THE UNIVERSITY OF NAIROBI

DEPARTMENT OF ELECTRICAL AND INFORMATION ENGINEERING

PROJECT REPORT TITLE:

ACQUISITION OF FREQUENCY HOPPING SPREAD SPECTRUM SIGNALS

PROJECT CODE: PROJECT 067

This project report is submitted in partial fulfilment of the requirement for the

award of the degree of Bachelor of Science in Electrical and Electronic

Engineering of The University of Nairobi.

Submitted by:

GABRIEL ETONGA OGWALI F17/2389/2009

Project supervisor:

PROF. V.K ODUOL

Project examiner:

DR. G.S ODHIAMBO

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DECLARATION OF ORIGINALITY

COLLEGE: Architecture & Engineering

FACULTY/ SCHOOL/ INSTITUTE: Engineering

DEPARTMENT: Electrical and Information Engineering

COURSE NAME: Bachelor of Science in Electrical & Electronic Engineering

NAME OF STUDENT: Gabriel Etonga Ogwali

REGISTRATION NUMBER: F17/2389/2009

PROJECT TITLE: Acquisition of Frequency Hopping Spread Spectrum Signals

PROJECT CODE: 067

1) I understand what plagiarism is and I am aware of the university policy in this regard.

2) I declare that this final year project report is my original work and has not been

submitted elsewhere for examination, award of a degree or publication. Where other

people’s work or my own work has been used, this has properly been acknowledged

and referenced in accordance with The University of Nairobi’s requirements.

3) I have not sought or used the services of any professional agencies to produce this

work.

4) I have not allowed, and shall not allow anyone to copy my work with the intention of

passing it off as his/her own work.

5) I understand that any false claim in respect of this work shall result in disciplinary

action, in accordance with University anti-plagiarism policy.

Signature: ………………………………………………………………………………………

Date: ……………………………………………………………………………………………

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DEDICATION

To my parents, Joel Ogwali Etonga and Bernice Karimi Ogwali, and my family for their unwavering support through all my endeavors. May God bless you abundantly.

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ACKNOWLEDGEMENT

I would like to thank my supervisor Prof. V.K. Oduol for offering me guidance and being a great source of motivation throughout the execution of this project. His guidance went a long way in ensuring that I accomplished the project objectives.

I would also like to thank all my colleagues who acted as a sounding wall. When things were not working they were always willing to listen and offer suggestions. I cannot mention all of them by name but I gained invaluable insight from all of them.

Thanks to God, Almighty for giving me the strength to carry on through the project.

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CHAPTER 1: INTRODUCTION..................................................................................................................1

1.1 Project Objectives:........................................................................................................................1

1.2 Basic Overview and the goal of communication:..........................................................................1

1.3 Challenges faced in transmitting information:..............................................................................1

1.4 Typical Communication Channels:................................................................................................2

1.4.1 Additive White Gaussian Noise (AWGN) Channel:.................................................................3

1.4.2 Binary Symmetric Channel:....................................................................................................3

1.4.3 Multipath Rayleigh Fading Channel:......................................................................................4

1.4.4 Multipath Rician Fading Channel:..........................................................................................4

1.5 Spread Spectrum Communications:.............................................................................................4

1.5.1 Definition of Spread Spectrum Communications:..................................................................5

1.5.2 Benefits of Spread Spectrum Communications:....................................................................5

1.5.3 The Basis for Spread Spectrum Communication:...................................................................6

1.5.4 Types of Spread Spectrum Systems:......................................................................................7

1.5.5 Historical Perspective of Spread Spectrum Communications:.............................................10

1.5.6 Applications of Spread Spectrum Communications:............................................................11

CHAPTER 2:FREQUENCY HOPPING SPREAD SPECTRUM:......................................................................13

2.1 Basic Overview of FHSS Systems:................................................................................................13

CHAPTER 3: SYNCHRONIZATION IN FHSS SYSTEMS:.............................................................................17

3.1 Definition of Synchronization:....................................................................................................17

3.2 The Need for Synchronization:...................................................................................................17

3.3 Types of Synchronization in FHSS Systems:................................................................................17

3.4 Pseudonoise (PN) Sequences:....................................................................................................18

3.5 FHSS Code Acquisition:...............................................................................................................19

3.5.1 Matched Filter Acquisition:..................................................................................................20

3.5.2 Serial Search Acquisition:.....................................................................................................22

3.6 Code Tracking:............................................................................................................................23

CHAPTER 4: DESIGN AND IMPLEMENTATION:......................................................................................25

4.1 Bernoulli Binary Generator:........................................................................................................26

4.2 PN Sequences:............................................................................................................................26

4.3 8-FSK Modulator:........................................................................................................................27

4.4 Align Signals Block:.....................................................................................................................27

4.5 Doppler Frequency Shift:............................................................................................................27

CHAPTER 5: RESULTS AND ANALYSIS:...................................................................................................29

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5.1 PN Sequence Results:.................................................................................................................29

5.2 Results for the case of transmission through an AWGN Channel:..............................................30

5.3 Results for transmission in a Multipath Rayleigh Fading Channel:.............................................33

5.4 Results for transmission in a Multipath Rician Fading Channel:.................................................35

CHAPTER 6: CONCLUSION AND RECOMMENDATIONS:........................................................................39

6.1 CONCLUSION:.............................................................................................................................39

6.2 RECOMMENDATIONS:................................................................................................................39

References:...........................................................................................................................................40

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LIST OF ABBREVIATIONS

FHSS Frequency Hopping Spread Spectrum

DSSS Direct Sequence Spread Spectrum

BPSK Binary Phase Shift Keying

MFSK M-ary Frequency Shift Keying

PN Pseudonoise

LFSR Linear Feed Back Shift Register

FH Frequency Hopping

TH Time Hopping

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LIST OF FIGURES

Figure 1.1 DSSS System: (a)Transmitter and (b) Receiver ………………………………..10Figure 2.1: Frequency Hopping Pattern of a FHSS system………………………………..14Figure 2.2 FHSS System……………………………………………………………… ……….15Figure 3.1 Connections in a maximal length sequence 4-stage LFSR…………………...18Figure 3.2: A Matched Filter Acquisition System………………………………................21Figure 3.3:FHSS Serial Search Acquisition System……………………………................23Figure 3.4: Early-late-gate tracking…………………………………………………………24Figure 4.1: Simulation Block for Serial Search Acquisition for a FHSS System………25Figure 5.1 PN Sequence Timing Diagram…………………………………………….28Figure 5.3: Correlation between two PN Sequences with a misalignment of 1s………29Figure 5.4 Frequency spectrum of a Bernoulli Binary Sequence……………………….30Figure 5.5: Received signal spectrum for acquisition in a Multipath Rayleigh Fading Channel.......................................................................................................……………31Figure 5.6: Received signal frequency spectrum for acquisition in an AWGN Channel…………………………………………………………………………………………32Figure 5.7:Received signal frequency spectrum for a Multipath Rician Fading Channel…………………………………………………………………………………………33Figure 5.8: Received signal frequency spectrum for a perfectly aligned PN sequence…………………………………………………………………………………………33

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ABSTRACT

Frequency hopping spread spectrum (FHSS) communication systems offer significant performance advantages in view of their low probability of intercept, improved performance in multipath fading environments and their ability to avoid interference by hopping into low interference frequency channels. For the transmitted sequence to be correctly received and demodulated, the frequency hop sequence used at the receiver should be similar to that employed in the transmitter. Code acquisition in frequency hopping attempts to address this problem by providing a frequency hop pattern at the receiver that is nearly identical to that used at the transmitter.

Code acquisition brings the alignment between the transmitter and the receiver hop pattern to at least one hop period

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CHAPTER 1: INTRODUCTION

1.1 Project Objectives:This is a project in spread spectrum communications that specifically deals with code acquisition in frequency hopping spread spectrum systems. The project objectives are as follows:

To study code acquisition in FHSS systems To describe and explain why FHSS is necessary. To design and demonstrate a FHSS code acquisition method.

