalent design options?

The most prevalent design options are

frequency diversity, by the use of direct-sequence and frequency-
hopping spread-spectrum techniques;

time diversity, by the use of time hopping;

spatial discrimination, by the use of a narrow-beam antenna, which
forces a jammer to enter the receiver via an antenna side lobe and
hence suffer, typically, a 20- to 25-dB disadvantage, and

Combinations of the previous three options

14. What is LFSR?

A linear feedback shift register (LFSR) is a shift register whose input
bit is a linear function of its previous state. The only linear function of
single bits is xor, thus it is a shift register whose input bit is driven by
the exclusive-or (xor) of some bits of the overall shift register value.

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15. Give the applications of LFSR.

Applications of LFSRs include generating pseudo-random numbers,
pseudo-noise sequences, fast digital counters, and whitening
sequences. Both hardware and software implementations of LFSRs
are common.

LFSRs can be implemented in hardware, and this makes them
useful in applications that require very fast generation of a pseudo-
random sequence, such as direct-sequence spread spectrum radio.
LFSRs have also been used for generating an approximation of white
noise in various programmable sound generators.

16. What is maximum length sequence?

A maximum length sequence (MLS) is a type of pseudorandom binary
sequence. They are bit sequences generated using maximal linear
feedback shift registers and are so called because they are periodic and
reproduce every binary sequence that can be reproduced by the shift
registers (i.e., for length-m registers they produce a sequence of length
(2m−1). A MLS is also sometimes called an n-sequence or a m-sequence.
MLSs are spectrally flat, with the exception of a near-zero DC term.
These sequences may be represented as coefficients of irreducible
polynomials in a polynomial ring over Z/2Z.

17. Give the application of maximum length sequence

Practical applications for MLS include measuring impulse responses
(e.g., of room reverberation). They are also used as a basis for deriving
pseudo-random sequences in digital communication systems that
employ direct-sequence spread spectrum and frequency-hopping spread
spectrum transmission systems, and in the efficient design experiments.

18. Define correlation.

Correlation is a measure of relationship between two mathematical
variables or measured data values, which includes the Pearson
correlation coefficient as a special case.

19. Write notes on gold codes.

A Gold code, also known as Gold sequence, is a type of binary
sequence, used in CDMA and satellite navigation. Gold codes are named
after Robert Gold. Gold codes have bounded small cross-correlations
within a set, which is useful when multiple devices are broadcasting in
the same range. A set of Gold code sequences consists of 2n − 1
sequences each one with a period of 2n − 1.

20. Write notes on Kasami sequences

Kasami sequences are binary sequences of length 2N where N is an
even integer. Kasami sequences have good cross-correlation values

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approaching the Welch lower bound. There are two classes of Kasami
sequences - the small set and the large set.
The process of generating a Kasami sequence starts by generating a
maximum length sequence a(n), where n=1..2N-1.

21. What is the significance of spread spectrum?

The narrow bandwidth signal is spread over wide band with the help
of special code. Hence the name-spread spectrum is given.

22. What is the use of special code in spread spectrum?

The special code decides the way in which narrowband signal is
spread over wide band.

23. What are averaging system and avoidance systems?

In averaging systems, the interference is reduced by averaging it over
long period. In avoidance a system making the signal to avoid the
interference a large fraction of time reduces the interference.

24. Where spread spectrum is used?

It is used in anti-jam capability; secure communication such as
military and banking purposes.

25. Is spread spectrum a modulation technique?

Sometimes people call spread spectrum modulation. But that does
not carry conventional meaning of modulation. Rather it includes
conventional digital modulation techniques to generate spread spectrum
modulated signals.

26. Explain direct sequence spread spectrum.

In the first stage, incoming data sequence modulates wideband code.
This transforms narrow-band incoming data sequence into wideband
signal. The wideband signal digitally modulates carrier.

27. Why pseudo-random code is used as special code for spreading the
spectrum?
Unintended receiver should not receive the signal. If the spreading
code is not random, then unintended receiver can obtain the code by
observing the signal over certain period of time. But if the code is
random, then it is very difficult to identify it.

28. What is the meaning of the word jamming and anti-jam?

In general, the word Jam means to block or resist the flow. A noise is
transmitted within the bandwidth of the channel. This noise interferes
with the signal, so that the receiver cannot interpret the signal. This is
called Jamming. The capability created against jamming is called anti-
jam.

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29. What is meant by PN sequence and what are the properties of PN

sequence?
The PN sequence is coded sequence of ones and zeros with certain
auto-correlation properties. There are three properties
1. Balance Property
2. Run Property
3. Correlation property

30. Define processing gain.

BW (spreaded signal)
Processing gain = ---------------------------
BW (unspreaded signal)

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UNIT-II
DIRECT SEQUENCE SPREAD SPECTRUM SYSTEM

1. What is DS-SS modulation ?

In DS-SS modulation, the pseudo-noise sequence is directly
modulated with data sequence. Thus pseudo-noise sequence acts as
high frequency carrier and data sequence acts as low frequency
modulating signal.

2. Define chip duration and chip rate?

The bit period PN sequence is called chip duration (Tc). Chip rate is the
rate at which bits of PN sequence are produced. Chip rate (Rc) =1 / Tc

3. What is the relationship between chip duration and bit duration?

Tb = N Tc
Where N is the period of PN sequence, Tb is the bit duration, Tc is chip
duration

4. How many stages of flip-flops are required to generate PN sequence

of length 31?
N=2m – 1 31 = 2m – 1 ,m = 5 stages

5. List the different type of jammers.

Pulse jammer

CW jammer

Multitone jammer

Broadband jammer

Partial-band jammer

6. Define pulse jammer.

Pulse jamming produces noise pulses for an instantaneous period,
The pulse jammer model can be deployed as a fixed, mobile, or satellite
node. This node model is called jam pulsed. It provides transmission on
a single fixed frequency band which is masked by a periodic pulse train
in time. Control of the transmission pulses is performed by the process
model, which creates packets sufficient to last the duration of one pulse
and sends them through a radio transmitter.

7. Define continuous wave jammer.

Continuous wave jammer is an another simple jamming signal is a
sinusoidal tone or continuous wave signal. This type of jammer produces
a high-power sinusoid or other very narrow bandwidth waveform.
A CW jammer has the form

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The figure below shows the frequency domain. Here all the phases are
assumed to be independent and uniformly distributed.

8. What do you mean by broadband jammer?

A broadband noise jammer spreads Gaussian noise of total power J
evenly over the total frequency range of the spread bandwidth Wss. This
results in an equivalent single-sided noise power spectral density,
J
NJ =
WSS
Since the signal energy per bit is STb where Tb=1/Rb,

9. What do you meant by partial-band jammer?

A partial-band noise jammer, spreads noise of total power J evenly over some
frequency range of bandwidth WJ, which is a subset of the total spread bandwidth
Wss. We define ρ as the ratio
W
ρ = J ≤1
WSS

10. How should an effective anti-jamming system be?

An effective anti-jam communication system is one that gives
performance close to or better than the baseline performance, regardless
of the type of jammer waveform used.

11. How spreading process is done in CDMA?

CDMA uses Direct Sequence spreading, where spreading process is
done by directly combining the baseband information to high chip rate
binary code.

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12. Define spreading factor and spreading process gain in CDMA?

The Spreading Factor is the ratio of the chips (UMTS =3.84Mchips/s)
to baseband information rate. Spreading factors vary from 4to 512 in
FDD UMTS. Spreading process gain can expressed in dBs (Spreading
factor 128 = 21dB gain).

13. Why near-far problem appears in CDMA?

The spreading of the data signal in a CDMA system is done by
applying a code, independent of the data-signal. Important property of
the codes is the cross-correlation. If the codes which are used are not
completely orthogonal, the cross-correlation factor is unequal to zero. In
this situation the different users are interferers to each other, hence the
near-far problem appears.

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UNIT-III
FREQUENCY HOPPING SS SYSTEM

1. What is frequency hop spread spectrum modulation?

In FH-SS , the data is transmitted in different frequency slots. These
frequency slots are selected with the help of pseudo noise sequence.
Selection of frequency slots is called frequency hopping. Frequency hop
spread spectrum is of two types, slow frequency and fast frequency
hopping.

2. What is slow and fast frequency hopping?

In slow frequency hopping is much similar to binary frequency shift
keying where in only two frequency changes occur. In fast frequency
hopping we may hay 10-100 frequency changes occurring within a bit
time.

3. Define TH-SS technique.

Time hopped spread spectrum is a modulation technique where in the
carrier is turned on and off by the pseudorandom code. In this technique,
each information bit is modulated by a sequence of much faster chips.
Therefore, the chip rate is much higher than the information signal bit
rate. The receiver can then use the same PN sequence to counteract the
effect of the PN sequence on the received signal in order to reconstruct
the information signal.

4. What is partial band noise jamming?

When the Gaussian noise jammer restricts its total power to a fraction,
Wj of its full SS bandwidth, Wss as shown in the diagram below,
increasing the power density is known as partial band noise jamming.

5. Briefly explain Non-coherent FH system model?

This is a conventional M-FSK scheme in which the carrier frequency
is pseudo randomly hopped over Wss under the control of a PN sequence.
Here a PN sequence of K segments drives a frequency synthesizer which
hops the carrier over 2k frequencies. But the FH synthesizer does not

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generally maintain phase coherence over successive hops consequently

coherent data demodulation techniques are possible only within a hop.

6. Briefly explain coherent FH system model?

This is a conventional M-FSK scheme in which the carrier frequency
is pseudo randomly hopped over Wss under the control of a PN sequence.
Here a PN sequence of K segments drives a frequency synthesizer which
hops the carrier over 2k frequencies. Carrier phase is maintained from
one hop pulse to another. Hence it is known to be Coherent FH systems.

7. What is frequency synthesizer and mention its applications?

A frequency synthesizer is an electronic system for generating any of
a range of frequencies from a single fixed time base or oscillator. They
are found in many modern devices, including radio receivers, mobile
telephones, radiotelephones, walkie-talkies, CB radios, satellite
receivers, GPS systems, etc.

8. Why do we go for differentially coherent modulation techniques?

Traditionally coherent modulations such as multiple phase-shift-
keying (MPSK) and quadrature amplitude-shift –keying (QASK) can also
be detected using differentially coherent techniques. These techniques
are useful in applications where the receiver is unable to provide an
exact carrier reference phase for demodulating each data symbol but is
capable of establishing a phase reference to within an arbitrary number
of radians.

9. Define slow frequency hopping.

Several symbols of data are transmitted in one frequency hop. This
means symbol rate is higher than hop-rate.

10. Explain frequency hop spread spectrum

In this technique, changing the carrier frequency in pseudo-random
manner widens the spectrum of data modulated carrier.

11. Define FH-SS.

Frequency-hopping spread spectrum (FHSS) is a method of
transmitting radio signals by rapidly switching a carrier among many
frequency channels, using a pseudorandom sequence known to both
transmitter and receiver. It is utilized as a multiple access method in the
frequency-hopping code division multiple access (FH-CDMA) scheme.

12. Give the advantages of FHSS

A spread-spectrum transmission offers three main advantages over a
fixed-frequency transmission:
• 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.

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• Spread-spectrum signals are difficult to intercept. An FHSS signal

simply appears as an increase in the background noise to a narrowband
receiver. An eavesdropper would only be able to intercept the
transmission if the pseudorandom sequence was known.

13. Give the applications of FH-SS

Spread-spectrum signals are highly resistant to deliberate jamming,
unless the adversary has knowledge of the spreading characteristics.
Military radios use cryptographic techniques to generate the channel
sequence under the control of a secret Transmission Security Key
(TRANSEC) that the sender and receiver share.

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UNIT-IV
SYNCHRONIZATION OF SS RECEIVERS
1. Define synchronization.
Synchronization is timekeeping which requires the coordination of
events to operate a system in unison. In electrical engineering terms, for
digital logic and data transfer, a synchronous object requires a clock
signal. Timekeeping technologies such as the GPS satellites and Network
time protocol (NTP) provide real-time access to a close approximation to
the UTC timescale, and are used for many terrestrial synchronization
applications.

2. Mention the uses of synchronization

Mobile phone synchronization using SyncML -standards or java based
technology to perform a backup.

Film synchronization of image and sound in sound film.

Synchronization is important in fields such as digital telephony, video
and digital audio where streams of sampled data are manipulated.

In electric power systems, alternator synchronization is required when
mulitple generators are connected to an electrical grid.

3. What is tracking?
Tracking is defined as a process which continuously maintains the
best possible waveform fine alignment by means of a feedback loop.It can
be classified as coherent or non-coherent. A coherent loop is one in
which the carrier frequency and phase are known exactly so that the loop
can operate on a baseband signal. A non-coherent loop is one in which
the carrier frequency is not known exactly (due to Doppler effects, for
example), nor is the phase.

4. What is acquisition?
Acquisition is a process of bringing the two spreading signals into
coarse alignment with one another. Acquisition schemes can be classified
as coherent or non coherent.

5. What are the types of acquisition?

Correlator Structures

Serial Search

Sequential Estimation

6. What is sequential estimation?

Cross correlation between the generated and incoming codes is done
to check whether synchronization has been attained or not. If not, the
next n bits are estimated and loaded. This algorithm usually yields rapid
acquisition and hence is called the RASE (Rapid Acquisition by
Sequential Estimation) algorithm. However, this scheme works well only
when the noise associated with the received spread signal is low.

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7. What is the draw back in sequential estimation?

While the RASE system has a rapid acquisition capability it has the
drawback of being highly vulnerable to noise and interference signals.
The reason for this is that the estimation process consists of a simple
chip-by-chip hard-decision demodulation, without using the interference
rejection benefits of the PN code.

8. Define matched filter

A matched filter is obtained by correlating a known signal, or
template, with an unknown signal to detect the presence of the template
in the unknown signal. This is equivalent to convolving the unknown
signal with a conjugated time-reversed version of the template. The
matched filter is the optimal linear filter for maximizing the signal to
noise ratio (SNR) in the presence of additive stochastic noise.

9. Define delay-locked loop

Delay-locked loop (DLL) is a digital circuit similar to a phase-locked
loop (PLL), with the main difference being the absence of an internal
oscillator. A DLL can be used to change the phase of a clock signal (a
signal with a periodic waveform), usually to enhance the clock rise-to-
data output valid timing characteristics of integrated circuits (such as
DRAM devices). DLLs can also be used for clock recovery (CDR). From the
outside, a DLL can be seen as a negative-delay gate placed in the clock
path of a digital circuit.

10. Define tau-dither loop or advantage of tau-dither loop

A time-shared early-late tracking loop frequently referred to as a tau-
dither loop. It tends to deal with this potential problem by intentionally
injecting a small error in the tracking correction, so that the loop kind of
vibrates around the correct answer. This vibration is typically small, so
that the loss in performance is minimal. This design has the advantage
that only one correlator is needed to provide the code tracking function
and the despreading function.

11.What are the things to be considered for tracking?

When determining the limits of uncertainty in time and frequency, the
following stuffs must be considered:

Uncertainty in the distance between the transmitter and the receiver
translates into uncertainty in the amount of propagation delay.

Relative clock instabilities between the transmitter and the receiver
result in phase differences between the transmitter and receiver
spreading signals that will tend to grow as a function of elapsed time
between synchronization.

Uncertainty of the receiver's relative velocity with respect to the
transmitter translates into uncertainty in the value of Doppler
frequency offset of the incoming signal.

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UNIT-V
APPLICATIONS

1. Expand CDMA.
Code division multiple access (CDMA) is a channel access
method used 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. CDMA is a form of
spread-spectrum signaling, since the modulated coded signal has a
much higher data bandwidth than the data being communicated.

2. What are the advantages of CDMA?

Dramatically improving the telephone traffic capacity

Dramatically improving the voice quality and eliminating the
audible effects of multipath fading

Reducing the incidence of dropped calls due to handoff failures

Providing reliable transport mechanism for data communications,
such as facsimile and internet traffic

3. What are disadvantages of CDMA?

One major problem in CDMA technology is channel pollution,
where signals from too many cell sites are present.

When compared to GSM lack of international roaming capabilities

Ability to upgrade or change to another handset is not easy with
this technology because the network service information for the
phone is put in the actual phone unlike GSM which uses SIM
card.

limited variety of the handset

4. Explain near far interference?

The near-far problem occurs when many mobile users share
the same channel. In general, the strongest received mobile signal will
capture the demodulator at a base station. In CDMA, stronger
received signal levels raise the noise floor at the base station
demodulators for the weaker signals, thereby decreasing the
probability that weaker signals will be received.

5. Give the features of CDMA.

The following features are unique to CDMA technology:

Universal frequency reuse

Fast and accurate power control

Rake receiver

Different types of handoff

6. What is meant by rake receiver and its uses?

A rake receiver is a radio receiver designed to counter the
effects of multipath fading. It does this by using several "sub-
receivers" called fingers, that is, several correlators each assigned to a
different multipath component. Each finger independently decodes a
single multipath component; at a later stage the contribution of all
fingers are combined in order to make the most use of the different
transmission characteristics of each transmission path. RAKE

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receivers are used to resolve and combine multipath components,

thereby reducing the degree of fading

7. What is anti jam military communication?

The receiver correlates the received signals to retrieve the
original information signal. It is either to resist enemy efforts to jam
the communications and it is called anti-jam. It is to hide the fact that
communication was even taking place

8. What are the methods to improve the capacity of cellular CDMA?

The first technique for reducing interference is anterma
sectorization. The second technique involves the monitoring of voice
activity such that each transmitter is switched off during periods of no
voice activity.

9. What is LPI? What are the advantages?

SS signal is generally difficult to detect and even harder to
decipher by an unauthorized receiver: this characteristic is usually
referred to as a low probability of intercept (LPI).Most interceptors
operate as energy detectors, and they have to monitor the received
signal long enough to achieve a sufficiently high signal-to-noise ratio
(SNR) for reliable detection in the presence of background noise.

The LPI advantage of an SS signal is that its power is spread

over a bandwidth considerably larger than conventional
transmissions, significantly increasing the noise in a receiver that is
not privy to the despreading sequence.

10. What are frequency followers?

When implementable FH systems operated at low hop rates,
their transmissions could conceivably be detected by narrowband
monitors capable of following the pseudorandom frequency variations
called “frequency followers” It is used to drive repeat-back jammers
which could effectively defeat the AJ capability of FH systems.

11. Give the uplink and downlink frequency of satellite system.

6/4 GHz and 14/12 GHz where 6GHz and 14GHz are
uplink frequencies and 4GHz and 12GHz are downlink
frequencies.

12. What is uplink and downlink?

A forward link is the link from a fixed location (e.g., a base
station) to a mobile user. If the link includes a communications relay
satellite, the forward link will consist of both an uplink (base station
to satellite) and a downlink (satellite to mobile user).
The reverse link (sometimes called a return link) is the link
from a mobile user to a fixed base station. If the link includes a
communications relay satellite, the reverse link will consist of both an
uplink (mobile station to satellite) and a downlink (satellite to base
station) which together constitute a half hop.

