performance analysis of differential phase modulation. for hf communication

7/29/2019 PERFORMANCE ANALYSIS OF DIFFERENTIAL PHASE MODULATION. FOR HF COMMUNICATION

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PERFORMANCE ANALYSIS OF DIFFERENTIAL PHASE MODULATION

FOR HF COMMUNICATION

NORHASHIMAH BINTI MOHD SAAD

A project report submitted in fulfillment of requirements for the award of the

degree of Master of Engineering (Electrical-Electronics & Telecommunications)

Faculty of Electrical Engineering

Universiti Teknologi Malaysia

OCTOBER 2004


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Dedicated to my beloved Mak and Abah:

Hj. Mohd Saad b. Hj. Kasim and Hjh. Siti J eliha bt. Hj. Zakaria


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ACKNOWLEDGEMENTS

I wish to express my deepest gratitude and appreciation to my supervisor,

Associate Professor Dr. Ahmad Zuri Shaameri, for his guidance, suggestions and

encouragements throughout this study.

I would like to thank the DSP Lab Technician, Mr. Jefri Ismail for the

cooperation, help and constant support throughout this study.

Very special appreciation and gratitude to Abdul Rahim Abdullah, and all my

colleagues in DSP Lab: Ahmad Sazali Senawi, Nurulfadzilah Hasan, Abdul Rahim Mat

Sidek and Fitri Dewi Jaswar, for all valuable suggestions, encouragements andunconditional supports to complete this study.

Last but not least, a special thanks to my parents, Hj. Mohd Saad b. Hj. Kasim

and Hjh Siti Jeliha bt. Hj. Zakaria who always pray for my success, and all my

colleagues in UTM for sharing ideas and knowledge to complete the Master study in

UTM. Without them, this research would not have been possible.


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ABSTRACT

Data transmission using HF spectrum (3-30 MHz) is widely used due to its

ability in providing long distance communications at low cost. Due to multipath fading

problems in HF channels, the maximum symbol rate of data transmission is limited to

100 baud per second. Differential multiple phase modulation techniques can be used to

increase the transmission rate without changing the baud rate. Advanced digital

modulation techniques based on PSK is used due to its reliability in providing lower

error rate compared to other modulation techniques, such as modulation based on FSK.

Unlike coherent detection, phase synchronization is not critical for the differential

detection, and implementation can be made simpler in differential multiple phase

modulations. For this study, the BER and PER performance of DPSK, DQPSK,

D8PSK and D16PSK modulation techniques are presented. The performance

evaluation for each modulation are investigated in additive white Gaussian noiseenvironment and random phase delay is included that is based on uniform distribution.

In general, the BER and PER performance for differential multiple phase detection

decrease for every doubling of phases, but the main advantage is the reliability in data

transmission in achieving higher transmission rate.


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ABSTRAK

Penghantaran data melalui spektrum HF (3-30 MHz) digunakan secara meluas

kerana keberkesanannya di dalam sistem komunikasi jarak jauh dengan kos yang

rendah. Walaubagaimanapun, saluran HF terdedah kepada masalah pemudaran

multipath, yang menghadkan kadar maksimum penghantaran data kepada 100baudper

saat. Bagi mengatasi masalah ini, pemodulatan pembezaan berbilang fasa boleh

digunakan, di mana kadar penghantaran data ditingkatkan tanpa mengubah kadar

simbol data. Pemodulatan digital berdasarkan fasa, PSK dipilih kerana kebolehannya

memberikan BER yang lebih rendah berbanding kaedah lain, seperti pemodulatan

frekuensi, FSK. Tidak seperti pengesanan secara koheren, pengesanan secara

perbezaan tidak dipengaruhi oleh lengah fasa, dan perlaksanaannya menjadi lebih

ringkas. Di dalam kajian ini, prestasi BER dan PER bagi DPSK, DQPSK, D8PSK dan

D16PSK di analisis di dalam persekitaran hingar putihGaussian, manakala lengah fasasecara rawak dikenakan pada isyarat mengikut taburan normal. Secara umumnya, nilai

BER dan PER merosot bagi setiap peningkatan gandaan fasa dalam pemodulatan, tetapi

kelebihannya adalah keberkesanannya meningkatkan kadar penghantaran data.