1.2 Basic Overview and the goal of communication:The main problem in telecommunications is generating a message and ensuring it reaches the recipient in the desired form. While this may sound like a rather mundane task numerous constraints imposed by factors such as channel imperfections offer a tremendous challenge towards achieving this goal. Nevertheless, a number of techniques such as information coding seem to address this challenge.

This is not the only challenge that may affect the sending of messages over a communication channel. One other challenge is how to efficiently utilize the available channel bandwidth. One such technique that has been successfully utilized in improving channel efficiency toward this front is frequency division multiplexing.

The period during which the Second World War took place witnessed numerous challenges as well as improvements in the way telecommunications takes place. The primary interest at the time was not merely getting the message to the recipient. Military espionage was a real threat and thus information integrity had to be guaranteed.

Information integrity was guaranteed in two main ways. The first step was ensuring that a potential jammer does not even get to know that information is even being transmitted in the first place. The second step was to transmit information in such a way as to ensure that only the sender knows where to get the information from. All this is effected by means of some code or algorithm.

Spread spectrum communication schemes ensure that the two mentioned criteria are met. Simply put, a spread spectrum communication scheme is a means of communication under which a message is transmitted at a bandwidth that is several times the size of the original message bandwidth. Such a scheme offers several advantages some of which will be highlighted in the next few paragraphs.

1.3 Challenges faced in transmitting information:Some of the challenges faced in information transmission are highlighted in the previous paragraph. One of these is the access to information by unintended parties. While such a challenge can be addressed by cryptography spread spectrum communications specifically

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direct sequence spread spectrum and frequency hopping spread spectrum may to a lesser extent offer a novel approach towards addressing this problem.

The above mentioned case is the case where there is an intentional jammer. An intentional jammer may attempt to intercept the message or even transmit a signal that drowns out the transmitted message signal. This ultimately makes communication ineffective.

In some other cases the jamming may not be intentional. The transmitted data may undergo interference due to the power of other transmitted signals. This will be henceforth referred to as interference.

It is also worth noting that some of the devices that effect communication may generate some noise. Noise is also known to exist along the transmission channel. In fact this results in one of the imperfections encountered in a typical communication channel.

When all these factors are taken into account in an overall scale, they result in bit errors. Bit errors are expressed by a ratio known as the bit error rate. The bit error rate is a measure of the performance of a communication channel. The bit error rate is usually expressed as 1 error per every given number of bits transmitted. While in practice the bit error rate cannot be reduced to zero, the smaller the value obtained the better the performance of the communication system being considered.

Having a low bit error rate is advantageous in two different perspectives. A low bit error rate improves the reliability of the data received. It also improves data efficiency. With appropriate coding schemes every bit that is received in error has to be retransmitted. This to a large extent reduces the efficiency with which the available bandwidth is being utilized. Nevertheless a coding gain arises from the whole of this process.

When coding is not employed, a higher signal to noise ratio may be required to attain a given bit error rate than in the case where coding is employed. Typical bit error rate versus signal to noise ratio curves take the classic waterfall shape.

1.4 Typical Communication Channels:In analyzing a given communication system, it is important to take note of the typical communication channels that exist. While there are several types of communication channels this does not imply that the channels that exist in practice conform to one channel characteristic.

In actual fact, a real communication channel has some aspect of each of the channel properties that will be described shortly. However, in simulating the performance of a communication system the channel behavior under each condition can be simulated. From this worst case scenario performance data is obtained. In practice, any system is then designed with consideration of the worst case operating situation.

Some of the typical types of communication channels that exist are as listed below: Additive White Gaussian Noise (AWGN) Channel Binary Symmetric Channel

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Multipath Rayleigh Fading Channel Multipath Rician Fading Channel

1.4.1 Additive White Gaussian Noise (AWGN) Channel:

In the discrete components such as resistors that might be used in some of the devices in a typical communication system, there exists thermal or Johnson noise. Thermal noise arises from electron motion in dissipative components such as resistors.

Thermal noise has a zero mean Gaussian distribution. This brings the classic bell shaped curve to mind. The Gaussian probability density function provided in equation (1.4.1.1) below best describes the probability density function of thermal noise.

p(n)=1

σ √2π exp[−1

2 ( nσ )

2] (1.4.1.1)

σ2 is the variance of n. The standardized Gaussian density function of a zero mean process is assumed by assuming that σ=1.

Although the individual noise components have different distributions other than the Gaussian distribution, the central limit theorem dictates that the aggregate of all these distributions will tend towards the Gaussian distribution.

The power spectral density for thermal noise is the same within a given frequency band of interest. This implies that the amount of noise power per unit bandwidth is equal from dc frequencies to frequencies of roughly 1012 Hz. A simplified model thus assumes that the power spectral density Gn(f) for white noise is flat for all frequencies. Thus the noise power spectral density in the case of an AWGN channel is given as:

Gn(f)=N 0

2 watts/hertz (1.4.1.2)

The factor of 2 is included since Gn(f) is a two sided noise power spectral density.

However, white noise is just an abstraction but it offers a good approximation in some cases. Provided the bandwidth of the system is appreciably less than that of noise, the noise can be assumed to have an infinite bandwidth.

Additive white Gaussian noise affects each transmitted symbol independently. A channel whose noise can be modeled as white is referred to as an additive white Gaussian noise channel.

1.4.2 Binary Symmetric Channel:

In a binary symmetric channel, the input and output alphabet sets consist of the binary elements (0 and 1). The conditional probabilities are symmetric. Thus:

P(0|1)=P(1|0)=p (1.4.2.1)P(1|1)=P(0|0)=1-p (1.4.2.2)

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The above two equations express the channel transition probabilities. The demodulator therefore makes a hard decision on each symbol.

1.4.3 Multipath Rayleigh Fading Channel:

In the typical propagation of electromagnetic signals different paths may exist. The direct path from a transmitter to a receiver is known as the line of sight path. The other paths that result due to the interaction of electromagnetic waves with scatterers is known as the scatter path.

Since a wave carrying the same information in this case travels through different paths they may experience different attenuations. They may also be received at the receiver in different phases. Due to these two effects these waves may either add constructively or destructively at the receiver.

This causes the received signal power at the receiver to fluctuate. The worst case scenario is the case where the signals that have travelled through different paths add destructively to a point that the total signal power that is received appears to be zero. In such a case a deep fade is said to have occurred. A deep fade is undesirable since it causes detection errors and this significantly increases the bit error rate.

The probability of errors appears to follow a Rayleigh fading distribution in this case and such a channel is consequently referred to as a multipath Rayleigh fading channel. This problem can be best addressed by effecting receive antenna diversity. With receive antenna diversity, there are many receiving antennas. The one that receives the maximum power is chosen. This reduces the probability of errors occurring.

The multipath propagation problem is mainly encountered in wireless communication systems. In wired communication systems this problem does not exist. It is worth noting that the error rate is inversely proportional to the antenna diversity applied. In actual fact if the diversity order is increased and tends to a very large figure, the bit error rate performance of a wireless communication system closely approaches that of a wired communication system.

1.4.4 Multipath Rician Fading Channel:

A multipath Rician fading channel is similar to a multipath Rayleigh fading channel in the sense that multipath propagation is involved. However, the difference between the two channel types arises from the Doppler effect.

In the case of the multipath Rayleigh fading channel, both the transmitter and the receiver were assumed to be stationary. However, in the case of a multipath Rician fading channel, both the transmitter and the receiver move relative to each other. This introduces Doppler shifts which calls for a more rigorous analysis of the system. Such a channel is as a consequence best modeled using the multipath Rician fading channel.

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1.5 Spread Spectrum Communications:

1.5.1 Definition of Spread Spectrum Communications:

A spread spectrum communication system is a communication system in which, broadly speaking, the transmission bandwidth used is much greater than the actual bandwidth that is required to transmit the information.