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13. What is satellite?

Satellite is a celestial body that orbits around a planet. In
aerospace terms, satellite is a space vehicle launched by humans and
orbits earth or another celestial body.

14. What are transponders?

A transponder is a wireless communications, monitoring, or
control device that picks up and automatically responds to an
incoming signal. The term is a contraction of the words transmitter
and responder. Transponders can be either passive or active.

15. What are the types of satellite?

A passive satellite simply reflects a signal back to earth and there
are no gain devices on broad to amplify signal.

An active satellite receives, amplifies and retransmits signal back
towards earth.

16. What are the benefits offered by SS for satellite communication?

SS may offer the following benefits for satellite
communications:

Rejection of uncorrelated interference permits system operation
where adjacent satellites (say at 1.5° spacing in the geostationary
arc) may lie within the beamwidth of a small-terminal antenna.
This may facilitate operation with small antennas at C-band, with
its relatively longer wavelength and correspondingly large
beamwidth.

Other link interference, multipath and adjacent channels may be
similarly tolerated, thereby facilitating operation in shared bands.

17. What are the channels in forward CDMA channel? Explain the
function of all three channels.
The pilot channel allows a mobile station to acquire timing for
the Forward CDMA channel, provides a phase reference for coherent
demodulation, and provides each mobile with a means for signal
strength comparisons between base stations for determining when to
handoff'. Synchronization channel broadcasts synchronization
messages to mobile stations and operates at 1200 bps. The paging
channel is used to send control information and paging messages
from the base station to the mobiles and operates at 9600, 4800, and
2400bps. The forward traffic channel (Fit) supports variable user data
rates at 9600, 4800, 2400, or 1200 bps.

18. What is QCELP?

QCELP (Qualcomm Code Excited Linear Prediction), also
known as Qualcomm PureVoice, is a speech codec developed in 1994
to increase the speech quality of the IS-96A codec used earlier in
CDMA networks. It provides better speech quality with fewer bits.

19. What is data scrambling?

Data scrambling is the process of obfuscating or removing
sensitive data, and can be used by functional administrators and
database administrators when cloning an environment that contains
sensitive information.

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20. What are Walsh codes?

Walsh Code is a group of spreading codes having good
autocorrelation properties and poor cross correlation properties.
Walsh codes are the backbone of CDMA systems and are used to
develop the individual channels in CDMA.

21. What is masking?

Masking is the technique of producing external "white noise"
sounds that will mask the tinnitus and make it less distracting. It is
used in CDMA PN long code sequence generation.

22. What are the types of masking used in long code generator?
Two types of masks are used in the long code generator: a
public mask for the mobile station's electronic serial number (ESN)
and a private mask for the mobile station identification number (MIN).
All CDMA calls are initiated using the public mask.

23. What is hadamard matrix?

Hadamard matrix is a square matrix whose entries are either
+1 or −1 and whose rows are mutually orthogonal. In geometric
terms, this means that every two different rows in a Hadamard matrix
represent two perpendicular vectors, while in combinatorial terms, it
means that every two different rows have matching entries in exactly
half of their columns and mismatched entries in the remaining
columns.

24. What is the purpose of data randomizer?

A data randomizer is used to transmit certain bits while
turning the transmitter off at other times. When the data rate is 9600
bps, all interleaver output bits are transmitted. The data burst
randomizer ensures that every repeated code symbol is transmitted
exactly once.

25. How near-far effect is is controlled in CDMA?

To combat the near-far problem, power control is used in most
CDMA implementations. Power control is provided by each base
station in a cellular system and assures that each mobile within the
base station coverage area provides the same signal level to the base
station receiver. This solves the problem of a nearby subscriber
overpowering the base station receiver and drowning out the signals
of far away subscribers.

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UNIT-I
INTRODUCTION

1.1 Origins of Spread Spectrum Communications

A spread spectrum system is one in which the transmitted signal is spread

over a wide frequency band, much wider than the minimum bandwidth required to
transmit the information being send. Initially, Spread Spectrum was known as
Noise Modulation. This was because the spread spectrum signals look more like a
noise to an ordinary AM/FM receivers due to spreading of signals over a large
bandwidth (typically several 1000 times the signal bandwidth). Spread Spectrum
techniques were used initially for military communications due to inherent coding
(encryption) of SS Communications System. Modern military communications
systems are increasingly adapting the digital method of transmitting information.
There was intensive use of communications warfare during World War II. This
technique outlined the ability to intercept and interfere with hostile
communications. Consequently, this procedure stimulated a great deal of interest
which led to the development of secure communications systems and work in this
field was carried out on two fronts. Firstly, development in communication theory
initiated encryption schemes introduced by Shannon in the year 1949, to provide
certain information protection. Secondly, work was initiated to harness the
development of a new technology. This technology is called the Spread-Spectrum
techniques introduced by Scholtz in the year 1982, which exchanges bandwidth
expansion for communications security and targets ranging for military
applications.

By the end of the war, the theory of spread-spectrum techniques had

developed and its anti-jamming capability had been recognized. Communication
systems were developed by the military establishments during the 1960s, using
frequency hopping and pseudo-noise spread-spectrum schemes. An interesting
system was also developed which combines pseudo-noise spread spectrum with
Fourier transform (Goldberg, 1981). This is conceptually similar to the
contemporary multicarrier spread-spectrum schemes. Work on spread spectrum
during the 1970s prompted commercial use of the spread spectrum techniques and
theoretical work on spread spectrum systems revealed the new system’s ability to
offer multiple access communications at an increased capacity compared to the
time division or frequency division schemes of that time. The RAKE receiver
concept was developed to further accelerate the implementation of the systems. By
the end of the decade, commercial applications of spread spectrum had become a
reality.

The 1980s witnessed the development of the Global System for Mobile
Telecommunications (commercially known as GSM) system, and a slow frequency
hopping concept from spread spectrum technique was implemented in the GSM
systems to randomize the affects of interference from multiple users accessing the
GSM network. The first trial of commercial spread spectrum system with multiple

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access capabilities was carried out by Qualcom in the USA in 1993. The Qualcom’s
system was built according to the interim standard IS-95. The first commercial
cellular radio phone service based on spread spectrum was inaugurated in Hong
Kong in 1995. Korea and the USA soon introduced similar services. During the
1990s, the spread-spectrum technique was further developed into ‘multicarrier
techniques’ providing a higher diversity gain against deep fade than a single carrier
spread-spectrum system could provide. The spread spectrum multicarrier
technique is based upon low rate data transmission over orthogonal frequency
division multiplexing. This scheme generates multiple copies of the conventional
spread spectrum, each copy is transmitted on a separate carrier. Finally, the
development of spread-spectrum proved high data rate for the next generation of
communication networks.

1.2 Spread Spectrum System Criteria

For a system to be described as a spread spectrum system the following two
criteria must be satisfied:
i. The transmitted signal must occupy a bandwidth much greater than the
bandwidth of the modulating signal (i.e. the input signal to the system).
ii. The bandwidth occupied by the transmitted signal must be determined by a
prescribed waveform and not by the modulating frequency (i.e. carrier
frequency)

1.3 Reasons for use of Spread Spectrum Systems

There are three major reasons for the use of spread spectrum techniques in
communication systems today.
i. They aid privacy of the transmission, since the spectral density of the spread
spectrum may be less than the noise spectral density of the receiver.
ii. The de-spreading process in the receiver will spread the spectra of unwanted
narrowband signals, thus improving interference rejection.
iii. The effect on a spread spectrum receiver, that receives a spread spectrum
from a different spread spectrum system using the same frequency bands
but implementing a different spreading pattern, approximates to noise in the
receiver.

1.4 Advantages of spread-spectrum technology

1.4.1 Avoiding interception

In military communications, interception of hostile communications is
commonly used for various operations such as identification, jamming, surveillance
or reconnaissance. The successful interceptor usually measures the transmitted
power in the allocated frequency band. Thus, spreading the transmitted power over
a wider band undoubtedly lowers the power spectral density, and thus hides the
transmitted information within the background noise. The intended receiver
recovers the information with the help of system processing gain generated in the
spread process. However, the unintended receiver does not get the advantage of the
processing gain and consequently will not be able to recover the information.

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Because of its low power level, the spread spectrum transmitted signal is said to be
a Low Probability of Interception (LPI) signal.

1.4.2 Privacy of transmission

The transmitted information over the spread-spectrum system cannot be
recovered without knowledge of the spreading code sequence. Thus, the privacy of
individual user communications is protected in the presence of other users.
Furthermore, the fact that spreading is independent of the modulation process
gives the system some flexibility in choosing from a variety of modulation schemes.

1.4.3 Resistance to fading

In a multipath propagation environment, the receiver acquires frequent
copies of the transmitted signal. These signal components often interfere with each
other causing what is commonly described as signal fading. The resistance of the
spread-spectrum signals to multipath fading is brought about by the fact that
multipath components are assumed to be independent. This means that if fading
attenuates one component, the other components may not be affected, so that un
faded components can be used to recover the information.

1.4.4 Accurate low power position finding

The distance (range) between two points can be determined by measuring
the time in seconds, taken by a signal to move from one point to the other and
back. This technique is exploited in the Global Positioning System (GPS). Since the
signal travels at the speed of light (3×108 metres/sec),




Range in metres = 3×108

It is clear from the above expression that the accuracy of the transit time
measurement determines the ultimate range accuracy. In practice, the transit time
is determined by monitoring the correlation between transmitted and received code
sequences. The transit time can be computed by multiplying the code duration by
the number of code bits needed to align the two sequences. Clearly, higher
resolution requires code symbols to be narrow which means high code rates. Thus,
the sequences are selected to provide the required resolution so that if the code
sequence has N chips, each with duration Tc seconds, then
Maximum range = 1.5 NTc —108 metres
The range resolution requires the chip duration Tc to be small so that sequence
chip rate is as high as possible. On the other hand, maximum range requires a long
sequence (i.e. N is large) so that many chips are transmitted in a single sequence
period.
Similarly, in radar systems use of the signal to measure propagation delay
which determine the position and direction of targets.

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1.4.5 Low transmit power density function per Hertz

This helps the spectral contamination issue making it easier to comply
with regulatory requirements. In addition, the interference generated from each
operating channel to others is reduced.

1.4.6 Interference rejection capability

This provides a performance advantage over classical narrowband
transmissions due to the fact that spread spectrum systems are more immune to
interference sources.

1.4.7 Improved multiple access scheme

Multiple access schemes are designed to facilitate the efficient use of a
given network resource by a group of users. Conventionally, there are two schemes
in use: the Frequency Division Multiple Access (FDMA) and the Time Division
Multiple Access (TDMA). In FDMA, the radio spectrum is shared between the users
such that a fraction of the channel is allocated to each user at a time. On the other
hand, in TDMA, each user is able to access the whole of the spectrum at a unique
time slot. The spread spectrum offers a new network access scheme due to the use
of unique code sequences. Users transmit and receive signals with access
interference that can be controlled or even minimized. This technique is called Code
Division Multiple Access (CDMA). Code Division Multiple Access schemes that allow
for simultaneous transmission of more than one signal. Communication security or
less expensive privacy protection aspects are also important to commercial
networks. The primary spread spectrum waveforms are Frequency Hoping (FH)
and Direct Sequence (DS) spread spectrum. Both of these techniques capitalize on
the utilization of a wide frequency bandwidth for their communications in order to
extract the stated benefits.

1.5 Types of techniques used for spread spectrum

A large number of users communicate with each other via the public mobile
communication system provided by a number of operators. The number of
simultaneous users is generally limited by the bandwidth each operator is assigned
and by the multiple-access technology used. Each operator is usually allocated a
certain bandwidth, which it uses to serve as large a number of simultaneous users
as possible. Several multiple-access techniques have been used in mobile
communications. The first-generation systems such as AMPS were based on the
FDMA technology. The second-generation systems, such as GSM, were based on
the TDMA technology. And the third-generation systems are based primarily on the
CDMA technology. This section gives a general overview of spread spectrum
modulation techniques. Based on this a basic Introduction is made to the CDMA
systems.

The spread spectrum communications technique is characterized by its use of

the frequency spectrum in that the spectrum of the transmitted signal is spread
over a very wide bandwidth a bandwidth exceeding that normally required
accommodating the information to be transmitted. This is categorized by two of the

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most widely used methods of direct sequence spread spectrum (DS-SS) and
frequency-hopping spread spectrum (FH-SS). In both of these methods, a
pseudorandom code sequence is utilized to spread or map the signal information
over a wide bandwidth. Most TDD-CDMA systems use the latter, although the
former is used in a number of communication systems such as GSM. Here we deal
with FH-SS technology only briefly and instead concentrate on the DS-SS mode,
which forms the basis for UMTS standards. The principle behind the spreading of a
signal is explained by the Shannon channel capacity formula:
 S
C = Bw log 2  1 + 
 N
where C is the capacity of a communication channel in bits per hertz, Bw is the
bandwidth in hertz, S is the signal power, and N is the noise power.
C  S
= 1.44 ln  1 + 
Bw  N
which at small SNRs can be approximated as follows:
C S NC
= 1.44 or Bw ≈
Bw N S
It demonstrates that as the relative noise level increases, reliable transmission is
possible by increasing bandwidth.

There are three ways to spread the bandwidth of the signal:

• Frequency hopping: The signal is rapidly switched between different

frequencies within the hopping bandwidth pseudo-randomly, and the receiver
knows beforehand where to find the signal at any given time.
• Time hopping: The signal is transmitted in short bursts pseudo-randomly, and
the receiver knows beforehand when to expect the burst.
• Direct sequence: The digital data is directly coded at a much higher frequency.
The code is generated pseudo-randomly, the receiver knows how to generate the
same code, and correlates the received signal with that code to extract the data.

1.5.1 Frequency Hop Spread Spectrum ( FH-SS )

Figure 1.1 Block diagram of an FH-SS transmitter

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An FH-SS system is similar to a frequency shift keyed (FSK) modulation. The

difference is that in FSK systems two frequency tones are used for the modulation
of 1 and 0 information, whereas in FH-SS a code-generator-controlled frequency
synthesizer is used to sequentially modulate the information onto a very large set of
frequency tones. The set of tones can be very large; an actual system is reported to
have 220different frequencies.

Figure 1.2 Block diagram of an FH-SS receiver

A simple block diagram of a BPSK FH-SS transmitter and receiver is shown

in Figure 1.1 and 1.2. The code-controlled oscillator sequentially modulates the
information onto a plane of frequencies. Because a very large number of
modulating frequencies are used, the signal spectrum is spread over a very wide
bandwidth. The BPSK modulated signal, represented by d(t), is equal to:
d ( t ) = 2 Pb(t ) exp( J ωt )
where P is the transmitted power, b(t) is the data stream consisting of a train of
data bits with duration Tb and which take the values of ±1 with equal probability,
ω=2πf is the carrier frequency, and J = −1 . The spreading hopping sequence is
the sum of a sequence of tones with a chip time duration Tc . It is represented by Ψ
(t) and is written as follows:
∞
ψ (t ) = ∑ 2 p ( t − nT ) exp( J ωt + jφ )
n =−∞
c n

where p(t) is a unit amplitude pulse of duration Tc and ωn and φ n are, respectively,
the radian frequency and its associated phase during the nth hop. The transmitted
signal can be written as
x ( t ) = d ( t )ψ ( t )
The received signal y (t) is the multiplication of the transmitted signal and the
channel impulse response h(t), summed with a noise term n(t):
y (t ) = x (t ) h (t ) + n (t )
where δ is the propagation delay of the channel. At the receiver, a replica of the
spreading frequencies Ψ(t) is generated to de-spread the frequency hopped signal.
The product of ψ (t − δˆd )ψ (t − δ d ) is equal to 1 after the band-pass filter if δˆd can be
estimated to be equal to δ d . If the delay is estimated accurately, then the
multiplication will remove the FH component and result in the original baseband

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signal. Based on the hopping rate, the FH-SS systems are classified into two
different groups. If the frequency hop occurs at every few bit intervals, system is
called a slow frequency hopping spread spectrum (SFH-SS) system, but if many
hops occur during a bit period, system is known as a fast frequency hopping
spread spectrum (FFH-SS) system.

Figure 1.3 A frequency versus time diagram of the two different types of
FH-SS terms (a) SFH-SS and (b) FFH-SS

1.5.2 Direct Sequence Spread Spectrum ( DS-SS )

A simple block diagram of a BPSK DS-SS system is shown in Figure 1.4. The
BPSK modulated data, represented by d(t), is spread after multiplication by a
pseudorandom (PN) sequence with a bandwidth much greater than the information
signal.

Figure 1.4 Block diagram of a DS-SS transmitter

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The transmitted signal x(t) can be expressed as

x ( t ) = 2 Pb(t )a(t ) exp( J ωt )
where a(t) is the spreading PN sequence with chips of ±1 of duration and code
length of N = Tb/Tc . The signal spectrum at various stages of transmission is
shown in Figure 1.5. As an information signal is multiplied by the PN sequence, its
energy is spread over a wide bandwidth while the total signal energy remains
constant. If the spreading ratio is large enough, the spread signal appears as very
low power
noise.

Figure 1.5 Signal spectrum of a DS-SS modulation before and after spreading

Figure 1.6 Block diagram of DS-SS receiver

a(t) is the spreading PN sequence with chips of ±1 of duration and code length of N
= Tb/Tc. As an information signal is multiplied by the PN sequence, its energy is
spread over a wide bandwidth while the total signal energy remains constant. If the
spreading ratio is large enough, the spread signal appears as very low power noise.
A block diagram of a DS-SS receiver is shown in Figure 1.6.

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The received signal y(t) is expressed as

y (t ) = h (t ) x (t − δd ) + n (t )
where h(t) represents the propagation channel impulse response, including
multipath fading, shadowing, and path loss; δd is the channel propagation delay;
and n(t) is zero mean additive white Gaussian noise (AWGN) with a two-sided power
spectral density of N0/2.
y ( t ) = h ( t ) 2 Pb ( t − δ d ) a ( t − δ d ) exp  J ω ( t − δ d )  + n ( t )

The received signal y(t) multiplied by a delayed replica of the spreading

( )
sequence a t − δˆd , where δˆd is a local estimate of the propagation delay δd .

( ) ( )
dˆ ( t ) = 2 Pb(t )b ( t − δ d ) a ( t − δ d ) a t − δˆd exp  J ω ( t − δ d )  + a t − δˆd n ( t )

The despreading of signal y(t) is realized if δˆd can be estimated at the receiver

to be equal to δ d , in which case a ( t − δ d ) a ( t − δˆd ) = 1. Noise power remains

unchanged.