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CONTENTS

CHAPTER ITEM

TITLE PAGE

TESTIMONY

DEDICATION

ACKNOWLEDGEMENT

ABSTRACT (ENGLISH)

ABSTRACT (MALAY)

CONTENTS

LIST OF TABLES

LIST OF FIGURES

LIST OF TERMSLIST OF APPENDIX

PAGE

i

ii

iii

iv

v

vi

vii

xi

xii

xivxv

CHAPTER 1 INTRODUCTION

1.1 Introduction

1.2 Purposes of Study

1.3 Scope of Work

1.4 Definition of Terms

1.5 Problem Statements

1.6 Research Methodology

1.7 Organization of Thesis

1

2

3

3

4

4

5


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CHAPTER II REVIEW OF LITERATURE

2.1 Introduction

2.2 HF Propagation Characteristics

2.3 Effects of Multipath Fading

2.4 HF Digital Protocols

2.5 Error Detection, Correction and Control

2.6 Recent Developments in HF

Communications

6

6

8

9

10

11

CHAPTER II I THEORY IN HF DIGITAL

COMMUNICATION

3.1 Introduction

3.2 Probability of Error

3.3 Match Filter

3.4 Poisson Distribution Function

3.5 Coherent Detection

3.5.1 Phase Shift Keying Coherent

Detection

3.6 Phase Synchronization Error in Coherent

Detection

3.7 Differential Phase Shift Keying

3.8 Robustness To Phase Synchronization Error

in DPSK Detection

14

15

18

21

22

22

24

25

29


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CHAPTER IV DESIGN OF DIFFERENTIAL MULTIPLE

PSK MODULATION

4.1 Introduction

4.2 Differential Multiple Phase Shift Keying

4.3 Union Bound On Probability of Error

4.4 Differential Quadrature Phase Shift Keying

4.4.1 DQPSK BER Performance

4.5 Differential 8 Phase Shift Keying

4.5.1 D8PSK BER Performance



4.7 Robustness to Phase Synchronization Error

in Differential Multiple PSK Detection

4.7.1 Case for DQPSK Detection

4.7.2 Case for Differential Multiple

Phase Detection

4.8 Signal Representation in Time and

Frequency Domain

30

31

33

35

41

43

46

49

57

58

59

60

63

CHAPTER V RESULTS AND DISCUSSIONS

5.1 Introduction

5.2 Analysis of BER Performance

5.3 Analysis of PER Performance

64

66

69


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CHAPTER VI CONCLUSIONS

6.1 Conclusions

6.2 Suggestions

73

74

REFERENCES

APPENDICES

76

80


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LIST OF TABLES

TABLES TITL E PAGE

3.1

3.2

4.1

4.2

4.3

4.4

4.54.6

4.7

5.1

5.2

5.3

5.4

Encoded sequence for DPSK transmitter

DPSK detected sequence

Combination for DQPSK Transmitted Signal

Encoded sequence for Inphase channel of DQPSK

transmitter

Encoded sequence for Quadrature channel of DQPSK

transmitter

DQPSK detected sequence for Inphase channel

DQPSK detected sequence for Quadrature channelLookup table for D8PSK detection

Lookup table for D16PSK detection

Theoretical BER Performance for a fixed BER of 10-4

BER performance of simulation result for a fixed

BER of 10-4

Theoretical PER Performance for a fixed PER of 10-2

Simulation PER Performance for a fixed PER of 10-2

27

27

36

37

37

37

3746

56

67

68

70

71


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LIST OF FIGURES

FIGURE TITLE PAGE

2.1

3.1

3.2

3.3

3.4

3.5

4.1

4.2

4.34.4

4.5

4.6

4.7

4.8

4.9

Types of HF propagation

Gaussian distribution for symbol x0 andx1

Block diagram of a system

Block diagram for PSK coherent detection

Block diagram of DPSK transmitter

Block diagram of DPSK receiver

Constellations diagram for differential multiple PSK

Basic differential multiple PSK modulator

Basic differential multiple PSK demodulatorUnion bound signal space diagram for differential

M-ary PSK

DQPSK constellations diagram

DQPSK receiver structure

Union bound for DQPSK BER performance

D8PSK constellations diagram

Demodulation structure for D8PSK detection

7

16

19

23

26

26

32

32

3334

36

38

40

42

43


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4.10

4.11

4.12

4.13

5.1

5.2

5.3

5.4

D8PSK union bound signal space plane

D16PSK constellations diagram

D16PSK receiver structure

Signals representation in time and frequency domain

Theoretical BER performance

Simulation result of BER performance

Theoretical PER performance

Simulation result of PER performance

47

49

50

64

66

68

69

71


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LIST OF TERMS

BER

DPSK

DQPSK

D8PSK

D16PSK

FSK

HF

PER

PSK

SNR

-

-

-

-

-

-

-

-

-

-

Bit Error Rate

Differential Phase Shift Keying

Differential Quadrature Phase Shift Keying

Differential 8-Phase Shift Keying

Differential 16-Phase Shift Keying

Frequency Shift Keying

High Frequency

Packet Error Rate

Phase Shift Keying

Signal to Noise Ratio


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LIST OF APPENDICES

APPENDIX TITLE PAGE

A

B

C

BER Performance

PER Performance

Detection based on FSK

81

82

83


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CHAPTER I

INTRODUCTION

1.1 Introduction

Ionospheric propagation is responsible for the ability to do broadcasting and

communications. The long distance transmission is carried out on the HF spectrum (3-

30 MHz) using skywave propagation, while for the short distance transmission, the

groundwave propagation will be used [Goodman, 1992]. Nowadays, the HF

communication system is widely used, not only for the tactical and strategic military

purposes, but also by the commercial world, amateur radios, maritime and aeronautical

operators.