Unlike standard modulation schemes such as frequency modulation, that also cause the spectrum of the modulated message signal to expand in excess of the information rate, spread spectrum systems employ spreading signals that are not related to the information.

The spreading sequences that are deployed “appear” to be random and are for this reason referred to as pseudorandom sequences. These sequences are used at the transmitter to spread the message signal and at the receiver to recover the transmitted message.

Essentially, for a system to be defined as a spread spectrum system it has to meet a set of conditions. The following conditions provide a rationale for determining whether or not a system is a spread spectrum system:

The message signal being transmitted must eventually occupy a bandwidth way larger than the minimum bandwidth that is necessary to send the information.

The spreading of the signal should be accomplished by means of a spreading signal which is unrelated to the message data.

The process of despreading i.e recovering the original data at the receiver is achieved by correlating the received spreading signal with a synchronized replica of the spreading signal that was initially used to spread the information at the transmitter.

It is instructive to note that commonly used modulation schemes such as frequency modulation and pulse code modulation also spread the spectrum of an information signal. However, they do not qualify as spread spectrum signals because they do not fulfill all of the three criteria laid out above.

1.5.2 Benefits of Spread Spectrum Communications:

Just like a road in the movement of vehicles bandwidth is an important resource in communication. In fact it is more desirable to transmit more information using limited bandwidth. This begs the question why spread spectrum communications is employed yet they appear to contradict this basic tenet of economizing a limited resource.

There is no doubt that spreading the spectrum of transmitted information has some benefits. From ensuring secure military communication to its applications in commercial mobile telephony, the following are some of the benefits of using a spread spectrum communication system:

Interference suppression: For a signal with a bandwidth W and a duration T the total number of dimensions is 2WT. Spreading offers no performance improvement in the case of white Gaussian noise. However, in the case of a jammer with finite power, there is a remarkable improvement in the performance. The jammer may either decide to jam all available coordinates effectively reducing the jamming intensity per

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coordinate or jam a few of the probable coordinates with more power. In either of the above options the power spectral density of the jammer interference is effectively reduced after spreading.

Low power spectral density: This makes it possible to achieve hiding of the signal and is the basis for low probability of intercept (LPI) communications. It also makes it possible to conform to acceptable regulator transmission power spectral density levels.

High resolution time of arrival measurements for precise ranging: Delay measurements can be used to take position measurements. Theoretically, uncertainty in delay has an inverse relationship with the bandwidth of a transmitted pulse. As a consequence, spread spectrum communication systems, which have a large bandwidth, provide a suitable way of determining position location.

Multiple access: Spread spectrum techniques offer a platform for simultaneous system access by several users in a coordinated manner thus allowing channel sharing.

Alleviation of multipath propagation: The good performance of spread spectrum systems in multipath channels enables them to be useful in fading channels. Both transmit as well as receive antenna diversity is possible with spread spectrum communication systems.

1.5.3 The Basis for Spread Spectrum Communication:

Shannon-Hartley theorem lays the ground for the possibility of spread spectrum communications in view of channel capacity. Based on Shannon-Hartley theorem, the channel capacity is given as:

C=Blog2(1+ SN ) (1.5.3.1)

In the above equation, C denotes the channel capacity of an additive white Gaussian noise channel in bits per second. S is the average power of the received signal while N is the average noise power. B is the bandwidth that is available to the band-limited system.

Based on Shannon-Hartley theorem it is possible in theory to maintain a low error probability provided the transmission rate R is less than or equal to the channel capacity C.

Consider the following analysis:log2(x )=1.44log e(x ) (1.5.3.2)

log e(1+ SN )= S

N−1

2 ( SN )

2

+ 13 ( S

N )3

−14 ( S

N )4

…… Provided |S|≪|N| (1.5.3.3)

Equation (1.5) therefore approximates to:C≈ 1.44B (1.5.3.4)

From equation (1.8) above it is evident that a reduction in the signal to noise ratio (SNR) can be compensated for by proportionately increasing the bandwidth B. This is the basis for spread spectrum communications. Spread spectrum systems spread data signals that are to be transmitted over a much wider frequency bandwidth as compared to the minimum bandwidth that is required to transmit the information. Consequently, the transmitted signal appears to be more resistant to intentional jamming, multiple-access interference, among other impairments.

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An important performance metric for spread spectrum communication systems. The processing gain is defined as:

PG=B ss

Bd (1.5.3.4)

In equation (1.9) above, Bss denotes the bandwidth of the transmitted spread spectrum signal s(t) and Bd is the bandwidth of the data signal d(t).

Based on Paley-Weiner theorem, a strictly band-limited signal is not achievable and as a consequence in this case the first null-to-null bandwidth of the sinc shaped frequency spectrum is assumed. The first null-to-null bandwidth measures the width of the main spectral lobe.

1.5.4 Types of Spread Spectrum Systems:

In the next few paragraphs, a brief description of some of the basic spread spectrum systems will be provided. Thereafter, they will be briefly compared with frequency hopping spread spectrum (FHSS) systems before an in depth look into FHSS systems.

There are two major classes of spread spectrum systems. These are: Pure spread spectrum systems Hybrid spread spectrum systems

Under pure spread spectrum systems the following three spread spectrum systems are obtained:

Direct Sequence Spread Spectrum (DSSS) Frequency Hopping Spread Spectrum (FHSS) Time Hopping Spread Spectrum (THSS)

This project deals with code acquisition in FHSS systems. However, it is important to gain an appreciation of the other SS systems. For this reason some of the other SS systems will be briefly described after which the focus will shift to FHSS systems then more precisely to code acquisition in FHSS systems.

Hybrid systems are obtained by combining two or more of the pure spread spectrum systems. The primary goal of hybrid systems is to tap into and exploit the unique advantages of each of the pure spread spectrum systems used. While doing this, hybrid systems combat each of the individual shortcomings of each of the spread spectrum systems.

As a case in point, consider a hybrid Direct Sequence- Frequency Hopping Spread Spectrum (DS/FH) system. When employed in a channel with interference in specific bands, a frequency hopping algorithm can be employed to effect hops only into suitable bands. After hopping into the desirable bands, a direct sequence spread can be effected. This improves the spreading gain of the hybrid system and as a result improves the system performance in channels where most of the noise occurs in few frequency bands which can be predicted.

The main hybrid spread spectrum systems are as follows: DS/FH DS/TH

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FH/TH DS/FH/TH

As earlier mentioned, spread spectrum systems use pseudo random signals to effect the spreading. These spreading sequences are referred to as pseudo noise (PN) sequences or PN codes. For the purposes of the project, PN sequences will be generated using linear feedback shift registers. PN sequences have a number of properties that make them reliable as compared to other codes during acquisition. Since the focus of the project is on FHSS systems, these codes will be discussed in detail in the next chapter where FHSS systems are comprehensively handled.

1.5.4.1 Direct Sequence Spread Spectrum Systems:

In DSSS spreading is achieved by representing each bit of the original message sequence using several bits. This process is achieved by using a spreading code in this case a PN sequence.

The PN sequence is XOR-ed with the message sequence. As a case in point, consider a case where the PN sequences are produced at a frequency that is 10 times higher than the message frequency. In this case, the message frequency will be spread by a factor of 10 after the XOR process. This step details the transmission process in a DSSS system.

At the receiver, the transmitted signal is again XOR-ed using a PN sequence that is similar to the one originally used at the transmitter. In this way the original message sequence can be recovered.

However channel imperfections bring in the need for synchronization of the spreading sequence used at the transmitter, and the one employed at the receiver. This makes the code synchronization steps of code acquisition and code tracking important. These steps are also important in FHSS systems as will be explained shortly.

In code acquisition, the PN sequence employed at the transmitter and the one employed at the receiver are brought to within one time period of the original spreading sequence. In code tracking, the PN sequence at the receiver that has already been brought to within one time period of that used at the transmitter by code acquisition is further refined and its accuracy is brought to within less than half of the time period of the code employed at the transmitter.