The DS-SS signal can be despread by a matched filter. In a matched filter,

the received signal is fed to a delay line, which consists of shift registers operating
at chip clock rate. A locally generated replica of the spreading sequence multiplies
the output of the shift registers. The results are summed, so when there is a match
between the input signal and the spreading sequence, the output is large.
Otherwise the output is minimal and depends on the autocorrelation and cross-
correlation properties of the PN code. In practice, less than perfect synchronization
between the received signals’s spreading phase and the locally generated spreading
signal’s phase results in loss of performance, assuming that the receiver can
perfectly estimate the delay and phase and therefore perfectly despread the
received signal. The output of the matched filter is a signal with the pre spreading
band-width. All other signals that are spread with different PN sequences remain
wideband, and most of their energy will be filtered out. This is the basis for the
CDMA systems, where different users are assigned a different spreading code. All
signals are then transmitted at the same carrier frequency and are distinguished at
the receiver by their unique spreading code.

The increase in the received signal level, caused by despreading, is defined

as process gain, Gp , of the spread spectrum systems and is equal to the bandwidth
ratio of the spread signal and the narrowband (before spreading) signal:

BWs Ts
Gp = =
BWn Tc
where Ts is the symbol period and Tc is the chip period.

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1.5.3 Advantages and Disadvantages of Spread Spectrum Techniques

The advantages of spread spectrum techniques as applied to communication

systems can be as follows:

All types: Multiple usage by different user groups, as each user group can be
allocated a different PN code.

This code is the key necessary to unlock the message from the system. Without this
key it is very difficult, almost impossible to extract the information.

A spread spectrum will see another spread spectrum signal as interference and
reject it as it would for a narrowband signal.

Frequency hopping: A narrow band will only cause minimal interference on the
wideband signal. Frequency jamming is extremely difficult and can only be
effectively achieved if the jamming receiver has the same PN code and channel
allocation.

The greater the hop set, the smaller the dwell time and the greater the bandwidth
the smaller the interference from narrowband signals.

Frequency hopping and direct sequence: The output power of the spread
spectrum is spread over a large bandwidth. This means that the spectrum has a
very low spectral density; 1W output power over an 8 MHz band gives a spectral
density of 125 nW/Hz.

These systems are particularly useful to the military and police. The low spectral
density may not even be recognized as valid communication, thus leading to low
probability of interception and recognition.

Disadvantages of spread spectrum techniques are:

All types:

• Complex circuitry
• Expensive to develop
• Very large bandwidth

Time hopping: Easily jammed and hence is not generally used in its true form.

Fundamental Parameters

i. Hop set: Number of channels that are used by the system (i.e. number of
different frequencies utilised).

ii. Dwell time: The length of time that the system transmits on an individual
channel (i.e. the length of time spent on one frequency).

iii. Hop rate: The rate at which the hopping takes place (i.e. how fast the system
changes from one channel to another or from one frequency to another).

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1.5.4 Time Hopping

A typical time hopping signal is illustrated in the figure below. It is divided

into frames, which in turn are subdivided into M time slots. As the message is
transmitted only one time slot in the frame is modulated with information (any
modulation). This time slot is chosen using PN generator. All of the message bits
gathered in the previous frame are then transmitted in a burst during the time slot
selected by the PN generator. If we let: T f = frame duration, k = number of message
Tf
bits in one frame and T f = k .tm , then the width of each time slot in a frame is and
M
Tf tm
the width of each bit in the time slot is or just . Thus, the transmitted
kM M
signal bandwidth is 2M times the message bandwidth.

Figure 1.7 Block diagram of a time hopping receiver

A typical time hopping receiver is shown in Figure 1.7. The PN code

generator drives an on-off switch in order to accomplish switching at a given time
in the frame. The output of this switch is then demodulated appropriately. Each
message burst is stored and re-timed to the original message rate in order to
recover the information. Time hopping is at times used in conjunction with other
spread spectrum modulations such as DS or FH. Table 1.1 presents a brief
comparison of major features of various SS schemes.

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Table 1.1 Comparison of features of various spreading techniques

SPREADING
MERITS DEMERITS
METHOD

i) Simpler to implement
i) Code acquisition may be
ii) Low probability of difficult
Direct interception
ii) Susceptible to Near-Far
Sequence
iii) Can withstand multi- problem
access interference
iii) Affected by jamming
reasonably well

i) Less affected by Near-Far

i) Needs FEC
Frequency problem
Hopping ii) Frequency acquisition may be
ii) Better for avoiding
difficult
jamming

i) Elaborate code acquisition is

i) Bandwidth efficient
Time Hopping needed.
ii) Simpler than FH system
ii) Needs FEC

1.5.5 Hybrid System: DS/(F) FH

The DS/FH Spread Spectrum technique is a combination of direct-sequence

and frequency hopping schemes. One data bit is divided over several carrier
frequencies (Figure 1.8).

Figure 1.8 A hybrid DS-FH spreading scheme

As the FH-sequence and the PN-codes are coupled, a user uses a

combination of an FH-sequence and a PN-code.

Features of Spreading Codes

Several spreading codes are popular for use in practical spread spectrum
systems. Some of these are Maximal Sequence (m-sequence) length codes, Gold
codes, Kasami codes etc.

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1.6 JAMMING CONSIDERATIONS

1.6.1 The Jamming Game

The goals of a jammer are to deny reliable communications to his adversary
and to accomplish this at minimum cost. The goals of the communicator are to
develop a jam-resistant communication system under the following assumptions:
(1) Complete invulnerability is not possible;
(2) Jammer has a priori knowledge of most system parameters, such as frequency
bands, timing, traffic so on.
(3) the jammer has no a priori knowledge of the PN spreading or hopping codes.
The signalling waveform should be designed so that the jammer cannot gain any
appreciable jamming advantage by choosing a jammer waveform and strategy other
than wideband Gaussian noise (i.e., being clever should gain nothing for the
jammer). The fundamental design rule in specifying a jam-resistant system is to
make it as costly as possible for the jammer to succeed in jamming the system.

1.6.2 Jammer Waveforms

There are many different waveforms that can be used for jamming
communication systems. The most appropriate choice depends on the targeted
system. Figure 1.9 shows power spectral density plots of examples of jammer
waveforms versus a communicator's frequency hopped M-ary FSK (FH/MFSK)
tone. The range of the abscissa represents the spread-spectrum
bandwidth W. The three columns in the figure represent three
instances in time (three hop times) when symbols having spectra
G1, G2, and G3, respectively, are being transmitted.

Figure 1.9 Jammer waveform (a) Full-band noise (b) Partial-band noise
(c) Stepped noise (d) Partial-band tones (e) Stepped tones

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Figure 1.9a illustrates a relatively low-level noise jammer occupying the full
spread spectrum bandwidth. In Figure 1.9b the jammer strategy is to trade
bandwidth occupancy for greater power spectral density (the total power, or area
under the curve, remains the same). The figure indicates that in this case, the
jammer noise does not always share the same bandwidth region as the signal, but
when it does, the effect can be destructive. In Figure 1.9c the noise jammer
strategy is again to jam only part of the band, so that the jammer power spectral
density can be in-creased, but in this case the jammer steps through different
regions of the band at random times, thus preventing the communicator from
using adaptive techniques to avoid the jamming. In Figure 1.9d and e the jammer
uses a group of tones, in-stead of a continuous frequency band, in partial-band
(Figure 1.9d) and stepped fashion (Figure 1.9e). This is a technique most often
used against FH systems. Another jamming technique, not shown in Figure 1.9, is
a pulse jammer, consisting of pulse-modulated band limited noise. Unless
otherwise stated, we shall assume that the jammer waveform is wideband noise
and that the jammer strategy is to jam the entire bandwidth Ws continuously. The
effects of partial band jamming and pulse jamming are considered later.

1.6.3 Tools of the Communicator

i. The usual design goal for an anti-jam (AJ) communication system is to force
a jammer to expend its resources over a wide-frequency band,
ii. for a maximum time, and
iii. From a diversity of sites.
The most prevalent design options are
i. frequency diversity, by the use of direct-sequence and frequency-hopping
spread-spectrum techniques;
ii. time diversity, by the use of time hopping;
iii. spatial discrimination, by the use of a narrow-beam antenna, which forces a
jammer to enter the receiver via an antenna side lobe and hence suffer,
typically, a 20- to 25-dB disadvantage, and (Combinations of the previous
three options).
Eb
Emphasis was placed on the signal-to-noise ratio parameters-required
N0
Eb
and available
N
0 for meeting a specified error performance. In this section we

are similarly concerned with link error performance as a function of interference.

However, here the source of interference is assumed to be wideband Gaussian
noise power from a jammer in addition to thermal noise. Therefore, the SNR of
interest is
Eb
( N0 + J 0 )
where JO is the noise power spectral density due to the jammer. Unless otherwise
specified, Jo is assumed equal to .W, where J is the average received jammer power
(jammer power referred to the receiver front end) and Ws, is the spread-spectrum

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bandwidth. Since the jammer power is generally much greater than the thermal
noise power, the SNR of interest in a jammed environment is usually taken to be
Eb  Eb 
 
J 0 therefore, similar to the thermal noise case, we define  J 0 reqd as the
bit energy per jammer noise power spectral density required for maintaining the
link at a specified error probability. The parameter Eb can be written as
S
Eb = STb =
R
 S 
 Eb   R 
  = J 
 J 0  reqd  Wss  reqd

where S is the received signal power, Tb the bit duration, and R the data rate in
bits/s. Then we can express as

 Eb 
 J 
 0  reqd

 S  Wss
 Eb   R  = R = Gp
  = J
 J 0  reqd  W 


ss  reqd
J
S reqd
( )
J
S reqd ( )
where
Gp =
W ss
R represents the processing gain, and
(J S) reqd
can be written

(J S)
Gp
=
reqd  Eb 
 
 J 0  reqd

The ratio reqd

(J S)
is a figure of merit that provides a measure of how
invulnerable a system is to interference.

The larger the reqd

(J S)
, greater is the system's noise rejection capability, since
this figure of merit describes how much noise power relative to signal power is
required in order to degrade the system's specified error performance. Of course,
communicator would like the communication system not to degrade at all.

Another way of describing the relationship is as follows. An adversary would

like to employ a jamming strategy that forces the effective
Gp
 Eb 
 
 J 0 reqd to be as large as possible. The adversary may employ pulse, tone, or

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partial-band jamming rather than wideband noise jamming. A large

Gp
 Eb 
 
 J 0  reqd

implies a small
( J )
S
reqd
ratio for a fixed processing again. This may force the
communicator to employ a larger processing gain to increase the

(J S) reqd
. The system designer strives to choose a signaling waveform such
that the jammer can gain no special advantage by using a jamming strategy other
than wideband Gaussian noise.

1.6.4 Anti-Jam Margin

Sometimes the
( J )
S reqd
ratio is referred to as the anti-jam (AJ) margin, since it
characterizes the system jammer-rejection capability. But this is not really a good
use of the phrase since AJ margin usually means the safety margin against a
particular threat we can define the AJ margin as

E  E 
M AJ ( dB ) =  b  ( dB ) −  b  ( dB )
 J 0 r  J 0  reqd

Figure 1.10 Satellite jamming scenario

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 Eb   Eb 
where   is the   actually received. We can express
 J 0 r  J0 
 Eb 
  as
 J 0 r
 Eb  Gp
  =
 J 0 r J( )
S r

where J ( S ) , or simply ( J S ) , is the ratio of the actually received jammer power to

r

Eb
signal power. Later, we develop an expression for received , where Io is the
I0
interference power spectral density due to other users in a CDMA cellular system.
The concept of computing such a bit-energy to interference ratio is the same,
whether the interference stems from a jammer, an accidental interferer, or other
users who are authorized to share the same spectral region.
Gp Gp
M AJ (dB) = (dB ) − (dB)
( )
J
S r
J( )
S reqd

J J
=   (dB) −   (dB)
 S  reqd  S r

1.6.5 Broadband Noise Jamming

If the jamming signal is modeled as a zero-mean wide-sense stationary
Gaussian noise process with a flat power spectral density over the frequency range
of interest, then for a fixed jammer received power, J, the jammer power spectral
density J o′ is equal to J/W, where W is the bandwidth that the jammer chooses to
occupy. If the jammer strategy is to jam the entire spread-spectrum bandwidth,
Wss, with its fixed power, the jammer is referred to as a wideband or broadband
jammer, and the jammer power spectral density is
J
J0 =
Wss

We know that bit error probability

PB for a coherently demodulated BPSK
system (without channel coding) is

 2 Eb 
PB = Q  
 N0 
The single-sided noise power spectral density No represents thermal noise at the
front end of the receiver. The presence of the jammer increases this noise power
spectral density from No to (No + J0). Thus the average bit error probability for a
coherent BPSK system in the presence of broadband jamming is

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 2 Eb 
PB = Q  
 N 0 + J0 
 E 
 2 b
No 
= Q 
 1 +  Eb  ( J S ) 
  N  G 
  o  p 
Eb
When PB is plotted versus for a given J/S ratio, shown for two different
N0
Eb
values of processing gain, tend to flatten out as increases, indicating that for a
N0
given ratio of jammer power to signal power, the jammer will cause some
irreducible error probability. The only way to reduce this error probability is to
increase the processing again.

Eb
Figure 1.11 Bit-error probability versus for a given J ratio.
N0 S

1.6.6 Partial-Band Noise Jamming

A jammer can often increase the degradation to a FH system by employing
partial-band jamming. Assuming that the frequency hopped modulation format is
non coherently detected binary FSK, the probability of a bit error is

1  E 
PB = exp  − b 
2  2N0 
Let us define a parameter, ρ, where 0 < ρ <- 1, representing the fraction of
the band being jammed. The jammer can trade bandwidth jammed for in-band
jammer power, such that by jamming a band W = ρ Wss, the jammer noise power
spectral density can be concentrated to a level Jo/ ρ, thus maintaining a constant
average jamming received power J where J = JoWss.

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In the case of partial-band jamming, a specific transmitted symbol will be

received unjammed, with probability (1 - ρ), and will be perturbed by jammer power
with spectral density Jo/ ρ, with probability ρ. Therefore, the average bit error
probability can be written as follows,

1− ρ  E  ρ  Eb 
PB = exp  − b  + exp  − 
2  2N0  2  2 ( N0 + J0 ρ ) 

Since, in a jamming environment, it is often the case that Jo >> No.

ρ  ρE 
PB ≈ exp  − b 
2  2 N0 

Figure 1.12 Partial band noise jammer

Eb
Figure 1.12 illustrates the probability of bit error versus J 0 for various values of
the fraction, ρ clearly, jammer would choose the fraction ρ = ρo that maximizes PB.
Notice that ρo decreases with increasing values of

Eb
(see the locus in Figure 1.12). An expression for ρo is easily found by
J0

dPB
differentiation (setting = 0 and solving for p). This yield
dρ

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where e is the base of the natural logarithm (e = 2.7183). This result is dramatic,
the effect of a worst-case partial-band jammer on a system with spread spectrum
but without coding changes the exponential relationship into the inverse linear.
The ρo locus in the PB vs Eb\J0 performance for the worst-case partial-band
jammer. Here at 1ow-bit-error probability there is over 40-dB difference between
broadband noise jamming and the worst-case partial-band jamming for the same
jamming power. Hence, an intelligent jammer, with fixed finite power, can
produce significantly greater degradation with partial-band jamming than is
possible with broadband jamming. Forward error correction (FEC) coding with
appropriate interleaving can mitigate this degradation . In fact, for codes with low
enough rates, FEC can force a partial-band jammer to be a worst-case jammer
only when operating as a broadband jammer.

1.6.7 Multiple-Tone Jamming

In the case of multiple-tone jamming, the jammer divides its total received
power, J. into distinct, equal-power, random-phase CW tones. These are
distributed over the spread-spectrum bandwidth, Wss, according to some strategy
[9]. The analysis of the effects of tone jamming is more complicated than that of
noise jamming, especially for DS systems. Therefore, the effect of a despread tone
is often approximated as Gaussian noise. Analysis of the performance of DS
systems in the presence of multiple-tone interference. For a non-coherent FH/FSK
system operating in the presence of partial-band tone jamming, the performance is
often assumed the same as that of partial-band noise jamming. However, multiple-
CW-tone jamming can be more effective than partial-band noise against FH/MFSK
signals because CW tones are the most efficient way for a jammer to inject energy
into non-coherent detectors. The function of such a circuit in a tone-jamming
environment can best be understood with the aid of the example shown in Figure
1.13. An 8-ary FSK frequency-hopping system with no diversity, indicated in
Figure 1.13a, is compared with a fast frequency-hopping system that combines
chip repeating (N = 4 in this example) with the clipping of each chip, indicated in
Figure 1.13b. Each row in the figures represents one of the M = 8 accumulators.
The presence of a signal in the accumulator is indicated by a vector. In Figure
1.13a we see that, for a particular frequency hop, the data band is occupied by a
received message symbol with received signal power S. If, by chance, a jamming
tone with received power J, where J ≥ S, falls on a different tone within this data
band during the same hop, the detector would not be able to decide reliably on the
correct symbol.

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Figure 1.13 Fast-hopping symbol repeat versus tone jamming

(a) One frequency hop (b) Four frequency hops
In Figure 1.13b, the communicator's four chips (the length of each vector is a
measure of the clipped signal power, S') sum to the maximum capacity of the
accumulator. If the jammer tones, by chance, fall in the same spectral region as
that of the signal, they will not confuse the detector, since the jamming tones are
also clipped to the same level, J' = S', as the signal chips. In Figure 1.13b, two of
the jamming tones fall in the data band, but because they are clipped, there is no
confusion about the correct symbol decision.

1.6.8 Pulse Jamming

Consider a spread-spectrum DS/BPSK communication system in the
presence of a pulse-noise jammer. A pulse-noise jammer transmits pulses of band
limited white Gaussian noise having a time-averaged received power J, although
the actual power during jamming pulse duration is larger. Assume that the jammer
can choose the center frequency and bandwidth of the noise to be the same as the
receiver's center frequency and bandwidth. Assume also that the jammer can trade
duty cycle for increased (concentrated) jammer power, such that if the jamming is
present for a fraction 0 < p < 1 of the time, then during this time, the jammer power
spectral density is increased to a level Jo/p, thus maintaining a constant time
averaged power J (where J = JOWss and Ws is the system spread-spectrum
bandwidth).
The bit error probability PB for a coherently demodulated BPSK system
(without channel coding) was given as

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The single-sided noise power spectral density No represents thermal noise at

the front end of the receiver. The presence of the jammer increases this noise
power spectral density from No to (No + J01p). Since the jammer transmits with
duty cycle p, the average bit-error probability is

We can generally assume that in a jamming environment, No can be

neglected. Therefore,

The jammer will, of course, attempt to choose the duty cycle p that
maximizes PB. Figure 1.14 illustrates PB for various values of p. The value of p = po
that maximizes PB decreases with increasing values of Eb/JO, as was the case with
partialband jamming. This is seen by differentiating Equation to obtain

which results in the maximum bit error probability

The effect of a worst-case pulse jammer upon a system with spread

spectrum but without coding, changes the complementary error function into the
inverse linear As a result, at an error probability of 10-6, there is about a 40-dB
difference in Eb/Jo between the broadband jammer and the worst-case pulse
jammer. For the same jammer power, the jammer can do considerably more harm
to an uncoded DS/BPSK system with pulse jamming than with constant power
jamming. The effect of a pulse noise jammer on uncoded DS/BPSK is similar to the
effect of a partial-band noise jammer on uncoded FH/BFSK, In both cases
considerable degradation is brought about by concentrating more jammer power on
a fraction of the transmitted uncoded symbols. Forward error correction coding
with appropriate interleaving can almost fully restore this degraded performance.