The advantages of this type of communication arise from its relative simplicity,

its ability to provide communication over thousand of miles and its moderate cost per

circuit mile. HF communication involves minimum infrastructure and inexpensive

maintenance compared to other technology such as satellite communication [Abdullah-

Husni et al, 2003].


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Due to variability of ionosphere, the HF signal is subjected to multipath fading

phenomenon, which limits the data transmission rate to 100 baud per second [Goodman,

1992]. In order to overcome this problem, the advanced modulation techniques can be

used to ensure the reliability in data transmission. Thus, the focus of this study is to

design a HF communication system that can improve the reliability in data transmission

using differential multiple phase modulation techniques.

1.2 Purposes Of The Study

The purpose of this study was to design and simulate a HF communication

system that can increase data transfer rate that is limited by using HF channel using

advanced modulation techniques specifically in differential multiple phase modulations.

The performances of the techniques are analyzed in term of the bit error rate and packet

error rate of the modulation. Differential detection is used to overcome phase

synchronization error in coherent detection.

1.3 Scope Of Work

This study was focused on differential multiple phase digital modulation, which

is important to design a system that can increase data transfer rate that is limited by

using the HF transmission channel. The modulation techniques used are DPSK,

DQPSK, D8PSK and D16PSK.


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System was designed to process within the voice band frequency and not on

radio band frequency. Sampling frequency used is 8000 Hz and the carrier frequency is

1000 Hz. The bandwidth of the signal is 4000 Hz.

Data format used is PACTOR, containing 8 characters or 64 bits of data and 16

bits for error control in a packet for 100 baud data transmission rate. The system was

designed to test in a present of additive white Gaussian noise and random phase delay in

received signals.

1.4 Definitions of Terms

For the purpose of this study, the following operational definitions are used:

BER Bit error rate number of error present within the period of data

transmission

DPSK Differential phase shift keying

DQPSK Differential Quadrature phase shift keying

D8PSK Differential 8-phase shift keying

D16PSK Differential 16-phase shift keying

FSK Frequency shift keying

HF High frequency band channel

PER Packet error rate number of packet with at least an error presents

PSK Phase shift keying

SNR Ratio of signal power to noise power


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1.5 Problem Statements

In HF communication system, the variability of ionosphere results multipath

fading phenomenon. This phenomenon gives several affects in the communication,

which are frequency selective fading and time selective fading [Goodman, 1992].

Frequency selective fading problems will cause for inter symbol interference

(ISI). Due to this problem, the maximum data transmission rate is limited to 100 baud

per second [Goodman, 1992][Willink et al, 1996]. By limiting the data transmission

rate to 100 baud per second, inter symbol interference (ISI) problem can be avoided.

As a solution, to increase the data transmission rate without changing or increasing the

baud rate, the differential multiple phase modulation can be used.

1.6 Research Methodology

There are several approaches taken in order to achieve the objective of this

study, which are:

1. Literature of review on HF communication system for understanding the

concept and problem that occur in this particular type of communication.

2. Understanding the basic theory on digital signal processing and digital

communication system to find ways on solving research problems.

3. Designing differential multiple PSK system which are DPSK, DQPSK, D8PSK

and D16PSK.

4. Programming in MATLAB for performance analysis purposes.


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5. Data analysis and simulation of the detection using MATLAB to analyze the

performance of modulation techniques in term of BER and PER.

6. Calculation and performance comparison between theory and simulation.

7. Thesis and report writing.

1.7 Organization Of Thesis

This thesis is divided into six chapters. The first chapter contains an overview of

this project. Some explanations about the literature and recent development in HF were

covered in chapter 2. Chapter 3 describes the theory in HF digital communication. The

design of differential multiple phase modulations were described in chapter 4. Chapter

5 presents the analysis of results. This thesis ends with the conclusion and suggestions

for further research.


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CHAPTER II

REVIEW OF LITERATURE

2.1 Introduction

This chapter describes the HF propagation characteristics, effects of multipath

fading, HF digital protocols, error detection, correction and control, and recent

developments in HF digital modulation techniques.

2.2 HF Propagation Characteristics

HF propagation is divided into two basic modes, which are [Goodman, 1992]:

a) Ground wave propagation

b) Sky wave propagation


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Figure 2.1 Types of HF propagation

Ground wave propagation is the dominant mode of propagation for short

distance communication. Here the electromagnetic tends to follow the contour of the

earth. The ground wave travels in direct contact with the earths surface, and it suffers a

severe frequency-dependent attenuation because of absorption by the ground. Sky wave

propagation is the dominant mode of propagation in the 3-30 MHz frequency range.