In practice code acquisition takes place before code tracking after which code tracking is initiated. In effecting this whole process a special algorithm that initiates the tracking phase as soon as acquisition is achieved is used.

The basis for code acquisition is correlating both the PN sequences used at the transmitter and the receiver and setting a threshold which once attained, acquisition is declared to have occurred. PN sequences are the most effective spreading sequences since as will be highlighted later they have maximum correlation when both PN sequences are in sync and minimum correlation which remains constant when the signals are out of sync.

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The code acquisition process takes place over a finite amount of time. When longer PN sequences are used the acquisition time may be longer. In order to appreciate this fact, a brief description of what acquisition involves is necessary.

During acquisition, the PN sequence received from the receiver is compared with the one that is to be employed at the transmitter. If the correlation is below a set threshold, the PN sequence at the receiver is delayed by a single time period of the PN sequence. This process goes on and on recursively until a set threshold is attained. Once this threshold is attained acquisition is said to have occurred.

If PN sequence has 15 output sequence orders while another one has 7 output sequence orders, the maximum amount of acquisition for the 15 sequence PN sequence will be 15 time durations on the one hand. On the other hand, for the 7 sequence PN sequence, the maximum acquisition time will be 7 time periods. This shows the effect of the length of the PN sequence on acquisition time. However, this is the worst case scenario and typical acquisition times may actually last a shorter time period.

However, making use of a longer spreading sequence increases the spreading gain but in light of the fact that a longer spreading sequence increases the acquisition time, a trade off definitely exists. The choice is between having a greater spreading gain and longer acquisition times and vice versa.

Generally, a DSSS system can be represented by equation 1.5.4.1.1 below:s(t)=Ad(t)p(t)cos(2πfct+θ) (1.5.4.1.1)where, A is the signal amplitude d(t) is the data modulation p(t) is the spreading waveform fc is the carrier frequency θ is the phase at t=0

Generally the data sequence is in this case BPSK modulated and is usually made up of a series of rectangular sequences that do not overlap. These pulses have a duration Ts and the the value of d(t) is usually +1 for 1 and -1 for 0.

Equation (1.4.4.1.1) above may be represented more compactly as equation (1.5.4.1.2) below by employing phase shift keying using the data modulation.s(t)=Ap(t)cos[2πfct+θ+πd(t)] (1.5.4.1.2)All the symbols have the same meanings as earlier defined.

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BPSK modulator

Binary data d(t)

Pseudonoise bit source

DSSS transmitted signal s(t)

BPSK Demodulator

Binary data d(t)

The block diagram representation of a DSSS system is shown in Figure.1 below.

(a)Transmitter

(b) ReceiverFigure 1.1 DSSS System: (a)Transmitter and (b) Receiver

Figure 1.1 above offers an overview of a DSSS system. The above block diagrams offer an idealistic view of DSSS systems. In this case synchronization has not been included as transmission is assumed to take place over an ideal channel where there is no channel distortion.

1.5.4.2 Frequency Hopping Spread Spectrum (FHSS) Systems:

In FHSS systems, the carrier frequency of a transmitted signal is periodically changed. These periodic variations in the transmitted carrier frequencies are carried out based on a predetermined PN sequence that determines the frequencies that the carrier frequencies are to hop into.

In order to effectively recover the transmitted signal, the carrier frequency used for demodulation at the receiver should hop into corresponding carrier frequencies that were employed at the transmitter at the precise times that messages that have been transmitted based on these carrier frequencies are transmitted.

However, due to the channel imperfections that were earlier highlighted, the PN sequence used to vary the carrier frequency at the transmitter during transmission and the one used to vary the demodulation carrier frequencies at the receiver during reception may not be in sync. Just like in the case of DSSS systems code synchronization is necessary. If synchronization is not carried out the transmitted signal will be wrongly demodulated yielding an incorrect signal at the receiver.

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In FHSS, code synchronization involves two steps namely: code acquisition and code tracking. Just like the situation in DSSS the code acquisition phase involves bringing the PN sequence to at least within a time period of the PN sequence used to generate the carrier frequency at the receiver. Code tracking involves further refining the acquired PN sequence improving its accuracy to less than half the time period of the transmitted signal.

Since the problem of synchronization in FHSS systems forms the crux of this project, this will be dealt with in depth in both Chapters 2 and Chapter 3 where FHSS systems are dealt with in general then the synchronization problem is dealt with more specifically respectively.

1.5.5 Historical Perspective of Spread Spectrum Communications:

The initial conceptualization of Spread Spectrum Communications Systems came from the most unlikely source- an actress. In 1941, Hedwig Eva Maria Kiesler, a Hollywood actress at the time popularly known by her screen name Hedy Lamar, in conjunction with a pianist known as George Antheil patented a spread spectrum communications system. This is the first known patent for such a communication system.

The motivation for the two entertainers to invent such a communication system came from the most common catalyst for inventions in the field of Telecommunications- War. Hedy and George developed this new communication system as their contribution to the American War effort.

During the Second World War, Americans were encouraged to make whatever manner of contributions to aid the American War Effort. Towards this front, Hedy and George provided their newly conceived idea as their contribution.

Through this novel invention, military espionage by enemies based on information jamming had been thwarted or at least been made a bit more complicated. At the time, information was transmitted under one frequency band. This made it easier for a malicious listening party to simply tune their receiver to only one frequency band of interest. This made for easy tapping.

Spread spectrum communications partly addressed this problem. Under this new technique, information of a given bandwidth could be spread over a much larger bandwidth and transmitted. This had two advantages. On the one hand, it made it more difficult for a potential jammer with finite jamming power to jam the entire frequency band. On the other hand, since the information was spread over a large bandwidth the power spectral density of the transmitted signal was so little that it would easily appear as noise that exists in typical communication channels to the jammer.

The interesting bit is that spread spectrum communications systems were note deployed commercially until later in the 1970s. Throughout the World War 2 period to the 1970s it was only used by military defense based organizations. Another interesting observation is that Hedy and George never really benefited economically from their patent. This is because their invention was solely a War Effort contribution.

Presently, DS-CDMA is a commercial variant of DSSS. This goes a long way in highlighting the importance of spread spectrum communications in modern day communications.

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1.5.6 Applications of Spread Spectrum Communications:

The most common use of spread spectrum communications is in low probability of intercept military communications. However, in military communications more protection is guaranteed through other techniques such as data encryption.

Commercially, the CDMA system is based on spread spectrum communications. The reason as to why CDMA became popular from the year 2000 is that it offered a multiple access system in a way in which a several users are able to use the same frequency channel. This is achieved by using orthogonal spreading codes at both the transmitter and the receiver. Orthogonal codes have a zero correlation. For this reason, it is easier to isolate the messages from the different senders at the receiver.

The reason for the popularity of spread spectrum communications systems can also be attributed to regulator standards. Regulators usually provide acceptable maximum transmission power densities. Since transmitting information over a larger bandwidth reduces the power spectral density of transmitted signals it enables transmitters to comply with regulator specifications.

The popular Bluetooth standard also employs a variant of spread spectrum communications specifically- FHSS. Bluetooth technology essentially provides a low power radio interface used in the provision of short range connectivity. It is popular in providing connectivity amongst devices such as laptops, mobile phones among many other consumer electronics devices. However the connected devices must be within a short distance from each other typically 10m.

Bluetooth devices operate within the unlicensed 2.4 GHz ISM band. Since FHSS is employed, the hop bandwidth is roughly 83.5 MHz. For a typical Bluetooth system the range of allowable frequencies ranges from 2400 to 2483.5 MHz.

Another improved version of Bluetooth systems are Bluetooth systems that employ adaptive Bluetooth frequency hopping. In systems that employ adaptive Bluetooth frequency hopping, the hopping algorithm is such the transmitted data only hops into frequency bands that have minimal interference.

DSSS and FHSS systems offer diverse examples of spread spectrum communication systems. While DSSS systems transmit the same information by spreading the data over a large bandwidth, FHSS systems spread the spectrum by hopping the transmitted information only into specific bands of a large available band by employing a PN sequence.