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Figure 1.14 Pulse Noise Jammer

1.6.9 Repeat-Back Jamming

The measure of jammer-rejection capability, namely processing gain, Gp, is
based on the assumption that the jammer is a "dumb" jammer; that is, the jammer
knows the extent of the spread-spectrum bandwidth, Wss, but does not know the
exact spectral location of the signal at any moment in time. We assume that the
hopping rate is fast enough to preclude the jammer from monitoring the
transmitted signal so as to usefully change this jamming strategy. Under what
condition is this assumption questionable? There are "smart" jammers that are
known as repeat-back jammers or frequency-follower (FF) jammers. These jammers
monitor a communicator's signal (usually via a side lobe beam from the
transmitting antenna). They possess wideband receivers and high-speed signal
processing capability that enable them to rapidly concentrate their jamming signal
power in the spectral vicinity of a communicator's FH/FSK signal. By so doing, the
smart jammer can increase the jamming power in the communicator's
instantaneous bandwidth, thereby gaining an advantage over a wideband jammer.
Notice that this strategy is useful only against frequency-hopping spread-spectrum
signals. In direct-sequence systems, there is no instantaneous narrowband signal
for the jammer to detect.

One method is to simply hop so fast that by the time the jammer receives,
detects, and transmits the jamming signal, the communicator is already
transmitting at a new hop (which of course will be unaffected by jamming at the
frequency of the prior hop). The following example should make this point clear.

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Figure 1.15 Example of fast hopping to evade the repeat-back

1.7 Binary pseudo-random sequences

Generation of binary pseudo-random sequences

Figure 1.16 Block diagram for shift registers with linear feedback

To explain the basic concept of the sequence generators, consider the simple
feedback shift registers shown in Figure 1.16 where the initial states of the r-stage
shift registers are (ar−1,ar−2, ... ,a1,a0) and the feedback function f(x0,x1, ... ,xr−1)is a
binary function.

At each clock pulse, the content of each register is shifted to the next
register on the left or right. Consider the block diagram of a general sequence
generator depicted in Figure where we use the following symbols:

j → jth shift register # j

+ → Modulo - 2 adder
h i → Modulo - 2 multiplier

Let x denote the time delay of a unit clock duration and xj denote the time
delay of j such units. The input A(x) specifies the initial states of the registers and
are denoted by the sequence (ar−1,ar−2, ... ,a1,a0).

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The generator connections can be expressed by polynomial h(x) where:

h(x) = h0 + h1 — x + h2. x2 ................. hr.xr

The coefficients hi are such that a connection is present if hi =1 and no

connection is present if hi =0. It is worth noting that there is no output from this
generator for the first r clock time shifts and that once all registers are loaded with
zeros (i.e. A(x)=0), the generator could not change it’s state. Therefore an all-zero
state is not allowed.

Considering Figure 1.16, the top numbers (from left to right 1, 2...... r −2, r
−1, r) represent the adders. The numbers in the figure represent the numbers of
registers (from right to left 1, 2, 3.... r −2, r −1, r). The output of the jth adder is:

x : B j ( x) = B j −1 ( x) x + A( x) hr − j

Let us start the iteration from right to the left:

B(x) = Br (x)—

= Br−1(x) x + A(x) h0

= Br−2(x) x2+ A(x) xh1 +A(x) h0

= Br−3(x) x3+ A(x)x2h2 + A(x) xh1 + A(x) h0

= B1(x) xr−1+ A(x)xr−2hr−2 + A(x) xr−1hr−1 +————————————+ A(x) h0

= A(x)xrhr + A(x)xr−1hr−1 + A(x)xr−2hr−2 + A(x) — xr−1hr−1 +————+A(x) h0

r
= ∑  A ( x ) x
j =0
j
h j

Thus B(x)=A(x).h(x), expresses the generator output B(x) as a product of two

polynomials, i.e. the input polynomial A(x) and the generator connections
polynomial h(x). The maximum period of the binary sequence generated by the r-
stage shift register is limited to 2r−1.Abinary sequence which achieves this
maximum period is called maximal-length sequence or simply m-sequence.
Primitive polynomials which can be used to connect the feedback are given in Table
It must be emphasized that the period of the generated sequence depends on the
choice of h(x) and only connections based on these primitive polynomials are
capable of generating sequences of length 2r−1.

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Figure 1.17 Block diagram of a general sequence generator

1.8 MAXIMAL-LENGTH SEQUENCES (M-SEQUENCES)

These are longest codes that can be generated by a shift register of a specific
length, say, r. An r-stage shift register and a few EX-OR gates can be used to
generate an m-sequence of length 2r -1. Figure 1.18 shows an m-sequence
generator using n memory elements, such as flip-flops. If we keep on clocking such
a sequence generator, the sequence will repeat, but after 2r -1 bits. The number of
1-s in the complete sequence and the number of 0-s will differ by one. That is, if r =
8, there will be 128 one-s and 127 zero-s in one complete cycle of the sequence.
Further, the auto-correlation of an m-sequence is -1 except for relative shifts of (0 ±
1) chips. This behaviour of the auto correlation function is somewhat similar to
that of thermal noise as the auto correlation shows the degree of correspondence
between the code and its phase-shifted version. Hence, the m-sequences are also
known as, pseudo-noise or PN sequences.

Figure 1.18 Maximal length pseudo random sequence generator

The m-sequences have found numerous applications in digital

communication systems, including spread-spectrum systems. These sequences
have a maximum period N=2r−1 for an r-stage LFSR generator connected according
to a primitive binary polynomial of degree r selected.

The salient features of the m-sequences are their two-valued autocorrelation

functions which are optimal, with the absence of any side-lobe peaks. This is the
key parameter which determines the probability of detection and false alarm,
during code acquisition and tracking.

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The periodic cross-correlation function between any pair of m-sequences of

the same period can be relatively large. However, the peak values depend on the
sequences chosen and their respective phases. To reduce interference, it is
desirable to constrain these peak values to a minimum. All m-sequences of the
same length can be derived from each other by a process of proper decimation.

Figure1.19 Auto-correlation functions for an m-sequence

Table 1.2 Peak periodic cross-correlation between a pair of m-sequences

Number of m Peak cross-

r N=2r−1
sequences correlation
3 7 2 5
4 15 2 9
5 31 6 11
6 63 6 23
7 127 18 41
8 255 16 95
9 511 48 113
10 1023 60 383
11 2047 176 287
12 4095 144 1407

A list of peak magnitude for the periodic cross-correlation between pairs of

m-sequences for 3 ≤ r ≤ 12.

The m-sequences have the following well-known properties

i. There are exactly N non-zero sequences representing the N different

phases of the m-sequence. If the m-sequence is x=(x0,x1,x2, ... ,xN−1), then
the non-zero sequences are (x1,x2,x3, ... ,xN−1,x0), (x2,x3,x4, ... ,xN−1,x0,x1),
(x3,x4,x5, ... , xN−1,x0,x1,x2), etc.

ii. Shift-and-add property of the m-sequences suggests that the modulo-2

sum of an m-sequence and any phase shifted version of itself is another
phase of the same m-sequence.

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 n +1 
iii. The Hamming weight of an m-sequence is   . This is because the
 2 
 n +1 
number of ones in an m-sequence is   . The number of zeros is of
 2 
 n −1 
course  .
 2 
iv. The periodic autocorrelation function of an m-sequence is a two-valued function
R(τ) = N for τ = jN
given by = -1 for τ ≠ jN

where j is any integer. A plot of autocorrelation for an m-sequence with chip

duration Tc and time period NTc

v. A run is defined as a set of identical symbols within the m-sequence. The length
of the run is equal to the number of these symbols in the run. For any m-
sequence generated by r-stage shift registers, it has the following statistics:
1 run of ones of length r
1 run of zeros of length r−1
1 run of ones and one run of zeros of length r−2
2 runs of ones and 2 runs of zeros of length r−3
4 runs of ones and 4 runs of zeros of length r−4
8 runs of ones and 8 runs of zeros of length r−5
•
•
•
•
2r−3 runs of ones and 2r−3 of zeros of length 1.

For example the m-sequence 000100110101111 contains a total of eight

runs as follows: one run of four 1s, one run of three 0s, one run of two 0s, two
runs of s single 1, and two runs of a single 0.

Several properties of PN sequences are used in the design of DS systems.

Some features of maximal length pseudo random periodic sequences (m-sequence
or PN sequence) are noted below:

a) Over one period of the sequence, the number of ‘+1’ differs from the number
of ‘-1’ by exactly one.

b) Also the number of positive runs equals the number of negative runs.

c) Half of the runs of bits in every period of the same sign (i.e. +1 or -1) are of
length 1, one fourth of the runs of bits are of length 2, one eighth of the runs
of bits are of length 3 and so on. The autocorrelation of a periodic sequence is
two-valued.

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1.8.1 Decimation of m-sequences

The application of code sequences in spread-spectrum communications

necessitates the generation of large sets of codes with highly peaked
autocorrelation and minimum cross- correlation. We now look at the generation of
number sequences by decimating a single sequence. As usual, we start by defining
the basic element involved in the decimation process.

Consider sequence u=u0,u1,u2,u3, ... , then sequence v, constructed by taking

every qth bit of the nonzero elements of sequence u denoted by u(q) and said to be
the decimation by q of u where q is a positive integer, that is:
v = u(q)
where v=u0,uq,u2q,u3q, ............... .
If u has a period N and is generated by LFSR with generator connection
polynomial h(x) then u(q) has period Nv
N
Nv =
gcd ( N , q )
The sequence u(q) can be generated using LFSR with generator polynomial ˆ
h(x) whose roots are the qth powers of the roots of h(x). The term gcd(N, q) denotes
the greatest common divisor of N and q. For example, the gcd(23, 7)=1 because two
numbers can only be divisible by 1, gcd(81, 45)=9 since 45 is divisible by 3, 5 and 9
and 81 is divisible by 3 and 9. The decimation of an m-sequence may or may not
yield another m-sequence. When decimation yields an m-sequence, it is called
proper decimation and if gcd(N, q)=1,sequence v=u(q) has a period N. Proper
decimation guarantees that sequence v=u(q) is an m-sequence and the polynomial
hˆ( x) is primitive. Clearly, there are N possible sequences that correspond to the N
phases of m-sequence u.
The decimation of any phase of sequence u will give a certain phase of v. In
general, regardless of which of m-sequences generated by h(x) we choose to
decimate, the result will be an m-sequence generated by hˆ( x) .

The characteristic sequence û of m-sequence u is such that uˆ = uˆ ( 2 ) . Since the

m-sequence u is periodic, we only need to consider values of less than or equal to
[N−1], that is u[q] = u[q mod N]. When proper decimation is achieved by odd integer
q, then u  2 j q  represents different phases of the same m-sequence u(q). Let them-
sequence u be generated by polynomial h(x) such that:

h(x) = h0xr +h1xr−1+————————————————————————————————————————————————+hr−1x+hr

1
Decimating u by q = ( N − 1) will generate the reciprocal polynomial of h(x) that is
2
hˆ( x ) where:

hˆ( x) = hrxr + hr−1xr−1 +—————————————————————————————————————————————+ h1x + h0

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1.8.2 Preferred Pairs of M-Sequences

The periodic autocorrelation of m-sequence is a two-valued function.

However, the cross-correlation between two m-sequences generated by two different
primitive polynomials can be three-valued, four-valued, or possibly many-valued. It
is possible to choose a pair of m-sequences which has a three-valued cross-
correlation function. These two chosen m-sequences are called the preferred pair.
The designated pair could be selected as the m-sequence u and its decimated
version v=u(q).

The preferred pairs that have period N (=2r–1) must satisfy the following
conditions:

i. r ≠ 0 mod 4, that is n is odd or r=2 mod 4

Where n is the degree of primitive polynomial and r could not take on such
values as: 4, 8, 12, 16, 20… That is, r=2, 6, 10, 14, 18… etc. These values of r give
odd values for N (=3, 63, 1023, 16383, 262143... etc.).

 2k + 1 
 
iii. v=u (q) q is odd given by: q =  or 
 2k − 2k + 1
 
iv. where k is given by property (iii).

iii. gcd (r, k) = 1 for n odd (4.23)

2 for r=2mod4

It is clear that because r ≠ 0 mod 4, N is not a power of 2. Typical values for k are
(1, 2). These values of k Make q=3, 5, 13. The preferred pairs of m-sequences have
three-valued cross-correlation function defined as [−1, −t(r), t(r)−2] where
r +1
t (r ) = 1 + 2 2
for r odd
r+2
t (r ) = 1 + 2 2
for r = 2 mod 4
Table 1.3 Maximum cross-correlation associated with preferred pair of
m- sequences

r 1 2 3 5 6 7 10

t(r) 3(4,24) 5(4,25) 5(4,24) 9(4,24) 15(4,25) 15(4,24) 6(4,25)

Cross -1,-9, -1,-15, -1,-15, -1,-64,

-1,-3,1 -1,-5,3 -1,-5,3
correlation 7 13 13 63

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Let us compute typical values of the cross-correlation for an assumed m-

sequences with r=1, 2, 3, 5, 6, 7, and 10. Using t(r) and maximum cross-
correlations are given in Table 1.3.

A collection of m-sequences where the property of each pair in the set is a preferred
pair is called a connected set. The largest possible connected set is called Maximal
connected set. The size of this set, Mn, is important in applications such as
multiple users’ spread-spectrum systems.

1.9 GOLD CODES SEQUENCE

If [u, v] is any preferred pair of m-sequences generated by primitive

⌢
polynomials h(x) and h ( x ) and each of degree n and period N=2n −1, then a set of
Gold sequences G[u, v] can be generated by u⊕v where ⊕ represents module-2
addition. Taking into consideration the N possible phases of the sequences, we can
define the set G[u, v] as:

u, v, u ⊕ v, u ⊕ Tv, u ⊕ T2v, u ⊕ T3v, .............................,u ⊕ TN−1v

Where Tiv represents m-sequence v phase shifted by i symbols with i=0, 1, 2, ...,
N−1.The Gold set of sequences contains N+2 sequences and is generated by
⌢
polynomial given by h(x) h ( x ) . A typical Gold generator can be constructed using
the preferred pair of m-sequences u[u, u(3)] where:

h 0 (x) = 1+ x 2 + x 5 gives m - sequence u

2 3 4 5
h 3 (x) = 1+ x + x + x + x gives u(3)

Considering the set of Gold sequences, the out-of-phase autocorrelation of any

sequence in the set and the cross correlation between any pair in the set have
three-valued correlation functions given by [−1, −t(r), t(r)−2] as mentioned
previously. However, Gold sequences have cross-correlation (−1) for many offsets of
the preferred pair of m-sequence. It turns out that attaching ‘0’ to the original Gold
sequences will eliminate the cross-correlation. In fact, simple zero-padding to the
Gold sequences can originate 2r code sequences which have zero cross-correlation
between them. These code sequences are called ‘orthogonal Gold codes’

It should be noted that the literature presents an earlier definition for the set
of Gold sequences as G[u, v] where v=u[t(r)].At present, it has been accepted that u
and v should be any preferred pair of m-sequences.

The lower bound on the peak cross-correlation ( Φ max ) between any pair of
binary sequences of period N in a set of M sequences is given by Welch bounds as

M −1
Φ max ≥ N
NM − 1

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Figure 1.20 Block diagram of Gold generator

For large values of N and M, Φ max can be approximated as: Φmax ≈ N . This
lower bound is commonly taken as a bench mark for the cross-correlation between
a set of binary sequences when computing the multiple access interference.

For a Gold sequence with a reasonably large value for m, N = 2 m − 1 ≈ 2 m

m
Thus the lower bound on Gold sequences Φ max is Φ max ≈ 2 2

The maximum cross-correlation between the preferred sequences of a Gold

sequence is:

m+1
2 2
+ 1 m is odd, i.e. 2 times lower bound
m+ 2
2 2
+ 1 m is odd, i.e. 2 times lower bound

1.9.1 Properties of Gold Codes

i. The number of Gold Codes is more than m sequences for the same number
of registers.

ii. Any slight change in phase between the two generators causes a new
sequence to be generated.

iii. The cross correlation function is uniform and bounded.

1.9.2 Applications of Gold Codes

i. The Gold Code algorithm supports CDMA, Frequency hopping multiple

accesses and ultra wide band spread spectrum communication systems.

ii. Gold Codes are used in Cell Phones, Secure wireless computer networks and
military field radios and various other applications.

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1.10 KASAMI SEQUENCES

Kasami-codes have the same correlation properties as Gold-codes. The

difference is the number of codes that can be created. For the large set of Kasami-
n

( )
codes this number is equal to 2 2 2 + 1 . Choosing n equal to 6 for an example gives
n

520 possible codes. As the number of codes determines the number of different
code addresses that can be created, the large set of 3-13 Kasami-codes are used as
a code-set. Where A large code-set enables us to select those codes which show
good cross-correlation characteristics.

A set of Kasami sequences can be generated using two different procedures

described below:

1.10.1 Generating a small set of Kasami sequences

Starting with the m-sequence u generated by a primitive polynomial hu(x)

with period N=2n −1 where n is an even number, we can generate a sequence v
n n
using primitive polynomial hv(x) by decimating u by 2 2 + 1 ; that is=u ( 2 2 + 1 )

It has been proven that v is an m-sequence with period derived as follows:

N 2n − 1
period = =
 n
   n 
gcd[ N ,  2 2 + 1 ] gcd ( 2 n − 1) ,  2 2 + 1  
     
 n2   n2 
 2 − 1  2 + 1
=   
 2n   2n   n2 
gcd  2 − 1   2 + 1 ,  2 + 1  
     
 2n   2n 
 2 − 1   2 + 1
Period = N v =   
 n2 
 2 + 1
 
n
= 22 −1

The small set of Kasami sequences is generated by the primitive polynomial

h(x)=hu(x)hv(x) using a module addition of u with all possible phases of v; that is

{u, u ⊕ v, u ⊕ Tv, ................................,u ⊕ T N v v }

n
2
The set contains 2 sequences, each of period N and with three-valued correlation
function [−1, −s(n), s(n)−2] where

n
s(n) = 2 2 − 1

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The maximum magnitude of correlation acquired is s(n) and it is approximately one

half of the maximum magnitude value achieved by Gold set.