Here long distance communication is obtained by reflecting the wave at the ionosphere

regions.

There may be four regions in ionosphere present called D, E, F1 and F2 regions

[McNamara, 1991]. Among these regions, only E, F1, sporadic E, and F2 refract HF

waves. Sky wave propagation is caused primarily by reflection from F layer [Couch,

1997]. Because of this layer, international broadcast stations in HF band can be heard

from the other side of the world at almost any time during day and night.


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2.3 Effects of Multipath Fading

Multipath fading may occur when the transmitted signals are diffracted by

different layers of ionosphere [Goodman, 1992]. When the path length of transmission

differs, the carrier frequency of the signal will also change. There might be loss data on

the detection part because of these changes. Multipath fading will lead to frequency

selective fading and time selective fading.

Frequency selective fading occurs when the received signals has a time delay in

millisecond unit due to diffraction in transmitted signals. In time domain, the delay will

introduce time delay spread problem that will cause for inter symbol interference (ISI)

and limit the data transmission rate to 100 baud per second [Willink et al, 1996]. In

frequency domain, this problem makes system attenuate certain frequency, which can

affect the sub-carrier frequency of the signal, and the signal might be loss.

Time selective fading or flat fading is caused by delay due to the diffraction

signals arrived at the receiver in different phases [McNamara, 1991]. This delay in

phase will result in cancellation of waves or attenuation in wave amplitude. The worst

case happens if the same signal from different paths arrive at the receiver at phase

different which resulting the wave practically cancels each other.

0180

The Doppler shift is caused by the motion of the electrons in the ionosphere

layer which introduce changes in radio frequency [Goodman, 1992]. The frequency

shift will cause error when the receiver is unable to recognize the signal, as the

frequency that has been shifted is too large. If the receiver is using a band-pass filter to

capture the signal, the frequency shift will reject some of the signal.


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2.4 HF Digital Protocols

Several types of data format exist in HF communication to produce a system

which performs robustly under wide range of typical HF channel conditions. Some of

the most frequently used data formats are listed as follows:

a) RTTY

b) AMTOR

c) PACTOR

d) CLOVER

e) G-TOR

Radio Teletypewriter (RTTY) has 5 bits code became available in the market in

the years following World War 2 [Kasser, 1991]. Radio amateurs experimented with

using that equipment for communications. There is no error detection technique in

RTTY. RTTY is a half duplex communication mode. RTTY is also a character

transmission mode that each character is transmitted as soon as it is typed. AMTOR is

a half duplex communication mode and a specialized form of RTTY [Kasser, 1991]. It

has 5 bits in a packet and cannot transfer ASCII. AMTOR provides good performance

in bit error rate particularly error correction in real time, but does not effectively

compete with the speed and error correction of more modern modes [Henry, 1992].

CLOVER is a PSK mode, which uses a full duplex simulation. It is well suited

for operation under good conditions. Clover uses Reed-Solomon error correction codes

to correct a moderate number of errors but it can also switch to ARQ whenever the

conditions are very bad and number of error exceeds the capacity of Reed-Solomon

error corrector.


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PACTOR is an improvement over AMTOR and packet radio. PACTOR is

cheap and reliable. In this context, this means fast, robust and error free data transfer

over HF. PACTOR employs structured packet which contains 8 characters of data for

100 baud per second or 20 characters for 200 baud per second of transmission rate.

PACTOR uses Automatic Repeat Request (ARQ) method with Cyclic Redundancy

Checking (CRC-16) which consists of 16-bit frame check sequence (FCS) for error

correction method [Stalings, 2000]. PACTOR-1 is a powerful FSK mode especially in

a very poor propagation condition. PACTOR-11 is a robust and powerful PSK mode

which operates effectively under both very good and poor conditions, and is as much as

8 times faster then PACTOR-1.

Golay-Transmission over Radio (G-TOR) is a FSK mode that offers a high

transfer rate under good conditions. It combines the error correcting properties of

Automatic Link Establishment (ALE), including Forward Error Correction (FEC)

coding and the ARQ cycle of packet and a new application of the inevitability of the

Golay code, to produce a faster new mode. Military is a major user in HF

communication system.

2.5 Error Detection, Correction and Control

In digital communication, signals that are affected with noise, tends to produce

error. Error occurs when signal detected at the receiver are not the same as the signal

sent from transmitter [Haykin, 1988]. Error control refers to mechanism to detect and

correct errors that occur in packets of data.


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The most prevalent methods for error detection include the application of

redundancy, exact count encoding schemes, parity checking in various forms, and cyclic

redundancy checking (CRC) [Goodman, 1992]. CRC is the most reliable method of

error detection. This method, although not simple to implement, will detect about

99.95% of all transmission errors. The most generally accepted code of this type is the

CRC-16, which employs 16 bits in the frame check sequence [Tomasi, 1987] [Stalings,

2000].