12

CHAPTER 2:FREQUENCY HOPPING SPREAD SPECTRUM:

2.1 Basic Overview of FHSS Systems:

FHSS is a spread spectrum communications technique whereby the carrier frequency of a transmitted message signal can be one of M possible carrier frequencies.

Each of the M possible carrier frequencies are determined by a PN sequence. Each bit of these sequences can be clustered so as to obtain a larger symbol size. As a case in point, if each of the three obtained PN sequences are clustered, there exist 7 possible M carrier frequencies at the transmitter. Generally, if N consecutive one bit symbols are clustered together, the highest possible number of M carrier frequencies is given by equation (2.1.1) below:

M= 2N−1 (2.1.1)

Since the PN sequence that is used in effecting frequency hopping appears to be random, the periodicity of the frequency hops follows a predetermined pattern. As a result, the sequence with which each of these frequency hops occur is known as the frequency hopping pattern.

The entire set of all the available carrier frequencies is known as the hopset with the value M referred to as the hopset size.

The spreading gain, that is the ratio of the transmitted message bandwidth to the original message bandwidth, is an important performance metric of a FHSS system. However, this is not the only important performance metric. Having a larger hopset size, M is also better.

The implication of the above statement is that even if the FHSS transmitted signal is transmitted over a large bandwidth if there are very few carrier frequencies, it increases the probability of a jammer determining the frequency range over which a message is being transmitted.

Based on this context it appears that having a very long PN sequence is good from an anti-jamming point of view. However, a very long PN sequence may tremendously increase acquisition times and ultimately resulting in large errors after the transmitted message is received.

Each of the carrier frequencies have a bandwidth that can be given as B. If each hopping band has a bandwidth of B with M possible carrier frequencies, the size of the allowable hopping bandwidth W is greater than or equal to the product of the number of carrier frequencies M and the bandwidth of each hop pattern B as provided by equation (2.1.2) below:

W≥ MB (2.1.2)

The duration of each of the possible carrier frequencies may either be less than or greater than the data bit duration. In the case where the duration of each of the carrier frequencies lasts longer than the data bit duration, the FHSS system is referred to as a slow FHSS system. In

13

the converse case where each carrier frequency of the FHSS system lasts smaller time durations than the data bit duration, the FHSS system is referred to as a fast FHSS system.

In the case of a slow FHSS system at least more than one bit of the data is transmitted using the same carrier frequency. In the case of a fast FHSS system, each bit of the data is transmitted using more than one carrier frequency.

The hop pattern of a typical FHSS system is provided in Figure 2.1 below:

Figure 2.1: Frequency Hopping Pattern of a FHSS system

As in the earlier equations W is the maximum allowable hopping bandwidth while B is the bandwidth of each hop that has been effected by each of the carrier frequencies. Generally the bandwidths of each of the hop frequencies should not overlap so as to minimize interference. Th is the duration each of the carrier frequencies takes. It provides the basis of determining whether the FHSS system is a slow or a fast FHSS system.

Figure 2.2 below represents an ideal FHSS communication system. In this case, it is assumed that there is no propagation delay. The communication channel is also assumed to be perfect such that there is no noise and whatever is transmitted from the transmitter is what is received at the receiver. However as it will be observed in Chapter 3 such channels do not exist in practice and it is necessary to synchronize the PN sequence employed at the transmitter with the PN sequence used to generate the MFSK frequencies at the receiver. The synchronization process goes a long way in reducing the bit error rate of the received message.

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(a)FHSS transmitter

(b)FHSS Receiver without synchronizationFigure 2.2 FHSS System

At the transmitter, a binary sequence of bits that represents the data is digitally modulated using either MFSK or BPSK modulation. The PN sequence source generates bit sequences that are used to specify one of the M carrier frequencies based on the criterion that was earlier highlighted. Based on the sequence that is received from the PN sequence generator, and a hopping algorithm that determines the carrier frequency that the frequency synthesizer should generate for a given carrier frequency, M carrier frequencies each lasting a period Th are generated.

The signal c(t) that is generated by the frequency synthesizer is usually several times larger as compared to the modulated binary data sd (t ). Once the modulated binary data is modulated using the high frequency signal generated by the frequency synthesizer, the frequency spectrum of the transmitted signal is observed to extend to roughly the size of the maximum frequency generated by the frequency synthesizer.

15

The bandpass filter immediately after the mixer at the receiver is set to be roughly equal to the sum frequency of the maximum mixed signal to be transmitted. The bandpass filter immediately after the transmitter is essentially used to eliminate double frequency components.

At the receiver the transmitted spread spectrum signal s(t) is demodulated by varying the receiver frequency synthesizer’s frequency in the same order as the transmitter’s frequency synthesizer hop pattern. For this to be achieved, the PN sequence generated at the receiver should be in sync with the PN sequence that was utilized at the transmitter.

Assuming 2FSK data modulation is used, the modulated sequence sd(t) is as shown in equation (2.1.3) below:

sd (t )=Acos (2 π ( f o+0.5 (bi+1 ) Δf ) t ) for iT¿ t< ( i+1 )T (2.1.3) where, A=amplitude of signal fo=base frequency bi=ith bit of data i.e + 1 for binary 1 and -1 for binary 0 Δf = frequency separation T= bit duration

The transmitted spread spectrum signal s(t) is given as:

s (t )=0.5 Acos (2π ( f o+0.5 ( bi+1 ) Δf + f i ) t ) (2.1.4)where fi is one of the I carrier frequencies generated by the frequency synthesizer.

16

CHAPTER 3: SYNCHRONIZATION IN FHSS SYSTEMS:

3.1 Definition of Synchronization:

In order for the transmitted signal to be correctly demodulated at the receiver, a PN sequence that is in sync with the PN sequence used at the transmitter has to be used at the receiver. The process of bringing the two PN sequences into alignment is referred to as synchronization.

3.2 The Need for Synchronization:

The need for synchronization is brought about by many factors within the channel. One of these factors is the propagation delay that exists between the transmitter and the receiver. Since in practical systems the distance between the transmitter and receiver keep on varying the propagation delay also keeps on varying. Synchronization is thus necessary so as to ensure correct demodulation.

The clocks used at the transmitter and the receiver may also tend to be relatively unstable. This makes the transmitter and receiver PN sequences to continue getting out of sync. Synchronization is therefore necessary to prevent such a situation.

In practical communication systems, both the transmitter and the receiver may move relative to each other as opposed to being in stationary positions. This relative velocity between the transmitter and the receiver results in Doppler shifts. Since there is a high degree in uncertainty in the relative velocities between the transmitter and the receiver, the Doppler frequency offset in the received signal cannot be accurately determined. This brings in the need for synchronization.

Communication channels that are encountered in practice give rise to all the above mentioned situations that necessitate synchronization. Therefore, in the FHSS system that will be simulated as part of this project, synchronization will be used. As will be evident, the performance of the FHSS system is better with than without synchronization.

3.3 Types of Synchronization in FHSS Systems:

There are two stages of synchronization in an FHSS system. These two stages namely are code acquisition and code tracking.

Code acquisition involves bringing the PN sequence used at the receiver to within one clock period of the PN sequence used at the transmitter. Typically acquisition brings the two PN sequences to an alignment that is not better than half a clock chip. After acquisition therefore, a second step known as code tracking is necessary. Once the alignment has been brought to within one time period and acquisition has been declared, tracking begins.

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X1 X2 X3 X4

Modulo-2 adder

Output

Code tracking improves the alignment of the PN sequence employed at the receiver and that used at the transmitter to less than half a clock period of each chip. Code tracking is therefore the final step of synchronization.

3.4 Pseudonoise (PN) Sequences:

PN sequences are codes that appear to be random but are not, strictly speaking, random since they are generated using predetermined circuit connections. Nevertheless, they meet a number of randomness criteria.

A discussion of PN sequences is necessary in the context of synchronization since one reason as to why PN sequences are chosen for FHSS systems are that they have specific correlation properties that make alignment of the PN sequences used at the transmitter and the receiver easier.