1.10.2 Generating a large set of Kasami sequences

Consider the following m-sequences: sequence u is generated by primitive

polynomial hu(x) of degree n and has a period N; sequence v is the decimation of u
n
by s(n),i.e. v=u[s(n)] generated by the primitive polynomial hv(x)of degree and has
2
n
period 2 2 − 1 and w=u[t(r)] generated by a polynomial hw(x) of degree n with period
N. Then the large set of Kasami sequences KL(u) is generated by primitive
polynomial h(x)=hu(x) hv(x) hw(x) and is given as, KL(u) = u ⊕ v ⊕ w and has a
n n

( )
period N= 2 n − 1 . The size of KL(u) is 2 2 2 + 1 for n≡2 mod 4, and 2 2 2 + 1 −1 for
n n
( )
n≡0 mod 4. The correlation function for KL(u) is many-valued with values chosen
from the set {−1, −t(r), t(r) −2, −s(n), s(n) −2}. The maximum magnitude of
correlation is t(r).

Table 1.4 Comparison between Gold and Kasami sequences

SMALL SET OF LARGE SET OF

PARAMETERS GOLD
KASAMI KASAMI

Period of individual
sequence
2n − 1 2n − 1 2n − 1

(2 + 1)
n
2 2 ( 2n + 1)
n n
Size of set 2
2

Odd or 2
Values of n Even 2 mod 4 or o mod 4
mod 4

Max correlation n+ 2 n n+ 2

between any pair 2 2

+1 22 +1 2 2
+1

It is interesting to compare the Kasami sequences with the Gold sequences

and such a comparison is given. For example, for n=6 (i.e. 6-stage LFSR generator),
the length of Kasami sequences is 63 bits, the size of the small set is 8 sequences;
the size of the large set is 520 sequences and the size of Gold set for the 6-stage
LFSR generator is 65. For the same 6-stage LFSR generator, the maximum
magnitudes of the cross-correlation between these sequences are as follows: 9 for
the Kasami small set, 17 for the Kasami large set, and 17 for the Gold set.

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UNIT-II
DIRECT SEQUENCE SPREAD SPECTRUM SYSTEM

2.1 Coherent Direct Sequence Systems

The general form a direct-sequence spread spectrum communication system
takes a binary data sequence and multiplies it by a higher rate pseudorandom (PN)
binary sequence. The result is a binary sequence at the PN binary sequence rate
which is then modulated. Compared to the usual modulation of the data, the data
multiplied by the PN sequence causes the modulated signal spectrum to spread by
a factor of N, the ratio of the PN sequence bit rate to the data bit rate. Figure 2.1
illustrates the general direct-sequence spread modulation.

Figure 2.1 Direct Sequence Modulation

The data waveform is given by

d (t ) = d n , nTb ≤ t < (n + 1)Tb

d n ∈ {−1,1}
n = int eger
where {d n } is the data sequence.

The PN binary waveform is

c(t ) = ck , kTc ≤ t < (k + 1)Tc

ck ∈ {−1,1}
k = int eger

where {ck} is the PN sequence.

Here,
Tb
N=
Tc
Where N is the signal spectrum-spreading factor, Tb is the bit time and Tc is
referred to as the "chip" time interval.

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In the above multiplication of the data and the PN binary sequence, it is important
that the data clock and the PN sequence clock are coincident. That is, the data
transition times must be at the transition time of a PN sequence binary symbol.
Figure 2.2 illustrates the general direct-sequence spread modulation waveform.

Figure 2.2 Direct-Sequence Spread Modulation Waveform

It is assumed that the data clock is divided down from the PN sequence clock so
that possible transition times in the data line up with transition times of the PN
sequence and no unscheduled transitions occur. Systems which have coincident
data and PN sequence clocks are often said to have a data "privacy" feature since
the data is hidden by the PN sequence.

2.2 Model of a DS/BPSK System

Bandwidth spreading by direct modulation of a data modulated carrier by a
wideband spreading signal is called direct-sequence (DS) spread spectrum. The
simplest form of DS spread spectrum employs binary phase-shift keying (BPSK) as
the spreading modulation. Consider a constant-envelope data-modulated carrier
having power P, radian frequency ω0 , and data phase modulation θ d (t ) defined
by
sd (t ) = 2 p cos[ω0t + θd t ]
BPSK spreading is accomplished by multiplying sd(t) by a function c(t)
representing the spreading waveform, as illustrated in Figure 2.3. The transmitted
signal is give as
st (t ) = 2 p c(t) cos[ω0t + θ d t ]

Figure 2.3 BPSK Direct-Sequence Spread Spectrum Transmitter

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Consider the signal st(t) is transmitted via a distortion less path having
transmission delay Td. Demodulation is accomplished in part by demodulating with
the spreading code appropriately delayed as shown in Figure 2.4.

Figure 2.4 BPSK Direct-Sequence Spread Spectrum Receiver

This demodulation or correlation of the received signal with the delayed spreading
waveform is called de-spreading and is a critical function in all spread-spectrum
system. The signal component of the output of the de-spreading mixer is
Λ
2 p c(t − Td ) c(t − Td ) cos[ω0t + θ d (t − Td ) + φ ]

Λ
Td
where is the receiver's best estimate of the transmission delay.
Figure 2.5 illustrates the direct-sequence spreading and despreading operation
when the data modulation and the spreading modulation are BPSK.

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Figure 2.5 BPSK direct sequence spreading and despreading

In this case, the data modulation is represented by a multiplication of the
carrier by d(t) takes on values of ± 1. Thus
sd (t ) = 2 p d (t ) cos[ω0t ]

st (t ) = 2 p d (t ) c(t ) cos[ω0t ]

Figure 2.6 - 2.9 illustrate the power spectral of the signals

Figure 2.6 Power spectral density of data modulation carrier

Figure 2.7 Power spectral density of data and spreading code

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Figure 2.8 Before despreading

Figure 2.9 After despreading

The power spectrum of the recived signal is given as

1
sr ( f ) =
2
{ } {
PTc sin c 2 ( f − f 0 )  Tc + sin c 2 ( f + f 0 )  Tc }
1
+ J {δ ( f − f 0 ) + δ ( f + f 0 )}
2
and the received signal is give as
r(t ) = 2 p d (t − Td ) c(t − Td ) cos[ω0t + φ ] + 2 J cos[ω0t + φ ]

2.3 Chernoff Bound

For a given jammer coordinate sequence J fixed consider the Chernoff
bound to the bit error probability as follows:

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for any λ ≥ 0. Next, following the approach use the inequality

x 2 /2
cosh x ≤ e
to obtain the form
−λ ( λ 2 / 2 N )ξ kN=−01 J k2
Pb( J ) ≤ e Eb
e
The λ ≥ 0that minimizes this Chernoff bound is
N −1
1 
λ * = Eb /  ∑ J k2 
 N k =0 
giving the result
 2 N −1

P b ( J ) = exp − Eb /  N ∑ J k 
2

  k =0 
In addition, note that a factor of 1/2 can be applied to the above Chernoff bound.
The final Chernoff bound is then
1   2 N −1  
Pb ( J ) ≤ exp − Eb /  ∑ J k2  
2   N k =0  
This bound applies for all N and J and only assumes the PN sequence {ck} is an i.i.d
sequence for binary symbols equally likely to be 1 or —1.

2.4 Uncoded Direct Sequence Spread Binary Phase Shift Keying ( DS/BPSK )

The simplest form of direct-sequence spread-spectrum communication

systems uses coherent binary phase-shift-keying (BPSK) data modulation and
binary PN modulation. This has some potential advantage against a single tone
jammer at the transmitted signal carrier frequency. It forces the jammer power
to be evenly distributed over the cosine and sine signal coordinates.
The uncoded direct-sequence spread binary phase-shift-keying
(DS/BPSK) signal which is given by
x(t) = c(t) d(t) 2 p cos ω0t

= c(t) s(t)

where ,

s(t) = d(t) 2 p cos ω0t

is the unspread BPSK signal. Defining Tb as the data bit time interval and Tc as the
PN sequence bit time interval, s(t) has a sin2x/x2 spectrum of bandwidth roughly
1/Tb while the spread-spectrum signal x(t) has a familiar shaped spectrum but of
bandwidth roughly

Wss = 1
Tc
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The processing gain is

Wss
PG =
Rb
Tb
=
Tc

=N

The jamming signal is represented by J(t) and in the absence of noise the signal
at the receiver is
x(t) + J(t)
The receiver multiplies this by the PN waveform to obtain the signal

r(t) = c(t)[x(t) + J(t)]

= c 2 (t)s(t) + c(t)J(t)
since, c 2 (t)=1
r(t)= s(t) + c(t)J(t)
Here c(t)J(t) is the effective noise waveform due to jamming.

The conventional BPSK detector output is give as

r = d Eb + n
where d is the data bit for the Tb second interval, Eb = STb is the bit energy, and n
is the equivalent noise component given by
T
2 b
Tb ∫0
n= c(t ) J (t ) cos ω0tdt

Uncoded bit error probability for arbitrary jammer waveforms:

Without coding, the BPSK detector decision rule is to decide d is the data bit
where

Λ  1, if r ≥ 0
d =
−1, if r < 0

Its bit error probability is give as

Pb = Pr {r ≥ 0 | d = −1}

{
= Pr n ≥ Eb }
Naturally, this bit error probability depends on the random variable n given by

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T
2 b
Tb ∫0
n= c(t ) J (t ) cos ω0tdt

For BPSK modulation the noise component has the form

Tb
2 N −1
n= ∑
Tb K =0 ∫ c(t ) J (t ) cos ω tdt 0
0

T
2 N −1 b
= ∑ Ck c(t ) J (t ) cos ω0tdt
Tb K =0 ∫0
where C0,C1,……,CN-1 are the N PN bits occurring during the data bit time
interval. Defining the jamming component
( k +1)Tc
2
JK =
Tc ∫
kTc
J (t ) cos ω0tdt

We have
N −1
1
n=
N
∑C J
K =0
k k

as the final form for the noise component.

The PN sequence is approximated as an independent identically distributed

binary sequence where
1
Pr {Ck = 1} = Pr {Ck = −1} =
2

Then for any fixed jammer sequence

J = (J0,J1,…….,JN-1)

the noise component given by n is a sum of independent random variables. We

next examine ways of evaluating the conditional bit error probability

P ( J ) = Pr {n ≥=
b
Eb | J }
for given jammer components J. The bit error probability may be in terms of a
parameter set characterizing a deterministic jammer model or a statistical
characterization of the jammer with evaluation of the overall average bit error
probability by

P b
= E { Pb ( J )}
where the expectation is over the jammer statistics.

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2.5 Under Constant Power Broad Band Jammer

Suppose a jammer is transmitting a signal J(t) with constant power J in the

system, an ideal coherent BPSK demodulator is assumed to follow the received
signal y(t) multiplied by the PN sequence c(t). The channel output is y(t)= x(t)+J(t).

At the receiver side this y(t) is multiplied by PN sequence c(t) to obtain

r(t) = c(t) . y(t)

= c(t) [ x(t) + J(t) ]
= s(t) + c(t) . J(t)
Then the BPSK detector output
r = d Eb + n
.
Where D is the data bit and Eb is the bit energy which is equal to Eb = S. Tb.

The noise equivalent is given as

T
2 b
Tb ∫0
n= C(t ) J (t ) cos ω0tdt

Decision rule is given as

Λ  1, if r ≥ 0
d =
−1, if r < 0
Its bit error probability is
r > 0 | d = −1
=
P b r ≤ 0 | d = 1
Pr


Substituting the value of r we get

P b {
= Pr d Eb + n > 0 | d = −1 }
P b {
= Pr − Eb + n > 0 }
P b {
= Pr n > Eb }
The noise term depends upon many PN chips, therefore
N −1 ( k +1)Tc
2
n = ∑ Ck ∫ J (t ) cos ω0tdt
k =0 Tc kTc

Assume the jammer transmits broadband noise of power spectral density given by
J
NJ =
Wss
Then,
( k +1)Tc
2
nk =
Tc ∫
kTc
J (t ) cos ω0tdt

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This term are independent zero mean Gaussian random variables with the variance
NJ / 2.
The noise term can be rewritten as
N −1
Tc
n = ∑ Ck nk
k =0 Tb
For a continuous broad band jammer of constant power J. The uncoded bit error
probability
 2 Eb 
Pb = Q  
 NJ 
where Q(x) is the Gaussian probability integrator.

∞
1 −t2
Q( x) = ∫ e 2
dt
x 2π
Under Pulse Jammer:
Detector output of BPSK is given as
r = d Eb + Z n
Corresponding probability function is give as
Pr { z = 1} = ρ ; Pr { z = 0} = 1 − ρ ;
Therefore , bit error probability under pulse jammer is given as,
Pb = Pr {r > 0 | d = −1}

{
= Pr d Eb + Z n > 0 | d = −1 }
= Pr {− Eb + Z n > 0 }
= Pr {− Eb + Z n > 0}

= Pr {Z n > Eb }
Z is random variable independent of noise terms. The random variable Z
specifies whether the jammer signal is present or not. During the particular time
Tb when one BPSK signal is transmitted its probability function is given as

{ } {
Pb = Pr Z n > Eb | Z = 1 .Pr {Z = 1} + Pr Z n > Eb | Z = 0 .Pr {Z = 0} }
this can be expressed in general form as,
 2 Eb ρ 
Pb = Q   .ρ
 NJ 

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The value of ρ that maximize Pb decreases with increasing values of Eb/NJ.

The maximum value of bit error probability is given as,

 2 Eb ρ 
Pb = Q   .ρ
 NJ 

 .709 , Eb > .709

 Eb NJ
 N
ρ = J

 Eb
 , ≤ .709
 1 NJ

 2 Eb ρ 
Pb = max Q   .ρ
0 ≤ρ < 1  NJ 
ρ* is the value in which the bit error probability Pb is maximum

 2E ρ *  *
Pb = Q  b
 .ρ
 NJ 
 

The specific value of Pb is

 .083
 Eb Eb
, > .709
 NJ NJ

ρ =

  2 Eb  , Eb ≤ .709
Q  N  N J
  J 

2.6 Coded Direct Sequence Spread Binary Phase Shift Keying ( DS/BPSK )
The impact of pulse jamming can be defeated by coding techniques,
coding is done in order to increase the bandwidth. dn is the data bit
sequence and constraint length is K=2, for the Kth transmission time interval
the two coded bits are
ak= (ak1, ak2)
where
ak 1 = d k 1

1, d k ≠ d k −1
ak 2 = 
0, d k = d k −1

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suppose Tb is the data bit time then each coded bit must be transmitted in
Ts ,
Tb
Ts =
2
Where Ts is the time period of each ordered symbol

a , kTb ≤ t < (k + 1/ 2)Tb

a ( t ) =  k1
ak 2 , ( k + 1/ 2)Tb ≤ t ≤ ( k + 1)Tb
With ordinary BPSK modulation coded waveform will have twice the
bandwidth of the uncoded waveform. Data bit (d) is encoded into a sequence
of (m) coded symbols which is identical to data bit (d). This coded bits are
scrambled in time by the interleaver and then BPSK modulated and direct
sequence spread by the PN sequences C(t).

Figure 2.8 Block diagram of coded DS/BPSK

Unknown Channel State:

With pulse jamming there is a possibility that the decoder may have
additional information about the values Z1,Z2,......Zm that might help in decision
rule. In unknown channel state the decoder has no knowledge about channel state
information.

Consider two decision rules,

i. Soft decision decoder

ii. Hard decision decoder

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Soft decision decoder:

This decoder not only determines whether the incoming signal is 1 or 0

based on the threshold but also provides a confidence factor in the decision. This
provides an indication of how far the signal is from the threshold.
Decoder output is given as
m

r i = ∑ a i m E b + z im i
i =1

Its bit error probability is given as,

P = Pr {r
b i
> 0 | d = −1}
At the receiver side ai is decoded as d
= Pr {a i
m E b + z i n i | d = −1 }
 m

= Pr d m E b + ∑ z i n i > 0 | d = −1
 i =1 
m 
= Pr ∑ − m E b + z i n i > 0
 i =1 
m 
= Pr ∑ zn i i
> mE b 
 i =1 
Hk denote the condition of K pulse jam symbols.
m 
P b Pr ∑
=
i =1
z ini
> mEb | H k 

 m

= Pr ∑ z i n i > mEb  P { H k}
 i =1 
Where ,
m
P { H k} =   p (1 − p )
k m−k

k
 2mEb p 
p = Q  
b
 N J 

Hard decision decoder :

Hard decision decoder makes a binary decision on each channel output symbol as,
 1 , r > 0
= i

d i −1, r ≤ 0
i

Where, i=1, 2 ...m

Then, the final decision is given by,
Λ
 
Λ  1 , di > 0 
= 
d 
Λ

−1 , di < 0 

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ξ = Pr {r i
> 0 | d = −1}
 m Eb 
= Pr ∑ ai + z i n i > 0 | d = −1
 i =1 m 
 Eb 
= Pr d + z i n i > 0 | d = −1
 m 
 
= Pr  − E + z ini > 0
b

 m 
 
= Pr  z i n i > E b 
 m 

 2 .ρ 
ξ = Q  E b  .ρ
 mN J 
 
 
= Pr  z i n i > E b  Pr { z = 1}
m 
 
m k
P b
=   ξ (1 − ξ )
m −k

k
For an odd integer m the probability of error is the probability that (m+1)/2 or more
the m symbol decisions are in error.

The probability that a particular coded symbol is in the error is given by

ξ = Pr {r i > 0 | d = −1}
Probability that more than half of the m coded symbols decision are in error gives
the overall bit error probability

P = ∑ mC ξ
k
b k (1 − ξ ) m − k
m +1
Where, k =
2
By increasing the value of m we can reduce pulse jamming. There is no reduction
in data rate by increasing the number of coded symbols, the hard decision decoder
performs better than soft decision decoder in the case of pulse jamming.

Known Channel State:

Because of the channel measurements the decoder knows which of the m channel
outputs r1, r2,......rm. have a jammer term in them. This is equivalent to knowing the
values of z1, z2,......zm at the decoder. When any zi=0 then
r = E and d is decided
b
i
m
correctly the only way an error can be made is when z1, z2,......zm=1 error can only
occur when all the m coded symbols encounter a jamming pulse. This occurs with
probability

Pr = (z z1, 2.................... z m )
=1 = ρm

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Soft decision decoder:

when z1, z2,......zm=1 the soft decision decoder makes the decision,

 
 m 
 1, ∑ ri > 0 
Λ  i =1 
=  
d  m 
− 1 
 , ∑ ri < 0 
 i =1 

Bit error probability is given as

P = Pr {r
b i
> 0 | d = −1}
m 
= Pr ∑ ai Eb m + z i n i > 0 | d = −1
 i =1 
{ }
= Pr d Eb m + z i n i > 0 | d = −1

= Pr {− E m + z n > 0} b i i

= Pr { z n > E m }
i i b

= Pr { z n > E m } Pr { z z .......z
i i b 1, 2, m
=1 }
 2 m.ρ 
ξ = Q Eb  .ρ m
 NJ 
 

Hard decision decoder:

When z1, z2,......zm=m the hard decision decoder makes the decisions on each
coded symbol bit error probability of single code symbol is

 Eb 
ξ = Pr  z n > i i 
  m 
 Eb 
= Pr  z i n i > 
m  Pr
{z z
1, 2, }
........z m = 1

 2 .ρ 
ξ = Q  mN E b  .ρ m

 J 

P b = ∑ mCk ξ (1 − ξ )
k m−k

Bit error probability is smaller than unknown channel state for hard decision
decoders with jammers state knowledge the soft decoder performs better than hard
decision.