Error correcting methods include Automatic Repeat Request (ARQ) and

Forward Error Correction (FEC) schemes. ARQ is generally viewed to be the most

reliable method for insuring the integrity of transmitted messages under most

circumstances, while FEC detects and corrects errors without the necessity to call for

retransmission [Goodman, 1992].

2.6 Recent Developments in HF Communications

[Raos et al, 2003] has presented the performance of a modem designed for HF

communications. The aim was to attain the real time communication for voice

transmission. In this paper, frequency selective HF channel was converted into a set of

frequency flat channels with multi-carrier modulation orthogonal frequency division

multiplexing (OFDM). Spread spectrum technique was applied to improve modems

performance. The performance of the modem with 16 sub-carriers and QPSK

modulation was analyzed via simulation in Rayleigh fading channel in terms of BER.

The data rates are approximately 2400 and 3600 bps and digital voice can be

transmitted interactively.


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[Jaswar-Shaameri, 2003] has explored the FPGA (field programmable gate

array) implementation for CPFSK (continuous phase FSK) modulation techniques for

HF communication. The paper describes the implementation of an FSK modem based

on CPFSK modulation techniques on the FLEX10K board EPF10K70RC240. Both

transmitter and receiver modules are adopted with the objective to minimized the

system size. Two types of modems were developed with different detection scheme:

conventional noncoherent and square wave detection. The square wave detection has

60% less components because of the parallel structure and no multiplier is used in the

algorithm. Thus, the system size was minimized.

[Charles-Tri, 2003] has discussed the performance of a Direct Sequence DPSK

(DS-DPSK) spread spectrum system over a Rician frequency non-selective, slowly

fading channel in the presence of pulsed noise interference and additive white Gaussian

noise. They indicate that the receiver is effective in mitigating the effects of pulse noise

jamming for all fading conditions that they considered.

The study on error probability for coherent PSK and noncoherent DPSK over

Rician fading channels was done by [Yao-Teng et al, 2002]. They have discussed the

performance of communication systems using both coherent PSK and noncoherent

DPSK modulation, in correlated with Rician fading channels with diversity reception.

The method with both coherent and non-coherent detections resulted better performance

in Rician fading channels compared to Rayleigh fading channels.

[J ohn-Mohamed et al, 2002] discussed the data recovery in Differential Encoded

QPSK (DEQPSK). The research presented a new algorithm for recovering step phase

changes for a DEQPSK modulated signal by computing the phase angle from the

arctangent of the ratio Quardrature/Inphase, and comparing it with previous phase.


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STANAG 5066 was developed in the course of modernizing the communication

services within NATO. A subnetwork profile for HF radio data communications

(STANAG 5066) was introduced through NATO to provide improved HF

communications for broadcasting [NATO][Reynolds-Gillespie, 1997]. [Trinder-Brown,

1999] was proposed the STANAG incorporates a data rate change (DRC) mechanism to

change the data rate of the link between the range of 75 to 2400 bps and above. This

was to optimize the modem data rate to changes in HF channel conditions, to maintain

the maximum throughput. The DRC algorithm was described as a requirement for an

effective data rate changes.

[Nilsson-Giles, 1997] explored the potential of multi-carrier or orthogonal

frequency division multiplexing (OFDM) for military HF communication. The

proposed system uses a differential binary PSK (DBPSK) modulation method on each

carrier. Number of carriers used in this system is 1024 over a bandwidth of 125 kHz

and symbol duration is 8.2ms. The modem proposed by Nilsson is capable of operating

until 1.22Mbps.


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CHAPTER II I

DIGITAL COMMUNICATION THEORY

3.1 Introduction

This chapter describes the theoretical foundation in HF digital communication.

The probability of error, match filter, Poisson distribution function for packet error rate,

PSK coherent detection and differential PSK detection, phase synchronization error in

coherent detection and robustness to phase synchronization error in differential PSK

detection were discussed in detail in this chapter.


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3.2 Probability of Error

In digital communication system design, the main objective is to receive data as

similar as the data sent from the transmitter. It is important to analyze the system in

term of probability of error to view the systems performance. Each modulation

technique has different performance while dealing with signals, which normally are

affected with noise. General explanation for probability of error is explained in this

section.

General equation for the output signal that is affected with the additive white

Gaussian noise can be shown in Equation (3.1) [Shanmugan, 1988][Proakis, 1995].

If is the true signal, then is the signal corrupted by noise,)(tx )(ty )(tn

)()()( tntxty += (3.1)

The performance of each modulation is measured by calculating its probability of errorwith assumption that systems are operating with this additive white Gaussian noise

[Shanmugan, 1988][Proakis, 1995].

The probability density function (pdf) for noise can be represented as a Gaussian

distribution [Proakis, 1995]

=

0

2

0

0

02

exp2

1)(

N

n

NnPN

(3.2)


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where is noise at time and is noise power at time .