PN sequences are usually generated using Linear Feedback Shift Registers based on Galois Field arithmetic. The length of the PN sequence depends on the number of shift register stages. If there are m shift registers used, the maximum possible PN sequence length, p is given as in equation (3.4.1) below:

p=2n−1 (3.4.1)

Such a sequence is referred to as a maximal length sequence and they are obtained from standard Galois Field Tables for the generation of maximal length sequences.

As an example consider the case of a 4-stage LFSR used to generate PN sequences. The generator polynomial that yields the maximal length sequence in such a case is given by equation (3.4.2) below. For other n-stage LFSRs, the generator polynomials for maximal length sequences can be obtained from standard generator polynomial tables.

Generator Polynomial for 4-stage LFSR= z4+z3+1 (3.4.2)

Figure 3.1 below shows the connections in a maximal length sequence 4-stage LFSR connection.

Figure 3.1 Connections in a maximal length sequence 4-stage LFSR

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The initial states of X1, X2, X3 and X4 can be any value but 0000 respectively. An initial state of 0000 would lock the output to 0. Assuming that the initial state were 1000,the output sequence for 15 clock pulses is:0 0 0 1 0 0 1 1 0 1 0 1 1 1 1

After 15 clock pulses the same sequence would again repeat.

In order for PN sequences to be considered random they exhibit a number of randomness properties.

One of these properties is the balance property. In the balance property, the number of output binary ones and the number of binary output zeros in a single period differs by at most one.

The other important property of PN sequences is the run length property. A run is defined as a continuous sequence of the same type of binary digit. A new run commences with the appearance of a different binary digit. The length of a run is the number of digits contained in a given run. In PN sequences about half of the runs are of length 1, about a quarter of the runs are of length 2, about an eighth of the runs are of length three and so on.

The other property that is very important in synchronization is the correlation property. Based on the correlation property if any PN output sequence is compared with any cyclic shift of itself, the number of agreements differs from the number of disagreements by at most one count. Therefore if the cross correlation is done for different shifts, there will be maximum correlation when there is no shift and minimum correlation when the cyclic shift is one or more.

The correlation property makes synchronization easier since during synchronization, by correlating the transmitter PN sequence with the receiver PN sequence the receiver PN sequence can be continuously delayed until a set threshold of the correlation under which acquisition can be declared is attained.

Based on the above fact it is evident that for a large stage PN sequence the acquisition time may be larger since the maximum possible number of cyclic shifts is also large. For shorter PN sequence lengths, the acquisition time lasts shorter time durations. However, the length of the PN sequence that is used is not the only factor that determines the acquisition time. The nature of the communication channel also plays a part in determining the acquisition time.

3.5 FHSS Code Acquisition:

Code acquisition in FHSS systems aims to align the demodulation carrier frequency pattern used at the receiver with that received from the transmitter to at least within one hop duration. As earlier mentioned, code acquisition is not the final synchronization stage in a FHSS system. In actual fact, it is a precursor to the other equally important synchronization stage referred to as code tracking.

Typical communication systems experience interference. This interference may come from other transmitters or jammers. In the case of systems that experience interference, two

19

methods of acquisition namely Matched Filter Acquisition and Serial Search Acquisition are used.

These methods will be given a comprehensive treatment in the next few paragraphs. However, it is worth noting from the outset that in the case of Matched Filter Acquisition, a bank of matched filters is used during acquisition. The number of matched filters used during this process is equal to the number of the different hop frequencies. Longer PN sequences can have more hop frequencies while shorter PN sequences have fewer hop frequencies. The matched filter acquisition technique is therefore suitable for use in cases where short PN sequences are used.

Serial search acquisition uses an algorithm that sequentially delays the PN sequence used at the receiver. Such an acquisition technique is suitable for long PN sequences. However, as compared to the matched filter acquisition technique, the serial search acquisition technique has a longer acquisition time. The good thing with the serial search acquisition technique is that it uses fewer components than the matched filter acquisition technique for a given PN sequence length.

The matched filter acquisition technique can be used together with the serial search acquisition technique. Under such a scheme, the matched filter acquisition technique aids in the acquisition of short frequency patterns within long frequency patterns. When operating in this mode, the matched filter acquisition technique supplements the serial search acquisition technique.

3.5.1 Matched Filter Acquisition:

In this case an FHSS system with N different carrier frequencies {f1,f2,…,fN} is assumed. The frequency synthesizers at the receiver also generate N demodulation carrier frequencies.

In a matched filter acquisition system, since all the N possible carrier frequencies can be determined, each of the N carrier frequencies is generated independently at the receiver. Each of these carrier frequencies are mixed with the received signal and the value from one of the N mixers that exceeds a set threshold is taken as the transmitted signal.

The matched filter acquisition system can be represented schematically as in Figure 3.2 below:

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Figure 3.2: A Matched Filter Acquisition System

If say the frequency f1 corresponds to the transmitter carrier frequency, then d1(t)=1. All the other values corresponding to the other N frequencies i.e d2(t) to d3(t) will be zero.

The comparator receives an input D(t) which corresponds to the successively received number of frequencies in the hop pattern. D(t) takes a discrete value and is represented by equation (3.5.1.1) below, where Th is the hop duration.

D(t )=¿ ∑k =1

N

dk [ t−( N−k+1 ) T h ] (3.5.1.1)

L(t) is the input to the threshold generator and it is given by:L(t)=D(t+Th) (3.5.1.2)

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Acquisition is said to have occurred when D(t) is greater than V(t) where V(t) is an adaptive threshold and is a function of L(t).In the case where acquisition is declared, assume d1(t) is 1 at time 1, d2(t) is Th at time 2Th and so on till dN(t) is 1 at time NTh.Since D(t) is an accumulator if will ideally have a magnitude N at time (N+1)Th and assuming it meets the acquisition threshold V(t) acquisition is declared.

Instead of using filters that are matched to the acquisition tones, Bandpass filters are instead used. The reason for the choice of Bandpass filters is the fact that the precise acquisition sampling times cannot be determined.

Acquisition can be falsely declared in a matched filter acquisition system. This phenomenon occurs especially in the presence of noise. If acquisition is falsely declared this implies that the PN sequence used for acquisition will not correspond to the one used at the transmitter as received at the receiver. The probability of false declaration of acquisition in a matched filter acquisition system increases with the amount of interference.

In a matched filter acquisition system, if λ chips each having a chip duration of Tc are examined, the largest amount of time required for a fully matched filter search is given by equation (3.5.1.3) below:

Maximum acquisition time=λTc (3.5.1.3)

In a matched filter acquisition system, the probability of detection can be given as PD. In the case that an incorrect detection decision is arrived at, an extra λ chips should again be observed in order to arrive at the correct detection decision. The mean acquisition time is therefore given by equation (3.5.1.4) below:

Mean acquisition time =λ T c

PD (3.5.1.4)

3.5.2 Serial Search Acquisition:

A serial search acquisition system is shown in Figure 3.3 below. In a serial search acquisition system, the received spreading PN sequence used at the transmitter is correlated with the one that is used at the receiver and periodically delayed until a set threshold is attained. Once this threshold is attained, acquisition is declared and the declaration of acquisition initiates tracking.

In serial search acquisition, a single correlator is used to serially search for the correct hopping pattern of the frequency hopped signal. As a result, a serial search acquisition system is less bulky as compared to the matched filter acquisition system.

In an FH system, the code generator controls the frequency synthesizer that generates the different carrier frequencies. Under such a scheme, acquisition is declared to have occurred once the hopping pattern generated by the frequency synthesizer at the receiver corresponds with that of the received FH signal.

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Figure 3.3:FHSS Serial Search Acquisition System

Depending on the amount of misalignment between the transmitter and receiver spreading codes an appropriate uniform search procedure is adopted. The timing uncertainty of the PN sequences is determined by the sequence length as well as the channel characteristics.