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UNIT-III
FREQUENCY HOPPING SPREAD SPECTRUM SYSTEM
3.1 Non-Coherent Frequency Hopping Systems

The type of spread spectrum in which the carrier hops randomly from
one frequency to another is called frequency hopping spread spectrum.
Taking a basic modulation technique by changing carrier frequency in some
pseudo manner is a frequency hopping (FH) approach. FH system in which
the carriers phases of transmitted hop frequency pulses have no
relationship with each other is called non coherent FH system. Phase
continuity is maintained from one hop pulse to another is called coherent
FH system.

Figure 3.1 Block diagram of FH/BPSK system

The position of the binary signal is shifted pseudo randomly within a

bandwidth WSS. In an FH /BFSK system the data symbol modulates a carrier. The
frequency of the carrier is pseudo randomly determined. There are two modulation
processes,

i. Data modulation and

ii. Frequency hopping modulation.

Frequency synthesizes can be used to generate several output frequencies from a

single stable frequency. K chip PN sequence generator controls a frequency
synthesizes which hops the carrier within 2k frequencies. A more jammer
resistance approach is to use M distinct frequency synthesizers to hop the binary
symbols.

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3.2 Uncoded FH/BFSH Performance Under Constant Power Broadband

Jammer

Figure 3.2 Block diagram of FH/BPSK system

BPSK signal have the form

s (t ) = 2 s sin(ω0t + d n ∆ωt )
Let t lies in the interval nTb ≤ t ≤ (n + 1)Tb and dn is the independent data bits
where,
 + 1 , w ith p r o b a b ility 1 
 2
dn =  
 − 1 , w ith p r o b a b ility 1
2 
select ∆ωt = π so that two possible transmission tones are orthogonal for all
relative shifts. Frequency hopping of BPSK signal is done with a PN sequence that
is used to select a set of carrier frequency shift resulting in the frequency hopped
signal.
x(t ) = 2s sin(ω0t + ωnt + dnπ )
ωn is the particular frequency hop chosen for the nth transmission interval. If L
binary PN symbols are used to select a frequency shift then there are 2L frequency
shift values are possible. The range of the values taken by the frequency shift
defines the total sprectrum bandwidth Wss.
The receiver PN sequence generator is synchronized with that of the
transmitter. The frequency dehops at the receiver removes the effect of the
frequency shift. The output of the energy detectors are e+ and e-. If b=1 is
transmitted then the detector outputs are e+=STb and e-=0.
Non-coherent decision rule is given as,
Λ  1, e+ > e− 
d = −
−1, e ≤ e 
+

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The instantaneous bandwidth is small faction of the total spread spectrum

bandwidth Wss which is determined by range of frequency shift values generated by
frequency by frequency hopping. The total bit error probability is the average of
particular bit error probability taken over all frequency hopped shift.

Constant power broad band noise jammer :

Assume that the jammer transmits broadband noise over the total spread
spectrum bandwidth with constant power J, regardless of the carrier frequency
shift there will be an equivalent noise process in the instantaneous bandwidth of
the transmitted signal.
The one sided band density is
J
NJ =
Wss
Since, an equivalent noise process is encountered in all parts of the total spectrum.
The bit error probability for uncoded FH/BFSH is same as there for a conventional
BFSK system
1 − ( Eb 2 N J )
Pb = 2
e

Where,
Eb PG
=
NJ J
S ( )
Partial band Noise jammer :
This jammer transmits noise over a fraction of the total spectrum
bandwidth.
ωJ
ρ=
wss
Jammer is allowed to change the band in which it is jamming and so the
transmitter and the receiver never known in which frequency range are being
jammed.
Introduce the jammed state parameter z,
z=1, signal in jammed band
z=0, signal not in jammed band
Bit error probability Pb

P b
= Pr {e + > e − | d = −1}
= Pr {e + > e − | d = −1, z = 1}
= Pr {e + > e − | d = −1, z = 1} , Pr{z = 1}
1 − ρ ( Eb 2 N J )
Pb = 2
e

Partial band noise jammer effect on the uncoded FH/BFSK system is same as the
pulse jammer effect on uncoded DS/BPSK system. In both systems these jammers
cause considerable degradation by concentrating more jammer power on fraction of
transmitted signal.

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Multitone jammer :
For total spread spectrum bandwidth Wss we have N numbers of signal tones
N=Wss .Tb
Where, Tb is the bit duration.
Consider a jammer that transmits many tones each of energy SJ.Tb with total power
J. There are almost Nt jammer tones randomly scattered across the bandwidth,
J
Nt =
SJ
The probability that any given signal tone position is jammed with a jammer tone is
N
ρ= t
N
J
SJ
=
Wss .Tb
J 1
=
SJ Wss .Tb
ρ is the fraction of the signal tone positions that are jammed.
Assume that the jammer has exact knowledge of N possible signal tone
position and places Nt jammer toned in some subset of the N signal tone positions.
During the transmission of a data bit one of the two possible adjacent tone
positions is used by the transmitter. An error occurs if the detected energy is
alternate tone position not containing the transmitted signal tone is larger than the
detected energy in the transmitted tone position.
Assume an error occurs if an only if a jammer tone with power S J = S occurs
in the alternate tone position.
J 1
Pb = ρ =
SJ Wss .Tb
J
ρ=
SJ WssT b

3.3 Code FH/BFSK Performance For Practical Band Multitone Jammer

Assume that FH/BFSH tone are transmitted for each data bit
T
contains m chips, the chip duration is Tc = b . Each of the chip tones
m
should be orthogonal resulting in the total number of orthogonal chip tones,
N c = Wss .Tc
Tb
= Wss .
m
Assume the jammer send multiple tones where the number of jammer tones is
J
given by N t = .
SJ

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Select SJ=S so that the probability that the particular chip tone position is jammed
is given by
Nt
ρ =
Nc
J
SJ
=
T
W ss b
m
J m
=
S J W ss .Tb
m
ρ =
Eb
NJ
after de-hopping the receiver is assumed to detect the energy in one of the two
possible chip tone frequencies. For every Tc interval. The decoder adds up the chip
energies for each of the two possible BFSK frequency and make a decision based on
energy level.
An error occurs only if a jammer tone occurs in all m chip tones frequencies
corresponding to the BFSK frequency. Therefore the total probability,
Pb = ρ m
m
 
 m 
= 
E
 bN 
 J 

3.4 Performance of FH/MDPSK In The Presence Of Partial Band Multitone

Jammer

DPSK stands for differential phase shift keying, this scheme depends on the
difference between successive phases. It is simple to implement than BPSK. There
is no need for demodulator to have a reference signal and it is a non-coherent
scheme. In differentially encoded BPSK a binary 1’s may be transmitted by adding
180o to the current phase and a binary 0’s is transmitted by adding 0o to the
current phase. In the receiver instead of demodulating, the phase between two
successive received symbols are combined and used to determine what data has
been transmitted.

Differentially encoded techniques are used in applications where the receiver

is unabled to provide an exact carrier reference phase for demodulating each data
symbol, it provides a possible solution to the effect of phase discontinuities
introduced by frequency hopping.

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In FH/DPSK system information to be transmitted in the ith interval is

conveyed by selecting once of the M phases.
(2 m − 1)π
θm =
m
The transmitted signal,
+θ ( i −1) )
S ( i ) (t ) = Ae j (θ
(i )

Where,
A is the amplitude of the transmitted signal
θ ( i −1) is the total accumulated phase in the i-1 interval.

A jamming J(t) constant in both phase and amplitude is added to the transmitted
signal, the jammer signal in complex form is given by

J = Ie jθ J
Where, θ J is a random phase distributed in the interval (0 to 2Π )
The channel output in complex form is given by
+θ ( i −1) )
y ( i ) = Ae j (θ + Ie jθ J
(i )

At the receiver side we get a phase estimate and is given by,

Λ
θ (i) = θ k
π
(
Where K is such that | arg y ( i ) − y ( i −1) − θ k | ≤) M
. If θm is the true value of θ (i) a
Λ
π
symbol error is made where θ (i) ≠θ k and whenever | arg y ( i ) − y ( i −1) − θ k | > ( ) M
, rotate

the actual transmitted by π radians so that the transmitted signal phases become
m
2π m , where m and Q 2πm denote that term probability of a
θm = m = 0, ± 1, ± 2,......, ±
M 2 M
particular error event.
π
Q 2π m = Pr{| arg ( y ( i ) − y ( i −1) ) − θ k | > }
M M

Average symbol error probability for MDPSK is presence of multitone jamming

ρ
Ps (M ) =
M
∑Q π
m
2 m
M

Since, θ J is uniformly distributed Q 2πm =Q −2πm

M M
( i −1)
If θ m = 0 is transmitted then y and y (i )
are identical vectors. (i.e) there is no
phase change y ( i −1) = y (i ) . Therefore | arg ( y ( i ) − y ( i −1) ) − θ k |= 0 then Q0=0.

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Then, Ps(M) is given as,

Finally, using the relation between average symbol and bit error probabilistic we
get,

The average bit error probability for MDPSK in the presence of multitone jamming
is given by,

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UNIT-IV
SYNCHRONIZATION OF SS RECEIVERS

4.1 Introduction

For both DS and FH spread-spectrum systems, a receiver must

employ a synchronized replica of the spreading or code signal to
demodulate the received signal successfully. The process of
synchronizing the locally generated spreading signal with the received
spread-spectrum signal is usually accomplished in two steps. The
first step, called acquisition, consists of bringing the two spreading
signals into coarse alignment with one another. Once the received
spread-spectrum signal has been acquired, the second step, called
tracking, takes over and continuously maintains the best possible
waveform fine alignment by means of a feedback loop.

4.2 Acquisition

The acquisition problem is one of searching throughout a region

of time and frequency uncertainty in order to synchronize the received
spread-spectrum signal with the locally generated spreading signal.
Acquisition schemes can be classified as coherent or non coherent.
Since the despreading process typically takes place before carrier
synchronization, and therefore the carrier phase is unknown at this
point, most acquisition schemes utilize non coherent detection. When
determining the limits of uncertainty in time and frequency, the
following points must be considered:

1. Uncertainty in the distance between the transmitter and the

receiver translates into uncertainty in the amount of propagation
delay.
2. Relative clock instabilities between the transmitter and the receiver
result in phase differences between the transmitter and receiver
spreading signals that will tend to grow as a function of elapsed
time between synchronization.
3. Uncertainty of the receiver's relative velocity with respect to the
transmitter translates into uncertainty in the value of Doppler
frequency offset of the incoming signal.
4. Relative oscillator instabilities between the transmitter and the
receiver result in frequency offsets between the two signals.

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4.2.1 Correlator Structures

A common feature of all acquisition methods is that received

signal and locally generated signal are first correlated to produce a
measure of similarity between the two. This measure is then
compared with a threshold to decide if the two signals are in
synchronism. If they are, the tracking loop takes over. If they are not,
the acquisition procedure provides for a phase or frequency change in
the locally generated code as a part of a systematic search through
the receiver's phase and frequency uncertainty region, and another
correlation is attempted.

Consider the direct-sequence parallel-search acquisition system

shown in Figure4.1.

Figure4.1 Direct-Sequence Parallel-Search Acquisition System

The locally generated code g(t) is available with delays that are
spaced one-half chip (Tc/2) apart. If the time uncertainty between
local code and received code is Nc chips, and a complete parallel
search of the entire time uncertainty region is to be accomplished in a
single search time, 2Nc. correlators are used. Each correlator
simultaneously examines a sequence of λ chips, after which the 2Nc
correlator outputs are compared. The locally generated code,
corresponding to the correlator with the largest output is chosen.
Conceptually, this is the simplest of the search techniques; it
considers all possible code positions (or fractional code positions) in
parallel and uses a maximum likelihood algorithm for acquiring the
code. Each detector output pertains to the identical observation of
received signal plus noise. As λ increases, synchronization error
probability (i.e., the probability of choosing the incorrect code
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alignment) decreases. Thus, λ is chosen as a compromise between

minimizing the probability of a synchronization error and minimizing
the time to acquire.

Figure 4.2 illustrates a simple acquisition scheme for a

frequency hopping system. Assume that a sequence of N consecutive
frequencies from the hop sequence is chosen as a synchronization
pattern (without data modulation). The N non coherent matched
filters each consists of a mixer followed by a band pass filter (BPF)
and a square-law envelope detector (an envelope detector followed by
a square-law device). If the frequency hopping sequence is fl, f2... fN,
delays are inserted into the matched filters so that when the correct
frequency hopping sequence appears, the system produces a large
output, indicating detection of the synchronization sequence.

Figure4.2 Frequency hopping Simple Acquisition Scheme

Acquisition can be accomplished rapidly because all possible

code offsets are examined simultaneously. Note that the presence of
band pass filters (BPF) in Figure 4.2 indicates that the local oscillator
frequencies fl, f2... fN, are chosen to have offsets by some intermediate
frequency (IF) from the expected received hop sequence. The
same system can be implemented with local oscillator frequencies
chosen (without offsets) so that the mixers yield baseband signals,
and thus the filters would need to be low-pass filters (LPF). The
mixers are typically complex, yielding in-phase and quadrature terms.

If, during each correlation, λ chips (each chip having a

duration of Tj are examined, the maximum time required for a fully
parallel search is
(T )
acq max = λTc

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The mean acquisition time of a parallel search system can be

approximated by noting that after integrating over λ chips, a correct
decision will be made with probability PD, called the probability of
detection. If an incorrect output is chosen, additional λ chips are
again examined to make a determination of the correct output.
Therefore, on the average, the acquisition time is

−
T acq = λTc PD + 2λTc PD (1 − PD ) + 3λTc PD (1 − PD )2 + .....
λTc
=
PD

Since the required number of correlators or matched filters can be

prohibitively large, fully parallel acquisition techniques are not usually
used. In place of Figures 4.1 and 4.2, a single correlator or matched
filter can be implemented that will serially search until synchronization
is achieved. Naturally, trade-offs between fully parallel, fully serial, and
combinations of the two involve hardware complexity versus time to
acquire for the same uncertainty and chip rate.

4.3 Serial Search

A popular strategy for the acquisition of spread-spectrum
signals is to use a single correlator or matched filter to serially search
for the correct phase of the DS code signal or the correct hopping
pattern of the FH signal. A considerable reduction in complexity, size,
and cost can be achieved by a serial implementation that repeats the
correlation procedure for each possible sequence shift.
Figures 4.3 and 4.4 illustrate the basic configuration for DS
and FH spread-spectrum schemes, respectively. In a stepped serial
acquisition scheme for a DS system, the timing epoch of the local PN
code is set, and the locally generated PN signal is correlated with the
incoming PN signal. At fixed examination intervals of ATE, (search dwell
time), where X >> 1, the output signal is compared to a preset
threshold. If the output is below the threshold, the phase of the locally
generated code signal is incremented by a fraction (usually one-half) of
a chip and the correlation is re-examined. When the threshold is exceeded,
the PN code is assumed to have been acquired, the phase-incrementing
process of the local code is inhibited, and the code tracking procedure
will be initiated. In a similar scheme for FH systems, shown in Figure
4.4, the PN code generator controls the frequency hopper. Acquisition
is accomplished when the local hopping is aligned with that of the
received signal.
The maximum time required for a fully serial DS search,

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assuming that the search proceeds in half-chip increments, is

(T )
acq max = 2 N c λTc
where the uncertainty region to be searched is Nc chips long.

Figures 4.3 Direct Sequence serial acquisition

The mean acquisition time of a serial DS search system can be

shown, for Nc >>1/2 chip, to be

− (2 − PD )(1 + KPFA )
T acq = N c λTc
PD

Figures 4.4 Frequency hopping serial acquisition

where λTc,. is the search dwell time, PD is the probability of

correct detection, and PFA is the probability of false alarm. We can
regard the time interval KλTc (. where K >> 1, as the time needed to
verify a detection. Therefore, in the event of a false alarm, KλTc,
seconds is the time penalty incurred. For Nc >> 1/2; chip and K << 2Nc.
the variance of the acquisition time is
1 1 1 
( var )acq = ( 2 N c λTc )
2
(1 + KPFA )  + 2 − 
 12 PD PD 
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4.4 Sequential Estimation

Another search technique, called rapid acquisition by sequential

estimation (RASE), proposed by Ward. The RASE system enters its best
estimate of the first n received code chips into the n stages of its local
PN generator. The fully loaded register defines a starting state from
which the generator begins its operation. A PN sequence has the
property that the next combination of register states depends only on
the present combination of states. Therefore, if the first n received
chips are correctly estimated, all the following chips from the local PN
generator will be correctly generated. The switch is next thrown to
position 2. If the starting state had been correctly estimated, the local
generator generates the same sequences as the incoming waveform, in
the absence of noise. If the correlator output after ATE exceeds a preset
threshold level, we assume that synchronization has occurred. If the
output is less than the threshold, the switch is returned to position 1,
the register is reloaded with estimates of the next n received chips,
and the procedure is repeated. Once synchronization has occurred,
the system no longer needs estimates of the input code chips. We can
calculate the minimum acquisition time for the case when no noise is
present. The first n chips will be correctly loaded into the register, and
therefore, the acquisition time is

Tacq = nTc

Figure 4.5 Rapid Acquisition by Sequential Estimation

While the RASE system has a rapid acquisition capability it

has the drawback of being highly vulnerable to noise and
interference signals. The reason for this is that the estimation
process consists of a simple chip-by-chip hard-decision
demodulation, without using the interference rejection benefits of
the PN code.