Consider to be two possibilities, and , at time , and

. Conditional probability for symbol and can be represented as

)( 00 tnn = 0t2

0 )]([ txEN = 0t

)(tx )(0 tx )(1 tx 0tt = )( 000 txx =

)( 011 txx = 0x 1x

=

0

20

0

|2

)(exp

2

1)(

0 N

xy

NyP xy

(3.3)

=

0

21

0

|2

)(exp

2

1)(

1 N

xy

NyP xy

(3.4)

The probability of occurrence for both symbols, also known as priori probability is

shown as follows

2

1)()( 10 == xPxP (3.5)

Probabilityof error

1x

Referencepoint

210 xxT

+=

0x

Figure 3.1 Gaussian distribution for symbol and0x 1x


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Figure 3.1 shows the Gaussian distribution for probability of getting error forx0andx1.

Probability of error is area under the graph can be calculated as

+= dyxPyPdyxPyPP xyxye )()()()( 1|0| 10 (3.6)

+=T

xy

T

xy dyxPyPdyxPyP )()()()( 1|0| 10

dyN

xy

Ndy

N

xy

N

T

T

+

=

0

21

00

20

02

)(exp

2

1

2

1

2

)(exp

2

1

2

1

Since the chances of occurrence for both symbol is the same, Equation (3.6) can be

expressed as

dyN

xy

NP

T

e

=

0

20

02

)(exp

2

1

2

1.2

(3.7)

If is shifted to 0, the probability of error can be expressed as0x

=

T

e dyN

y

NP

0

2

02

exp2

1

(3.8)

where2

01 xxT

= . Substitute0

22

N

yz = into Equation (3.8) and probability of error

can also be shown as

dzz

QPe

=

=

2exp

2

1

2

2

2

(3.9)


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where0

01

22 N

xx =

. Q( ) is referred as the Q function and is given in table form. To

maximize the probability of correct detection, value of has to be increased2

[ ]

0

2

012

N

xx = (3.10)

Factor of time is inserted since changes with time)(tx

[ ]

0

2

012 )()(

N

txtx = (3.11)

The probability of correct detection is obtained from Q(/2). To maximize probability

of correct detection, the match filter structure is adopted.

3.3 Match Filter

Match filter is a method to detect signal by maximizing signal power in the

presence of noise [Proakis, 1995][Rodger, 2000]. The idea behind a match filter is

correlation using convolution. The output of a match filter does not necessarily look

like the signal being detected, but the amplitude of each point in the output signal is a

measure of how well the filter kernel matches the corresponding section of the inputsignal. Theory for match filter is shown as follows [Rodger, 2000][Haykin, 1988].


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Figure 3.2 Block diagram of a system

Figure 3.2 shows the relationship between input and output of a system. The

relationship between the output and input in the presence of noisen(t) that is

a convolution process is

)(ty )(tx

(t)(t) +n(t)h(t)

(3.12))]()([*)()( tntxthty +=

where is true signal and deterministic, is additive white Gaussian noise,

is system impulse response and is output. If noise is not considered, the

relationship between input and output as follows

)(tx )(tn )(th

)(ty

) (3.13)(*)()( txthty =

The objective is to findh(t) that maximizes the probability of correct detection ofx(t).

Referring to Equation (3.11), this is done by maximizing the quantity of where

is value ofy(t) at time and

2 )( 0ty

0t [ ]2

0)(tnE is the noise power at time .0t

[ ]20

2

02

)(

)(

tnE

ty

= (3.14)


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20

Applying Schwartz Inequality function, can be expressed as follows2MAX

=dffHfS

dffXdffH

nn

MAX2

22

2

)()(

)()(

dffXN

=2

0

)(1

(3.15)

where and represents noise power. Based on [Couch L.W. 1997] the

maximum value of is obtained whenh(t) is chosen such that equality is attained.

This occurs when system impulse response or filter kernel h(t)

)(0 fSN nn= 0N

2MAX

) (3.16)()( 0 ttxth =

where filter kernel h(t) is in a non-causal form. Output is a convolution of system

impulse response and input signal.

)(ty

) (3.17)(*)()( txthty =

= dthx )()(

The end result is correlation of . Thus, the matched filter can be realized using a

correlater.

)(tx

=T

dttxtxty0

)().()( (3.18)


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21

3.4 Poisson Distribution Function

Poisson distribution is the discrete probability density function used in

communication to determine the packet error rate within the transmitted data especially

for large packet size and low bit error rate. Two important parameters used to evaluate

the Poisson distribution are bit error rate and the packet size used in transmitted data.

Discrete probability density function can be expressed as

( )kxkbex

k

kb

x=

=

0 !