The search control system lays the basis for declaring acquisition. It outlines the intervals within which the correlation should be performed and provides thresholds for the declaration of acquisition.

In the serial search acquisition technique, the output of the integrator used for correlation has a shape that is similar to the correlation for two shifted PN sequences. Ultimately, when the sequences are in alignment, acquisition is declared as having occurred. Due to channel imperfections, a threshold is usually set for the declaration of acquisition in a serial search acquisition system. Thereafter, tracking is initiated to provide fine alignment.

3.6 Code Tracking:

Code tracking offers fine alignment after acquisition has been declared. Tracking ensures alignment of the hop pattern to within a fraction of the hop duration. Tracking reduces the misalignment that exists even after acquisition.

The delay-locked loop and tau-dither loop used for tracking in DSSS systems can be adapted for use in FHSS systems. However, the early-late -gate tracking loop is predominantly used in FHSS systems.

The early late gate within predefined time intervals subdivides a chip of the spreading sequence into two. Each of the two portions of the chip is squared and the difference between them computed. If the difference between them is not zero, then the sequence is misaligned. The chip is then slightly delayed until the value obtained through the above process approaches zero.

23

A gating signal with an intermediate frequency is usually used to effect early-late-gate tracking. The gating signal is a square wave clock signal with amplitude +1 and -1.The discriminator characteristic expresses the error signal. Figure 3.4 below highlights some of the salient features of an early-late-gate tracking loop.

(a)Early-late-gate tracking loop

(b)Early-late-gate tracking signals

(c)Early-late-gate discriminator characteristicFigure 3.4: Early-late-gate tracking

The output of the early-late -gate tracking loop is the product of the gating signal and the envelope detector output.

24

At times during tracking it may be discovered that tracking cannot be declared. In such a case reacquisition is necessary. In such a case the tracking system is said to have lost lock. Such a situation may even have been caused by prior false acquisition.

25

CHAPTER 4: DESIGN AND IMPLEMENTATION:

Code acquisition in a FHSS was simulated using the MATLAB Simulink simulation software. Appropriate Simulink block sets were used and their parameters varied to conform to design specifications.

For generation of the hopping codes PN sequences were used due to their correlation properties that allow for easier acquisition.

For simulation purposes the following channel situations were simulated: The case where there is no channel distortion and there is no propagation delay for

both the transmitted and received sequence. The case where the frequency hopped signal is transmitted over an AWGN channel. The case where the frequency hopped signal is transmitted over a Multipath Rayleigh

Fading channel. The case where the frequency hopped signal is transmitted over a Multipath Rician

Fading Channel.

All these channel conditions would offer the performance of the FHSS system from the most ideal performance scenario to the least ideal performance scenario.

The Simulink block diagram in Figure 4.1 outlines the design circuit for the case of the AWGN channel. For the other three channel situations, only the channel was varied.

PN SequenceGenerator

PN SequenceGenerator

8-FSK

M-FSKModulator

Baseband1

BernoulliBinary

Bernoulli BinaryGenerator

2-FSK

M-FSKModulatorBaseband

Product

8-FSK

M-FSKModulator

Baseband2

PN SequenceGenerator

PN SequenceGenerator1

Divide2-FSK

M-FSKDemodulator

Baseband

Error Rate Calculation

Tx

Rx

Error RateCalculation

0

0

1078

Display

-K-

Gain

-K-

Gain1

SpectrumAnalyzer

SpectrumAnalyzer1

SpectrumAnalyzer2

AlignSignals

s1

s2

s1 del

s2

delay

Align Signals

0

Display1

Bit to IntegerConverter

Bit to IntegerConverter

Bit to IntegerConverter

Bit to IntegerConverter2

TimeScope

TimeScope1

AWGN

AWGNChannel

26

Figure 4.1: Simulation Block for Serial Search Acquisition for a FHSS System

A few of the various design aspects of the common block parameters are designed in the next few paragraphs. The rationale for arriving at each of the design parameters is also discussed.

4.1 Bernoulli Binary Generator:

The Bernoulli binary generator was chosen as the simulation data source since it outputs a random sequence of 0 and 1 bit sequences. The probability of getting a 0 and a 1 were all set to be equal i.e both have a probability of 0.5.

The bit rate for the Bernoulli binary generator was set at 10,000 bits per second. Before the generated Bernoulli sequence is mixed with the carrier frequency generated through the 8-FSK modulator, it is first 2-FSK modulated.

At the receiver, a 2-FSK demodulator was used for demodulation. If the demodulation process is effective, an exact replica of what has been transmitted should be received.

4.2 PN Sequences:

A 4-stage LFSR with a PN sequence length of 15 was used. The LFSR used was a maximal sequence LFSR. Similar PN sequence generators were used at both the transmitter and the receiver. The output bit rate for both PN sequence generators was set at 90,000 bits per second.

The generated bits from the PN sequence generator are then clustered into groups of 3 bits and a bit to integer converter is used to generate eight possible integer values ranging from 0 to 7. The output of the bit to integer converter is then fed to an 8-FSK modulator which then outputs the different carrier frequencies that are used to effect frequency hopping.

Since the output bit rate from the PN sequence generator is 90,000 bits per second and they are grouped into clusters of 3, there are 30,000 clusters generated per second. Therefore, ideally, the output frequency of the 8-FSK modulator varies 3 times per symbol of the data sequence generated by the Bernoulli Binary Generator.

The designed system is therefore a fast Frequency Hopping system with 3 frequency hops per symbol.

4.3 8-FSK Modulator:

The 8-FSK modulator is set to have a carrier frequency separation of 100 kHz. The eight possible carrier frequencies therefore range from 100 kHz to 800 kHz.

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4.4 Align Signals Block:

The align signals block is the block that performs the serial search acquisition. The align signals block compares two signals by correlating them and then adjusts the signal to be adjusted based on the correlation peak. PN sequences offer a lot of demodulation ease since they have specific correlation peaks.

In the design highlighted above, before the PN sequence that is used at the transmitter is transmitted to the align signal block at the receiver, it is first 8-FSK modulated. The PN sequence at the receiver is also 8-FSK modulated and after this the PN sequence at the receiver is aligned to that received from the transmitter. The align signal block periodically delays the PN sequence at the receiver until it is aligned to the one at the receiver.

4.5 Doppler Frequency Shift:

For the channels that are to be used, the Doppler frequency shift is an important parameter that will have to be set. The worst case Doppler shift situation will be set. The maximum possible Doppler shift is given by equation (4.6.1) below:

Maximum possible Doppler shift = ( vc ) f c (4.6.1)

where, v= relative velocity between the transmitter and the receiver, assumed to be100 km/h c= speed of light (300,000,000 m/s) fc= carrier frequency, in this case the maximum carrier frequency is 800 MHz

By substituting the above values into equation (4.6.1) the maximum doppler shift is found to be roughly 74 Hz.

A value of 75 Hz is used in the designs since this offers a value way above the maximum possible Doppler shift and gives a guarantee as to the worst case design scenario.

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CHAPTER 5: RESULTS AND ANALYSIS:

5.1 PN Sequence Results:

The properties of the PN sequence used were first tested for their randomness properties. Figure 5.1 shows the timing diagram for a 4-stage LFSR maximal length sequence.

0 5 10 15 20 25 30

0

0.2

0.4

0.6

0.8

1

Ampl

itude

Time (secs)Offset=0

Figure 5.1 PN Sequence Timing Diagram

The sample time for the PN sequence is set at 1s just for illustrative purposes. For a larger sampling frequency, the basic properties will remain the same. Since the sample time is 1s, and a maximal length sequence is utilized, the expected PN sequence period is 15s. From the graph, after a time interval of roughly 15s the sequence repeats itself.

The correlation properties of the PN sequences were also tested. From Figure 5.1 above, if a sequence similar to the one in the Figure 5.1 is compared for the number of agreements and disagreements for every 1s interval for 15s, the number of agreements would be 15 while the number of disagreements would be zero. This would yield the maximum correlation value. Any shift by a value that is not a multiple of 15s would increase the number of disagreements between the undelayed and delayed version of the PN sequence. This would effectively reduce the correlation between the two signals.