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4.5 Tracking

Once acquisition or coarse synchronization is completed, tracking

or fine synchronization takes place. Tracking code loops can be
classified as coherent or non-coherent. A coherent loop is one in which
the carrier frequency and phase are known exactly so that the loop can
operate on a baseband signal. A non-coherent loop is one in which the
carrier frequency is not known exactly (due to Doppler effects, for
example), nor is the phase. In most instances, since the carrier
frequency and phase are not known exactly, a priori, a non-coherent
code loop is used to track the received PN code. Tracking loops are
further classified as a full-time early-late tracking loop, often referred to
as a delay-locked loop (DLL), or as a time-shared early-late tracking
loop, frequently referred to as a tau-dither loop (TDL). A basic non-
coherent DLL loop for a direct-sequence spread-spectrum system using
binary phase shift keying (BPSK) is shown in Figure 4.6. The data x(t)
and the code g(t) each modulate the carrier wave using BPSK, and as
before in the absence of noise and interference, the received waveform
can be expressed as
r ( t ) = A 2 Px(t ) g (t ) cos(ω0t + Φ )

Figure 4.6 DLL Loop for Tracking Direct-Sequence Signal

Figure 4.7 DLL Feedback Signal

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where the constant A is a system gain parameter and is a random

phase angle in the range (0, 2π). The locally generated code of the
tracking loop is offset in phase from the incoming g(t) by a time r, where
Tc
τ < . The loop provides fine synchronization by first generating two
2
 T   T 
PN sequences g  t + c + τ  and g  t − c + τ  delayed from each other by one
 2   2 
chip. The two band pass filters are designed to pass the data and to
 Tc 
average the product of g(t) and the two PN sequences g  t ± + τ  .The
 2 
square-law envelope detector eliminates the data since x ( t ) = 1 . The
output of each envelope detector is given approximately by

 T  T
ED ≈ E{ g (t ) g  t ± c + τ  } = Rg (τ ± c )
 2  2

where the operator E{•} means expected value and Rg(x) is the
autocorrelation function of the PN waveform. The feedback signal Y( τ )
is shown in Figure 4.6. When T is positive, the feedback signal Y( τ )
instructs the voltage-controlled oscillator (VCO) to increase its
frequency, thereby forcing T to decrease, and when r is negative, Y( τ )
instructs the VCO to decrease. There by forcing r to increase. When r
is a suitably small number, g(t)g(t+ τ ) ~ 1 yielding the despread signal
Z(t), which is then applied to the input of a conventional data
demodulator. A problem with the DLL is that the early and late arms
must be precisely gain balanced or else the feedback signal Y( τ ) will
be offset and will not produce a zero signal when the error is zero. This
problem is solved by using a time-shared tracking loop in place of the
full-time delay-locked loop. The time-shared loop time shares the use
of the early-late correlators. The main advantages are that only one
correlator need be used in the design of the loop and further that dc
offset problems are reduced.

Figure 4.8 Tau-dither tracking loop

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A problem with some control loops is that if things are going

well and the loop is tracking accurately, the control signal is
essentially zero. When the control signal is zero, the loop can get
"confused" and do erratic things. This is especially the case in more
sophisticated tracking loops that modify their own loop gain in
response to the perceived environment. An offshoot of the time-shared
tracking loop, called the tau-dither loop (TDL), shown in Figure 4.8,
tends to deal with this potential problem by intentionally injecting a
small error in the tracking correction, so that the loop kind of vibrates
around the correct answer.

This vibration is typically small, so that the loss in performance

is minimal. This design has the advantage that only one correlator is
needed to provide the code tracking function and the despreading
function. Just as in the case of a DLL, the received signal is correlated
with an early and a late version of the locally generated PN code. As
shown in Figure 6, the PN code generator is driven by a clock signal
whose phase is dithered back and forth with a square-wave switching
function; this eliminates the necessity of ensuring identical transfer
functions of the early and late paths. The signal-to-noise performance
of the TDL is only about 1.1 dB worse than that of the DLL if the arm
filters are designed properly.

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UNIT-V
APPLICATIONS

5.1 Application of Spread Spectrum in Satellite Commmunication

The multiple access (MA) technique, code division multiple access (CDMA) is
a combination of both frequency and time separation. It is the most complex technique
to implement, requiring several levels of synchronization at both the transmission and
reception levels. CDMA is practical for digital formatted data only, and offers the
highest power and spectral efficiency operation of the three fundamental techniques.

Each uplink station is assigned a time slot and a frequency band in a coded
sequence to transmit its station packets. The downlink transmission is an interleaved
set of all the packets as shown in Figure 5.1. The downlink receive station must know
the code of frequency and time locations in order to detect the complete data
sequence. The receive station with knowledge of the code can recoup the signal from
the noise-like signal that appears to a receiver that does not know the code. Code
Division Multiple Access is often referred to as Spread Spectrum or Spread
Spectrum Multiple Access (SSMA) because of the signal spreading characteristics of
the process.

Figure 5.1 Code Division Multiple Access (CDMA) for Satellite Communication

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CDMA offers several advantages over FDMA or TDMA due to its architecture.

• Privacy: The code is distributed only to authorized users, protecting the information
from others.

• Spectrum Efficiency: Several CDMA networks can share the same frequency band,
because undetected signal behaves as Gaussian noise to all receivers without
knowledge of the code sequence. This is particularity useful in applications such as
NGSO Mobile Satellite Service systems, where bandwidth allocations are limited.

• Fading Channel Performance: Only a small portion of the signal energy is present
in a given frequency band segment at any one time, therefore frequency selective
fading or dispersion will have a limited effect on overall link performance.

• Jam Resistance: Again, because only a small portion of the signal energy is present
in a given frequency band segment at any one time, the signal is more resistant to
intentional or unintentional signals present in the frequency band, thereby reducing
the effects on link performance.

Selection of the appropriate code sequence to use in the CDMA process is

critical to its successful implementation. The code sequence must be conFigure d to
avoid unauthorized decoding, yet short enough to allow efficient data transmissions
without introducing latency or synchronization problems. The most successful type of
code sequence for CDMA, which meets both of the above criteria, is the
pseudorandom (PN) sequence. Pseudorandom means ‘like random,’ that is,
appearing random but having certain non-random or deterministic features. The PN
sequence used in CDMA systems is a finite length binary sequence, in which bits are
randomly arranged. The autocorrelation of the PN sequence resembles the
autocorrelation of band-limited white noise.

As we know the CDMA operates on the principle of spread-spectrum

transmission; see Figure 5.2. The uniquely separable address signatures (codes) are
embedded within the uplink carrier waveform. Each uplink uses the entire satellite
bandwidth and transmits through the satellite whenever needed, with all active
stations superimposing their waveforms on the downlink. As such, no time or
frequency separation is required. Carrier separation is achieved at each earth station
by identifying the carrier with the proper signature. The uplink station, as in Figure
5.2(b), spreads the user’s spectrum of Figure 5.2(a). The spread spectrum might
contain some noise and other interference when it is retransmitted. The receiver
recovers the useful information by reducing the spectrum of the carrier transmitted in
its original bandwidth, as in Figure 5.2(c).

The effect of noise and other interference has been suppressed in Figure 5.2(c)
for brevity. This operation simultaneously spreads the spectrum of other users in such

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a way that they appear as noise of low spectral density. It should be noted that one
could not simply use codes of arbitrary different phases to provide CDMA, because the
codes have high-autocorrelation side lobes at the subsequent periods. Furthermore,
the power spectral density of the codes has line components at frequencies
corresponding to each of the code periods

Figure 5.2 CDMA system (a) user’s carrier spectrum (b) uplink spread spectrum
(c) recovered spectrum

The spreading ratio is determined primarily by the code ratio kc/rc and can be
achieved either with low-rate channel codes or long address codes,

where

kc = Ts B

1
rc =
Ts rb

kc B
Thus, the spreading ratio = . This ratio is commonly referred to as the
rc rb
spreading ratio of the code modulation or CDMA bandwidth expansion factor. In some
texts, this ratio is halved because the carrier bandwidth is taken as B/2.

CDMA has some features:

1. It is simple to operate.

2. It does not require any transmission synchronization between stations. The only
synchronization required is that of the receiver to the sequence of the received carrier.

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3. It offers sufficient protection against interference from other stations and that due to
multiple paths. This makes CDMA attractive for networks of small stations with large
antenna beamwidths and for satellite communication with mobiles.

However, on the average, its main disadvantage is the low throughput

Figure 5.3 Spread-Spectrum Rejection of Interference

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Spread spectrum in itself does not fundamentally provide any link budget
advantage in terms of performance in additive thermal noise. The basic link bit-error
ratio is determined by the link carrier-noise density, C/ N0, and it is of no first-order
consequence that the carrier power, C, is spread. However, for a practical system, SS
can offer benefits which may be very important and even necessary, and these will
affect resultant system performance.

SS may offer the following benefits for satellite communications:

i. Rejection of uncorrelated interference permits system operation where adjacent

satellites (say at 1.5° spacing in the geostationary arc) may lie within the
beamwidth of a small-terminal antenna. This may facilitate operation with small
antennas at C-band, with its relatively longer wavelength and correspondingly
large beamwidth.

ii. Other link interference, multipath and adjacent channels may be similarly
tolerated, thereby facilitating operation in shared bands.

iii. The effect of SS transmissions upon other users is relatively benign, appearing
simply as additional noise rather than as potentially destructive interference.
Again, this allows operation in shared bands.

iv. Power flux-density values per unit bandwidth are reduced by virtue of the
spreading (but the overall power flux density is unchanged). This may permit
operation within the letter of regulatory limits for some high EIRP downlinks.

v. Spread spectrum generally provides good LPI (low probability of intercept), which
may highly be significant in some military scenarios.

SS in itself makes inefficient use of bandwidth, but the bandwidth efficiency may
not always be a real problem, especially in very-small-terminal systems. The real price
paid for SS is the complexity and cost of the synchronization circuitry in the receiver,
with the difficulty in synchronizing the despreading code. Code lock is generally
maintained by means of a code-tracking loop, the behavior of which is analogous to
that of a phase-lock loop. Prior to such lock, however, it may be necessary to instigate
a code-search phase, where all possible relative code states are examined to find the
one producing a correlated product within a narrow BW. Such search and acquisition
processes are usually performed sequentially, and can take an appreciable amount of
time and represent a costly system overhead.

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Spread spectrum (with or without a CDMA multiple-access capability, as

described below) has been advocated for some VSAT systems, where the small ground
terminal antenna apertures mean that interference will be received from (or radiated
to) adjacent satellites. The interference-rejection capability of SS allows operation
under such conditions. Essentially, the interfering power is uniformly spread so as to
constitute an increased noise level, rather than represent potentially destructive
narrowband interference against which large narrow beamwidth antennas would be
needed. The effect of terrestrial interference (i.e. microwave links) is also mitigated.

5.1.1 Direct Sequence Spread Spectrum

A direct sequence spread spectrum (DS-SS) system spreads the baseband

data bits with the PN sequence. In the most widely used satellite network
implementation, a phase modulated baseband data stream is generated, and then
used to phase modulate an RF carrier with the PN spread signal.

Figure 5.4 shows the elements present in the DS-SS communications satellite
system. The data bit stream is phase modulated onto a carrier, then directed to the PN
Code Modulator which phase modulates the RF carrier to produce the spread signal.
After passing through the satellite channel, the signal is ‘despread’ with a balanced
modulator, then phase demodulated to produce the original data bit stream.

Figure 5.4 DS-SS satellite system elements

If the transmitter and receiver PN code sequences do not match, random phase
modulation occurs and the spread signal looks like noise to the demodulator.

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5.1.2 Frequency Hopping Spread Spectrum

The second basic approach to spectrum spreading in CDMA is referred to
as frequency hopping spread spectrum (FH-SS).With FH-SS, the transmission
(carrier) frequency is acted upon by a PN sequence, producing a sequence of
modulated data bursts with time varying pseudorandom carrier frequencies. This
‘frequency hopping’ spreads the information data sequence across a broader band,
producing the benefits of CDMA similar to the DS-SS approach.

The possible set of carrier frequencies available for frequency hopping in FH-SS
is called the hopset. Each of the hopped channels contains adequate RF bandwidth
for the modulated information, usually a form of frequency shift keying (FSK). If BFSK
is used, the pair of possible instantaneous frequencies changes with each hop. Two
bandwidths are defined in FH-SS operation:

• Instantaneous Bandwidth, bbb – the baseband bandwidth of the channel used in the
hopset.

• Total Hopping Bandwidth, brf – the total RF bandwidth over which hopping occurs.

Larger the ratio of brf to bbb, better the spread spectrum performance of the FH-
SS system. Figure 5.5 shows the elements of a FH-SS satellite system. The data
modulated signal is PN modulated with a PN sequence of carrier frequencies, fc,
generated from the PN sequence pPN(t). The frequency-hopped signal is transmitted
through the satellite channel, received, and ‘dehopped’in the carrier demodulator
using a stored replica of the PN sequence. The dehopped signal is then demodulated
by the data demodulator to develop the input data stream.

Figure 5.5 FH-SS satellite system elements

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There are two classifications of FH-SS, based on the hopping rate with respect
to the data symbol rate:

• Fast Frequency Hopping – more than one frequency hop during each transmitted
symbol.
• Slow Frequency Hopping – one or more data symbols are transmitted in the time
interval between frequency hops.

Both types of FH-SS offer similar performance, and the implementation

depends on system parameters and other considerations. The parameters used to
define CDMA system performance – processing gain and capacity – are similar for DS-
SS or FH-SS implementations.

Table 5.1 Comparismn bewteen FDMA /TDMA/ CDMA

Characteristic FDMA TDMA CDMA

Bandwidth Single channel Multiple channels per SCPC, partial or full
utilization per carrier carrier – partial allocation
(SCPC) allocation

Interference Limited Limited with Can suppress

rejection frequency hopping interference, up to
noise limit

Inter-modulation Most sensitive Less sensitive (less Least sensitive (least

effects (most back-off back-off required) back-off required)
required)

Doppler frequency Bandwidth Burst time limiting Removed by receiver

shift limiting

Spectrum Uses least Moderate bandwidth Largest demand for

flexibility bandwidth per use per carrier contiguous segment
carrier

Capacity Basic capacity Can provide capacity Capacity

available improvement through indeterminate due to
hopping loading unknowns

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5.2 ANTIJAM (AJ) COMMUNICATIONS

One of the key applications of spread spectrum is for antijam communications
in a hostile environment. Assume the received signal, denoted r(t), is given by

r ( t ) = Ax ( t ) + I ( t ) + nw ( t )

x(t ) = c ( t ) d ( t ) exp [ jωct + θc ]

where x(t) is given by, A is a constant amplitude, where d(t) is a binary-valued

data waveform of rate 1/Tb bits and θc are phase of the data-modulated carrier and
c(t) is the BPSK signal.

I ( t ) = α cos (ωct + θ )
and nw(t) is additive white Gaussian noise (AWGN) having two-sided spectral density
N0 /2 α is the amplitude of the tone jammer and θ is a random phase uniformly
distributed in [0, 2π]. If we employ the standard correlation receiver of Figure 5.6, it is
straightforward to show that the final test statistic out of the receiver is given by

Tb
g (Tb ) = ATb + α cos θ ∫ c ( t ) dt + N (Tb )
0

Figure 5.6 Block diagram of correlation receiver

where N(Tb) is the contribution to the test statistic due to the AWGN. Noting
that, for rectangular chips, we can express

M
c ( t ) dt =Tc ∑ ci
Tb
∫0
i =1

where

M= Tb/Tc

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is one-half of the processing gain, it is straightforward to show that, for a given value
of θ, the signal-to-noise-plus-interference ratio, denoted by S/Ntotal , is given by

S 1
=
N total NO  J  2
+  cos θ
2 Eb  MS 

α2 A2
J ≜ S≜
The jammer power is 2 and the signal power is 2

If we look at the second term in the denominator of Eq, we see that the ratio
J/S is divided by M. Realizing that J/S is the ratio of the jammer power to the signal
power before despreading, and J/MS is the ratio of the same quantity after
despreading, we see that, as was the case for noise jamming, the benefit of employing
direct sequence spread spectrum signalling in the presence of tone jamming is to
reduce the effect of the jammer by an amount on the order of the processing gain.
Finally, one can show that an estimate of the average probability of error of a system
of this type is given by

1 2π  S 
Pe =
2π ∫
0
φ  −
N total
dθ
 
x 2
1 −y
φ ( x) ≜ ∫e 2
dy
where 2π −∞

Figure 5.7 Graph plot between power and noise ratio

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It is evaluated numerically and plotted, the results are as shown in Figure 5.7.
It is clear that a large initial power advantage of the jammer can be overcome by a
sufficiently large value of the processing gain.

5.3 LOW-PROBABILITY OF INTERCEPT (LPI)

The opposite side of the AJ problem is that of LPI, that is, the desire to hide
your signal from detection by an intelligent adversary so that your transmissions will
remain unnoticed and, thus, neither jammed nor exploited in any manner. This idea of
designing an LPI system is achieved in a variety of ways, including transmitting at the
smallest possible power level, and limiting the transmission time to as short an
interval in time as is possible. The choice of signal design is also important, however,
and it is here that spread spectrum techniques become relevant.

The basic mechanism is reasonably straightforward; if we start with a

conventional narrowband signal, say a BPSK waveform having a spectrum as shown in
Figure 5.8a, and then spread it so that its new spectrum is as shown in Figure 5.8b,
the peak amplitude of the spectrum after spreading has been reduced by an amount
on the order of the processing gain relative to what it was before spreading. Indeed, a
sufficiently large processing gain will result in the spectrum of the signal after
spreading falling below the ambient thermal noise level. Thus, there is no easy way for
an unintended listener to determine that a transmission is taking place.

Figure 5.8 Amplitute vs frequency

That is not to say the spread signal cannot be detected, however, merely that it
is more difficult for an adversary to learn of the transmission. Indeed, there are many

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forms of so-called intercept receivers that are specifically designed to accomplish this
very task. By way of example, probably the best known and simplest to implement is a
radiometer, which is just a device that measures the total power present in the
received signal. In the case of our intercept problem, even though we have lowered the
power spectral density of the transmitted signal so that it falls below the noise floor,
we have not lowered its power (i.e., we have merely spread its power over a wider
frequency range).

Thus, if the radiometer integrates over a sufficiently long period of time, it will
eventually determine the presence of the transmitted signal buried in the noise. The
key point, of course, is that the use of the spreading makes the interceptor’s task
much more difficult, since he has no knowledge of the spreading code and, thus,
cannot despread the signal.

5.4 MOBILE COMMUNICATIONS

5.4.1 CODE DIVISION MULTIPLE ACCESS

In code division multiple access (CDMA) systems, the narrowband message

signal is multiplied by a very large bandwidth signal called the spreading signal. The
spreading signal is a pseudo-noise code sequence that has a chip rate which is orders
of magnitudes greater than the data rate of the message. All users in a CDMA system,
as seen from Figure 5.9, use the same carrier frequency and may transmit
simultaneously. Each user has its own pseudorandom codeword which is
approximately orthogonal to all other codewords. The receiver performs a time
correlation operation to detect only the specific desired codeword. All other code-
words appear as noise due to decorrelation. For detection of the message signal, the
receiver needs to know the codeword used by the transmitter. Each user operates
independently with rio knowledge of the other users.

Figure 5.9 Basic CDMA transmitter

Let bk(t) bits for k users i.e.bits transmitted by users, Ck be sprading codes, J be
spreading factor. Sk(t) be transmitted signal and y(t) be received signal

In CDMA, the power of multiple users at a receiver determines the noise floor
after decorrelation. If the power of each user within a cell is not controlled such that

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they do not appear equal at the base station receiver, then the near-far problem
occurs.

Figure 5.10 Basic CDMA receiver

k
y (t ) = ∑ h (t ) * S
k =1
k k (t ) + n (t )

Where hk(t) is impulse response for user and n(t) is the noise.