)((3.19)

The distribution of error within a packet of binary data assuming thatb


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22

3.5 Coherent Detection

Coherent detection involves the use of matched filter to detect the transmitted

signals [Haykin, 1988]. The detection method will be explained here and the bit error

rate (BER) will be derived. Coherent detection is optimum in terms of the BER

performance but requires the exact form of the reference signal at the receiver. The

BER performance increases if exist any phase synchronization error between the

received and reference signal at the receiver. This problem is resolved at increase

complexity by introducing a carrier recovery circuit [Shaameri-Jaswar, 2003].

3.5.1 Phase Shift Keying Coherent Detection

Phase shift keying, or PSK for coherent detection is a basic method for

transmitting and receiving digital signals, which the phase of transmitted signal is

varied to convey information [Roden, 1988][Rodger, 2000]. There are several schemes

that can be used to accomplish PSK. The simplest method uses two signal phases: 0

degrees and 180 degrees. The state of each bit is determined according to the state of

the preceding bit. If the phase of the wave does not change, then the signal state stays

the same (low or high). If the phase of the wave phase reverses, then the signal state

changes.

Figure 3.3 is derived from Equation (3.22) [Proakis, 1995]

[ ] =Tb

dttxtxtxty0

01 )()()()( (3.22)


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23

where and are represented as)(1 tx )(0 tx

"1"02cos)( 11 TbttfAtx =

"0"02cos)( 10 TbttfAtx =

Tb

0)(tx

ftfAtx11 2cos)( =

Tb

0

tfAtx10 2cos)( =

Figure 3.3 Block diagram for PSK coherent detection

From Equation (3.11), to maximize the probability of correct detection

( ) =Tb

MAX dttxtxN

0

2

01

0

2 )()(1

(3.23)

Value of and are substituted into Equation (3.23) and result of the

calculation is

)(1 tx )(0 tx

+=TbTb

MAX dttfN

A

dtN

A

01

0

2

00

22

22cos

22

(3.24)


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24

From Equation (3.24), the following equation can be derived

0

22 2

N

TbAMAX = (3.25)

BER for PSK can be shown as follows

=

2MAXQBER

=

0

2

2N

TbAQ (3.26)

where Q denotes for Q function. Signal-to-noise ratio can be calculated as follows

=

0

2

2log10)(

N

TbAdBSNR (3.27)

3.6 Phase Synchronization Error in Coherent Detection

Synchronization is critical to ensure that the BER performance is optimal for

coherent detection [Shaameri-Jaswar, 2003]. Given that a received signal within bit

duration is

( ) += tfAty 12cos)( bTt 0 (3.28)


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25

whereis the phase present in the signal. If the reference signal is

( tfAtx 11 2cos)( )= bTt 0 (3.29)

The output signal is

=bT

dttxtytz0

1 )()()(

( ) ( +=bT

dttfAtytfA0

11 2cos)(2cos )

( ) ( ++=

bT

dttfA

A

01

2

cos4cos2 )

( )cos2

2bTA= (3.30)

The result shows how critical the phase shift affects the output signal. Thus, it is

desired to have the detection scheme a compromise between robustness to phase

synchronization error and BER performance.

3.7 Differential Phase Shift Keying

Differential phase shift keying (DPSK) is a type of phase modulation

noncoherent detection, where it uses the received phase of the previous signal as a

reference signal. DPSK is developed as a solution to the phase synchronization error in

coherent PSK detection [Goodman, 1992] [Roden, 1988]. The problem phase

synchronization can be resolved by introducing differential encoding in the modulation


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26

signal. The structure for the DPSK transmitter and receiver are shown in Figure 3.4 and

Figure 3.5.

Figure 3.4 Block diagram of DPSK transmitter

Figure 3.5 Block diagram of DPSK receiver


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27

The DPSK is developed to simplify the PSK by not requiring carrier recovery circuit.

The input sequence is encoded as

kkkkksasaa 11 = (3.31)

Table 3.1 shows the example of encoded sequence for DPSK transmitted signals. The

process for detecting the transmitted sequence is shown in Table 3.2.

Table 3.1: Encoded sequence for DPSK transmitter

k 0 1 2 3 4 5

sk 1 1 0 1 0

ak 1 1 1 0 0 1

x(t) tf12cos tf12cos tf12cos - tf12cos - tf12cos tf12cos

Table 3.2: DPSK detected sequence

k 0 1 2 3 4 5

x(t) tf12cos tf12cos tf12cos - tf12cos - tf12cos tf12cos

k 0 0 0 0

Phasediff

+ + - + -

sk 1 1 0 1 0

It is assumed that two consecutive binary bit 1 are transmitted and A=1. The phase

shift is zero. The input of the low pass filter is

)2cos(*)2cos()( 11 tfAtfAtq =

)22cos(2

1

2

11tf+= (3.32)


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28

Since theq(t) is filtered, only the dc terms remains and output of the low-pass filter is

2

1)( =tr

(3.33)

The BER for differential PSK is

=

p

eN

AP

2exp

2

1 2(3.34)

The filtered noise power is

b

op

T

NN

2=(3.35)

whereTb is the bit-duration, andN0 is the power of the additive white Gaussian noise.