Figure 5.2 below shows the correlation output for two perfectly aligned PN sequences while Figure 5.3 below shows the correlation output between two PN sequences with a misalignment of 1s between each other.

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0 5 10 15 20 25 30

0

0.2

0.4

0.6

0.8

1

Ampl

itude

Time (secs)Offset=0

Figure 5.2: Correlation between two perfectly aligned PN Sequences

0 5 10 15 20 25 30

0

0.2

0.4

0.6

0.8

1

Ampl

itude

Time (secs)Offset=0

Figure 5.3: Correlation between two PN Sequences with a misalignment of 1s

Accumulating the output of Figure 5.2 over a period of 15s and doing the same thing for the output in Figure 5.3, the output of Figure 5.2 yields a larger accumulated value than that of Figure 5.3. The output of Figure 5.3 represents the situation for all other cyclic shifts. It is therefore evident that the PN sequence has a finite accumulated correlation maximum only when two PN sequences generated by the same generator polynomial are in sync.

5.2 Results for the case of transmission through an AWGN Channel:

The continuous time transmitted and received Bernoulli binary sequence was compared.Their time scopes appear as shown on Figure 5.4 and 5.5 below.

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0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

Ampl

itude

Time (ms)Offset=0

Figure 5.4: Transmitted Bernoulli Binary Signal

0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

Ampl

itude

Time (ms)Offset=0

Figure 5.5: Received Bernoulli Binary Signal

In this case the bit error rate is found to be 0.

In case a unit time delay is effected in the loop, the two spreading signals are aligned and the bit error rate is in the range of 10-5 .

Figures 5.6, 5.7 and 5.8 show the frequency spectrum of the transmitted signal, the frequency spectrum after frequency hopping and the frequency spectrum after code acquisition respectively.

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-8 -6 -4 -2 0 2 4 6 8

x 104

-80

-60

-40

-20

0

20

Frequency (kHz)

dB

m

RBW: 166.02 Hz, NFFT: 1537Span: 170 kHz, CF: 0 Hz

Figure 5.6: Frequency Spectrum of the Transmitted Signal after 2-FSK Modulation

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

x 105

-10

0

10

20

30

40

Frequency (kHz)

dB

m

RBW: 498.05 Hz, NFFT: 1537Span: 510 kHz, CF: 0 Hz

Figure 5.7: Frequency Spectrum after Frequency Hopping

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-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

x 105

-50

-40

-30

-20

-10

0

10

20

30

Frequency (kHz)

dB

m

RBW: 498.05 Hz, NFFT: 1537Span: 510 kHz, CF: 0 Hz

Figure 5.8: Frequency Spectrum after Code Acquisition

5.3 Results for transmission in a Multipath Rayleigh Fading Channel:

The Transmitted Bernoulli Binary Signal and the Received Bernoulli Binary Signal in the case of a Multipath Rayleigh fading channel is shown in Figure 5.9 and Figure 5.10 below.

0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

Ampl

itude

Time (ms)Offset=0

Figure 5.9 Transmitted Bernoulli Binary Signal

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0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

Ampl

itude

Time (ms)Offset=0

Figure 5.10 Received Bernoulli Binary Signal

In this case, the bit error rate is found to be roughly 0.1. This implies that 1 out of every 10 bits are transmitted in error.

The frequency spectrum for the transmitted signal, frequency hopped signal and received signals are shown in Figure 5.11, 5.12 and 5.13 respectively.

-8 -6 -4 -2 0 2 4 6 8

x 104

-80

-60

-40

-20

0

20

40

Frequency (kHz)

dB

m

RBW: 166.02 Hz, NFFT: 1537Span: 170 kHz, CF: 0 Hz

Figure 5.11: Frequency Spectrum of the transmitted signal after 2-FSK Modulation

34

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

x 105

-10

0

10

20

30

40

Frequency (kHz)

dB

m

RBW: 498.05 Hz, NFFT: 1537Span: 510 kHz, CF: 0 Hz

Figure 5.12: Frequency Spectrum of the transmitted signal after frequency hopping

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

x 105

-40

-30

-20

-10

0

10

20

30

Frequency (kHz)

dB

m

RBW: 498.05 Hz, NFFT: 1537Span: 510 kHz, CF: 0 Hz

Figure 5.13: Frequency Spectrum of the signal after code acquisition

5.4 Results for transmission in a Multipath Rician Fading Channel:

The continuous-time time scopes for both the transmitted and the received signals are shown in Figure 5.14 below:

35

0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

Ampl

itude

Time (ms)Offset=0

Figure 5.14: Time showing transmitted signal

0 2 4 6 8 10

0

0.2

0.4

0.6

0.8

1

Ampl

itude

Time (ms)Offset=0

Figure 5.15: Time scope showing received signal

The frequency spectrum of the transmitted 2-FSK modulated signal, the frequency hopped signal and the signal after code acquisition are shown in Figures 5.16, 5.17 and 5.18 below respectively.

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-8 -6 -4 -2 0 2 4 6 8

x 104

-80

-60

-40

-20

0

20

40

Frequency (kHz)

dB

m

RBW: 166.02 Hz, NFFT: 1537Span: 170 kHz, CF: 0 Hz

Figure 5.16: Frequency spectrum of the transmitted 2-FSK signal

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

x 105

-10

0

10

20

30

40

Frequency (kHz)

dB

m

RBW: 498.05 Hz, NFFT: 1537Span: 510 kHz, CF: 0 Hz

Figure 5.17: Frequency Spectrum after Frequency Hopping

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-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

x 105

-60

-50

-40

-30

-20

-10

0

10

20

30

40

Frequency (kHz)

dB

m

RBW: 498.05 Hz, NFFT: 1537Span: 510 kHz, CF: 0 Hz

Figure 5.18: Frequency spectrum of the signal after code acquisition

The bit error rate in this case is in the range of 10-5.

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CHAPTER 6: CONCLUSION AND RECOMMENDATIONS:

6.1 CONCLUSION:

The objectives of the project were met. Spread spectrum communication systems were studied and the importance of code acquisition in frequency hopping spread spectrum communication systems was observed.

The need for code acquisition in FHSS systems arises due to clocking instabilities at the receiver and uncertainty in the propagation delay of signals. Code acquisition is a precursor to the fine alignment process of code tracking. Therefore, the results obtained from code acquisition process are not perfect but fine alignment improves the accuracy.

A serial search acquisition system was designed and simulated with the performance under a range of channel conditions getting noted. The reason for settling for a serial search acquisition system is informed by its use of fewer components as compared to the matched filter acquisition technique which requires a bank of bandpass filters.

6.2 RECOMMENDATIONS:

There is a scope for further work in this project area. Some of the recommendations for future work around this project include:

Comparing acquisition in DSSS with acquisition in FHSS systems Determining how acquisition would be carried out in a hybrid DS/FH Spread spectrum

system

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References:[1] Bernard Sklar, Digital Communications: Fundamentals and Applications, Second Edition, Upper Saddle River, New Jersey: Prentice Hall PTR, 2009.

[2]William Stallings, Data and Computer Communications, Eighth Edition, Upper Saddle River, New Jersey: Pearson Education Inc. 2007.

[3]Marvin.K.Simon, Jim.K.Omura, Robert.K.Scholtz and Barry.K.Levitt, Spread Spectrum Communications Handbook, Electronic Edition, McGraw-Hill Inc. 2004.

[4]Don Torrieri, Principles of Spread Spectrum Communication Systems, Springer Science + Business Media Inc. 2005

[5]Andrew. J. Viterbi, CDMA: Principles of Spread Spectrum Communications, Addison-Wesley Publishing Company.1995.

[6] Hans- Jurgen Zepernick and Adolf Finger, Pseudo Random Signal Processing, Theory and Application, John Wiley & Sons. 2005.

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