The near-far problem occurs when many mobile users share the same channel.
In general, the strongest received mobile signal will capture the demodulator at a base
station. In CDMA, stronger received signal levels raise the noise floor at the base
station demodulators for the weaker signals, thereby decreasing the probability that
weaker signals will be received. To combat the near-far problem, power control is used
in most CDMA implementations. Power control is provided by each base station in a
cellular system and assures that each mobile within the base station coverage area
provides the same signal level to the base station receiver. This solves the problem of a
nearby subscriber overpowering the base station receiver and drowning out the signals
of far away subscribers.Power control is implemented at the base station by rapidly
sampling the radio signal strength indicator (RSSI) levels of each mobile and then
sending a power change command over the forward radio link. Despite the use of
power control within each cell, out-of-cell mobiles provide interference which is not
under the control of the receiving base station. The features of CDMA including the
following:

Many users of a CDMA system share the same frequency. Either TDD or FDD may
be used.

Unlike TDMA or FDMA, CDMA has a soft capacity limit. Increasing the number of
users in a CDMA system raises the noise floor in a linear manner.Thus, there is
no absolute limit on the number of users in CDMA. Rather,the system
performance gradually degrades for all users as the number of users is increased,
and improves as the number of users is decreased.

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Multipath fading may be substantially reduced because the signal is spreadover a

large spectrum. If the spread spectrum bandwidth is greater than thecoherence
bandwidth of the channel, the inherent frequency diversity willmitigate the effects
of small-scale fading.

Channel data rates are very high in CDMA systems. Consequently, the symbol
(chip) duration is very short and usually much less than the channel delay
spread. Since PN sequences have low autocorrelation, multipath which is delayed
by more than a chip will appear as noise. A RAKE receiver can beused to improve
reception by collecting time delayed versions of the required signal.

Since CDMA uses co-channel cells, it can use macroscopic spatial diversity to
provide soft handoff. Soft handoff is performed by the MSC, which can
simultaneously monitor a particular user from two or more base stations. The
MSC may chose the best version of the signal at any time without switching
frequencies.

Self-jamming is a problem in CDMA system. Self-jamming arises from the fact that
the spreading sequences of different users are not exactly orthogonal, hence in the
despreading of a particular PN code, non-zero contributions to the receiver
decision statistic for a desired user arise from the transmissions of other users in
the system.

The near-far problem occurs at a CDMA receiver if an undesired user has ahigh
detected power as compared to the desired user.

Figure 5.11 Simple System Capacity Comparison

It can be shown that, in a simple model scenario, CDMA is fundamentally inferior

to FDMA or TDMA in terms of capacity or spectral efficiency. For a practical very-
small-terminal scenario, however, the difference between CDMA and FDMA is not so
great, especially where performance is power limited owing to small antenna size and

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where thermal noise predominates. As the total power in the system increases, the
performance of CDMA becomes inferior to that of FDMA as the former is limited by the
self-jamming noise. This leads to a graceful degradation of CDMA as the number of
terminals in the network is increased.

CDMA does, however, offer a number of advantages when other effects are taken
into account, and particularly where interference from adjacent spot beams, or other
systems, is a factor. This is akin to the terrestrial cellular situation with adjacent cell
interference. Such factors can enhance CDMA performance to a level exceeding that
which may be achieved by FDMA or TDMA in those scenarios.

Because satellite downlink EIRP may be shared between transmissions on a pro

rata basis, and since other users contribute to the effective noise level, a CDMA
system for speech traffic can benefit directly from voice activation. If the carrier can be
removed during speech pauses, the residual active channels can take advantage of the
total EIRP at the same time as the average aggregate self-interference-noise
contribution is reduced. Hence, the overall network capacity is optimised without the
need for specific DSI techniques.

Note that in the satellite channel itself the CDMA transmission occupies a very
wide bandwidth and, consequently, the channel signal-to-noise ratio (SNR) may be
very small (≪1). The despreading process restores this to a decent value. The link
C/N0 requirements, however, which relate to the more relevant and fundamental noise
spectral density, are unchanged to a first order. Thus it cannot be said that either
spread spectrum or CDMA fundamentally implies low transmit power or a
performance which is any different from FDMA etc., although it may be that other
practical benefits can arise.

A feature of CDMA is that the spread signals in the satellite transponder give rise
to noise-like IPs at low level and without peaks, having an effect smaller and more
manageable than that of narrowband IPs (as might arise with SCPC/FDMA). As a
result, a transponder may be operated closer to saturation than may an FDMA
system, giving capacity benefits. Conversely, a CDMA system is relatively immune to
narrowband IPs or interference. Another benefit of CDMA is resistance to multipath
propagation, since once correlation lock has been achieved other multipath signals will
represent simply uncorrelated interference. This is of value especially to mobile and
VSAT systems. CDMA may additionally provide advantage where polarisation diversity
is employed, through rejection of crosspolar components.

CDMA offers a further practical benefit in that the frequency agility of an FDMA
transmitter/receiver is not required. In operation CDMA signals may be overlaid on
the same carrier frequency, partially overlapping, or given non-overlapping
frequencies; it is also possible to share a transponder with other signals on an FDMA
basis.

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The application of CDMA tends to be limited by the cost and complexity of the
receiver, together with the time taken to achieve synchronisation. In simple theory
terms its performance is inferior to that of FDMA or TDMA for a given power and
bandwidth, but in practice the performance can be superior to FDMA allowing for the
latter's limitations of guard bands and TWTA backoff. There is no need for network
timing references as in TDMA, and speech duty cycles may be readily exploited. CDMA
is invariably used in conjunction with forward-error-correcting (FEC) coding, and in
practice may offer greater flexibility in this regard than either FDMA or TDMA.

Some military satellite communications use CDMA as a multiple-access scheme.

These take advantage of the random-access nature of CDMA, where fixed or highly
planned schemes are impractical, and where downlink EIRP needs to be maximized for
operation to small terminals. (Although a degree of jamming and interference rejection
is provided, other spread-spectrum schemes with much greater processing gain and
code security tend to be used for specific antijam purposes.)

Spread-spectrum techniques (such as CDMA) became established in civil satellite

communications with the early equatorial VSAT system operating at C-band in the US.
The main reason for the adoption of CDMA in that system is understood to be the
need for SS-derived rejection of adjacent satellite interference experienced with the
relatively wide antenna beamwidths. It has also been suggested that the use of spread
spectrum enabled operation within the letter of FCC flux-density regulation limits. It
appears that few if any Ku-band VSAT systems currently employ CDMA, principally
because the relatively narrow antenna beamwidths at the shorter wavelengths reduce
potential adjacent satellite interference.

As a topic, CDMA has been given a boost by its application in terrestrial cellular
systems (e.g. the US IS-95 scheme). A variant of this system is also employed in the
Globalstar satellite personal communication network of 48 satellites. In satellite
systems there has been some work under ESTEC sponsorship looking at synchronous
CDMA for satellite communication application; here all codes are time aligned, and by
choice of orthogonal sets the selfjamming noise may be reduced such schemes may,
however, have certain difficulties and practical limitations. There is also renewed b

5.4.2 CAPACITY OF CELLULAR CDMA

Channel capacity for a radio system can be defined as the maximum number of
channels or users that can be provided in a fixed frequency band. Radiocapacity is a
parameter which measures spectrum efficiency of a wireless system.

The capacity of CDMA systems is interference limited, while it is bandwidth

limited in FDMA and TDMA. Therefore, any reduction in the interference will cause a
linear increase in the capacity of CDMA. Put another way, in a CDMA system, the link
performance for each user increases as the number of users decreases.

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A straightforward way to reduce interference is to use multisectorized antennas,

which results in spatial isolation of users. The directional antennas receive signals
from only a fraction of the current users, thus leading to the reduction of interference.

Another way of increasing CDMA capacity is to operate in a discontinuous

transmission mode (DTX), where advantage is taken of the intermittent nature of
speech. In DTX, the transmitter is turned off during the periods of silence in speech. It
has been observed that voice signals have a duty factor of about 3/8 in landline
networks and 1/2 for mobile systems, where background noise and vibration can
trigger voice activity detectors. Thus, the average capacity of a CDMA system can be
increased by a factor inversely proportional to the duty factor.

For evaluating the capacity of CDMA system, first consider a single cell system.
The cellular network consists of a large number of mobile users communicating with a
base station

Let the number of users be N. Then, each demodulator at the cell site receives a
composite waveform containing the desired signal of power S and (N - I) interfering
users, each of which has power, S. Thus, the signal-to-noise ratio is

S 1
SNR = =
( N − 1) S N − 1
In addition to SNR, bit energy-to-noise ratio is an important parameter in
communication systems. It is obtained by dividing the signal power by the base band
information bit rate, R, and the interference power by the total RF band width, W. The
Eb
SNR at the base station receiver can be represented in terms of given by
N0
Eb S R W R
= =
N 0 ( N − 1)( S W ) N − 1

Equation does not take into account the background thermal noise, in the
Eb
spreadbandwidthη . To take this noise into consideration, can be represented as
N0
Eb W R
=
N 0 ( N − 1) + (η S )

The number of users that can access the system is thus given as
W R
N = 1+ − (η S )
Eb N 0

where W R is called the processing gain. The background noise determines the
cell radius for a given transmitter power.

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In order to achieve an increase in capacity, the interference due to other users

should be reduced.

The first technique for reducing interference is anterma sectorization. As an

example, a cell site with three antennas, each having a beam width of 1200, has
interference N0' which is one-third of the interference received by an onini-directional
antenna. This increases the capacity by a factor of 3 since three times as many users
may now be served within a sector while matching the performance of the omni-
directional antenna system. The same number of users in an omni-directional cell may
now be served in 1/3rd the area. The second technique involves the monitoring of
voice activity such that each transmitter is switched off during periods of no voice
activity. Voice activity is denoted by a factor α , and the interference term
becomes ( N s − 1) α , where Ns is the number of users per sector. With the use of these
Eb
two techniques, the new average value of within a sector is given as
N 0′
Eb W R
=
N 0′ ( N s − 1) α + (η S )

When the number of users is large and the system is interference limited rather
than noise limited, the number of users can be shown to be

 
1 W R

Ns = 1 +  
α  Eb 
 N 0′ 

If the voice activity factor is assumed to hate a value of 3/8, and three sectors
per cell site are used, the above equation demonstrates that the SNR increases by a
factor of 8, which leads to an 8 fold increase in the number of users compared to an
omni-directional antenna system with no voice activity detection.

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REFERENCES

1. Rodger E. Ziemer, “Fundamentals of Spread Spectrum Modulation” University of

Colorado at Colorado Springs, 2007.
2. M.K. Simon, J.K.Omura, R.A Schiltz and B.K Levitt, “Spread spectrum
communication”, Vol-I,II &IV, Computer science Press,USA , 1985.
3. G.R Coopeand, CD.Mc.Gillem, “Modern communications and spread spectrum”,
McGraw Hill,1986.
4. R.C.Dixon, “Spread spectrum systems”, John Wiley, 1984.
5. Mosa Ali Abu-Rgheff, “Introduction to CDMA Wireless Communications”
Elsevier, 2007.
6. http://www.electronicsforu.com/EFYLinux/efyhome/cover/dec2005/Spread-Spectrum-
Radio.pdf
7. http://en.wikipedia.org/wiki/Spread_spectrum
8. http://www.wirelesscommunication.nl/reference/chaptr05/cdma/cdma.htm

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QUESTION BANK
SPREAD SPECTRUM COMMUNICATION

UNIT-I
PART –A
1. Define spread spectrum.
2. What are the principal advantages of spread spectrum?
3. What are the types of techniques used for spread spectrum?
4. List out the various applications of spread spectrum communication.
5. List four beneficial attributes of spread spectrum system.
6. Define processing gain for spread spectrum system.
7. What is jamming margin?
8. Name the jamming methods.
9. What is Maximum length sequence?
10. What are gold codes?
11. What are kasami sequences?
PART-B
1. Explain in detail the origins of spread spectrum communication.
2. Define spread spectrum. State the requirement and classification of spread spectrum.
3. Explain in detail the types of techniques used for spread spectrum.
4. Explain the various advantages and limitation of spread spectrum systems.
5. Explain the model of the spread spectrum communication system.
6. Write briefly about direct sequence spread spectrum.
7. Write briefly about Frequency hopping spread spectrum.
8. How to generate PN sequence using linear feedback shift register?
9. Write briefly about non-linear sequences.
10. Define and explain the processing gain and other fundamental parameters of spread
spectrum in detail.
11. Derive the processing gain of spread spectrum system.
12. Describe the M-sequence and its statistical properties.
13. Discuss the various jamming methods of spread spectrum communication.
14. Explain in detail about kasami sequence and chaobic sequences.
15. What is PN sequence? Explain its need for spread spectrum techniques and list their
characteristics with a suitable example sequence generator.
16. Describe three randomness properties that makes pseudo random signal appear to be
random.
17. Explain the M-sequence and their statistical properties in detail.
18. Discuss the properties of PN sequence used in spread spectrum system.

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19. Explain the generation of linear feedback shift registers sequences.

20. Explain the following:
a. Correlation properties.
b. Gold codes.
21. a. Write the advantages of spread spectrum techniques.
b. Explain the processing gain and Jamming margin.
22. a. Discuss the statistical properties of M-Sequence.
b. Write short notes on Kasami sequences.
23. Write short notes on:
a. M-sequence and its statistical properties.
b. Kasmic Sequence.

UNIT-II
PART –A
1. Define coherent reception.
2. Define direct sequence spread spectrum.
3. What is a jammer?
4. Define pulse jammer.
5. What is partial-band noise jammer?
6. What is a multi-tone jammer?
7. What is a noise jammer?
8. What is chernoff bound?
9. Define bit error rate.
10. Define bit error rate.
PART-B
1. Sketch and explain the block diagram of DS/BPSK system.
2. Explain the multi tone jammer with a neat diagram.
3. Explain the various coherent direction sequence systems used in spread spectrum.
4. Describe the coded DS/BPSK performance for known channel status.
5. Derive the bit error probability of DS/BPSK system.
6. Briefly explain the concept of multi tone jammer.
7. Discuss direct sequence spread spectrum with coherent BPSK transmitter and receiver.
8. Write short notes on pulse noise jammer.
9. Write short notes on probability of error and jamming margin.
10. Discuss the performance of direct sequence spread spectrum system.
11. Write short notes on single and multi-tone jammer.
12. Obtain an expression for bit error probability for arbitrary jammer waveforms.
13. What is meant by chernoff bound?
14. Give an account on partial band jammer.

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15. Derive the probability of error for DS/BPSK signal.

16. Explain the multi-tone jammer with neat diagram.
17. Describe briefly about uncoded bit error probability for arbitrary jammer?
18. Describe briefly about coded DS/BPSK system.
19. Explain the performance of pulse jammer and partial band jammer.
20. Discuss the concept of multi-tone jammer.

UNIT-III
PART –A

1. Distinguish between coherent and non- coherent FH systems.

2. What is the principal of frequency hopping spread spectrum?
3. What are advantages of frequency hopping SS systems?
4. Define frequency hop.
5. Define fast frequency hopping.
6. Describe chip rate.
7. What is the different between fast and slow hopping?
8. Define total hopping band with?
9. What are the characteristics of DS-SS system?
10. What are the performance parameters of FH/DPSK system?
11. What are the characteristics of FH SS system?
12. What is constellation?
PART-B
1. Explain in detail frequency hopping spread spectrum technique.
2. Explain the time hopping SS techniques in detail.
3. Discuss the performance of FH/QPSK systems in partial band jamming.
4. Differentiate between Direct sequence spread spectrum and frequency hopping spread
spectrum.
5. Discuss in detail about partial band noise jammer.
6. Explain the performance of FH/QPSK system in partial band noise jamming.
7. Explain the performance of FH/MDPSK system in partial band noise jamming.
8. What is frequency hopping spread spectrum? Explain its ability to reject the effects of
jammers.
9. Write short notes on frequency synthesis.
10. Explain the following non- coherent FH System model
11. Explain the coherent FH system model with a neat diagram.
12. Compare and contrast the coherent FH systems and non-coherent FH systems.
13. Explain the function of fast FH-SS with neat diagram.

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14. Discuss and compare the performance of FH/QPSK and FH/DPSK system in partial band
jamming.
15. Discuss the performance of FH/DPSK system.
16. Write the advantage of frequency hopping compared to direct sequence system.

UNIT-VI
PART –A
1. Define synchronization.
2. What is acquisition?
3. Define matched filter.
4. What is delay locked loop?
5. Describe Tau-Dither loop.
6. What are the advantages of Tau-Dither loop?
7. What is acquisition and tracking?
8. What is acquisition in FH SS receiver?
9. What is the need for synchronization in SS receivers?
10. Enumerate the characteristics of FH SS receiver.
11. What is the need for synchronization in SS receivers?

PART –B
1. Discuss briefly about acquisition and tracking in DS spread spectrum receivers.
2. Briefly explain the sequential estimation techniques of acquisition.
3. Draw the block diagram of delay locked loop for tracking and explain.
4. Explain the acquisition and tracking in FH-SS receivers.
5. Discuss briefly about acquisition and tracking in FH spread spectrum receivers.
6. Draw the block diagram of delay locked loop for PN code tracking and explain.
7. Write short notes sequence estimation.
8. Write short notes tau-dither tracking loop.
9. Explain the FH acquisition scheme.
10. Explain the rapid acquisition by sequential estimation (RASE).
11. Explain the concept of acquisition and tracking in DS SS receiver with neat diagrams.
12. Describe in detail the matched filter techniques of acquisition and tracking.
13. Draw the block diagram and explain the system for acquisition of an FH signal.
14. Draw the block diagram for Tau-dither loop for tracking DS signal and explain.
15. Explain the sequential estimation.

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UNIT-V
PART –A

1. What is satellite communication?

2. What is mobile communication?
3. What is low probability of intercept communication?
4. What is anti jam military communication?
5. What are the benefits offered by spread spectrum for satellite communication?
6. Give two advantages of spread spectrum.
7. What is multipath interference?
8. What are the satellite communication characteristics?
9. Write the working principal of code division multiple access.
10. What are the advantages of CDMA in spread spectrum communication?
11. List the potential applications of spread spectrum communication.
PART-B
1. Explain the concept of spread spectrum in anti jam military communication.
2. Discuss the application of spread spectrum in anti jam military communication.
3. Explain the concept of spread spectrum in mobile communication.
4. Discuss the application of Spread spectrum in mobile communication.
5. Discuss the application of spread spectrum in satellite communication.
6. Discuss in detail code division multiple access.
7. Explain the low probability of intercept communication.
8. Explain the mobile receiver.
9. Write short notes on:
a. Direct sequence CDMA.
b. Mobile communication.
10. Explain in detail the application of spread spectrum in mobile communication.
11. Write technical notes on:
a. SS in military communication.
b. CDMA.
12. Discuss the application of spread spectrum in Satellite communication.
13. Describe briefly about the ant-jam military communication and Mobile Communication.
14. Discuss the application of spread spectrum in satellite communication.
15. List the features of CDMA.
16. Discuss the application of spread spectrum in satellite communication.
17. Explain the concept of spread spectrum in code division multiple access.
18. Explain the concept of spread spectrum in anti-jam military communication.
19. Explain the concept of spread spectrum in satellite communication.

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