The BER for differential PSK is

=

o

be

N

TAP

4

exp

2

1 2

(3.36)


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29

3.8 Robustness To Phase Synchronization Error in DPSK Detection

Given that1 is the phase delay present in the received signal. It is assume that

A=1. The input of the low pass filter is

)2cos(*)2cos()( 1111 ++= tftftq

( ))(22cos2

1)cos(

2

111111 +++= tf

( )11 222cos

2

1

2

1 ++= tf

(3.37)

The high frequency component inq(t)is filtered by the filter. Then the output signal is

only the dc term of the signal.

2

1)( =tr

(3.95)

The result shows that the phase is not present in DPSK detection. Thus, the

DPSK detection is robust to phase synchronization error.


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CHAPTER IV

DESIGN OF DIFFERENTIAL MULTIPLE PSK MODULATION

4.1 Introduction

This chapter describes the design of differential multiple PSK modulation

techniques proposed in this study, which are DQPSK, D8PSK and D16PSK modulation

techniques. The theoretical BER performance, robustness to phase synchronization

error in differential detection and signal representation of the modulated signals were

discussed in detail in this chapter.


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31

4.2 Differential Multiple Phase Shift Keying

Multiple differential PSK modulations are very important to increase the

transmission rate without changing the baud rate. In DQPSK detection, two bits of data

represents one symbol of information. D8PSK is capable to transmit 3-bit per symbol,

and if D16PSK modulation is used, the transmission rate is four times greater than

DPSK modulation. The modulation technique represents 4-bit per symbol for 100

bauds data transmission rate. Similar to DPSK modulation technique, the problem

phase synchronization can be resolved by introducing differential symbol coding in

differential multiple PSK modulation. Detection can be made simpler since no carrier

recovery detection is required.

For the general case of differential M-ary PSK, the various signals are given by

Equation (4.1) [Roden, 1988][Rodger, 2000]

ii tfAts += 12cos)( (4.1)

where the index, i, takes on values from 0 to M-1. The angles are given by

( )M

ii

12 +=

(4.2)

M is the number of phases used in the modulation.


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32

The signal space diagram in differential multiple PSK is shown in Figure 3.9.

Figure 4.1 Constellations diagram for differential multiple PSK

The waveform can be generated from the binary signal by combining groups of

bits and then performing a digital-to-analog conversion. Thus, for example, if M=8, the

combination of bits are in triplets. A serial to parallel converter converts each three

input bits to a 3-bit binary number, which forms the input to the D/A converter [Roden,

1988]. This is shown in Figure 4.2.

Serial toarallel

3-bitD/A

d(t) s(t)

PhaseModulator

Figure 4.2 Basic differential multiple PSK modulator

The corresponding receiver is shown in Figure 4.3. The phase demodulators are

then processed by an analog-to-digital converter to reconstruct the data sequence. The

parallel bit streams are converted into a series bit stream for detection of the data

sequence [Roden, 1988].


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33

Figure 4.3 Basic differential multiple PSK demodulator

Code search for multi level differential PSK modulation require excessive

search time, which a wide range of coefficient need to be check to demodulate signal

accurately.

4.3 Union Bound On Probability of Error

When the geometry of the signal set is difficult to analyze, union bound is used

to find the probability of error. The additive noise will cause an error if the phase angleof the received signal varies from the transmitted phase angle by more than/M in

either direction, or in other words, error will occur if the symbol,sj varies more than the

distance, dj between adjacent phase states [Roden, 1988][Proakis, 1995].

Phasedemodulator

3-bitA/D

Parallel toserial

s(t) d(t)


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34

Figure 4.4 views the union bound signal space plane for differential M-ary PSK.

Figure 4.4 Union bound signal space diagram for differential M-ary PSK

The error distance, dj is expressed by

=

MQd MAX

j

sin

2(4.3)

where M is the number of phase states. For case in differential detection, dj can be

written as

=

MN

TAd

o

b

j

sin

4exp

2

1 2(4.4)


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53/100

36

1101

1000

Figure 4.5 DQPSK constellations diagram

The constellation diagram in Figure 4.5 shows the different four angles used in

DQPSK modulation technique. The transmitted signal has one of four possible forms as

shown in Table 4.1.

Table 4.1: Combination for DQPSK Transmitted Signal

x(t)

Symbol(s

0,s1)

Inphase (I) Quadrature (Q)

11 +Acos2f1t + Asin2f1t

10 +Acos2f1t - Asin2f1t

01 -Acos2f1t + Asin2f1t

00 -Acos2f1t - Asin2f1t

The combination of DQPSK transmitted signal shown in Table 4.1 can be expressed as

[Kolimbiris, 2000]

x(t) =+(Acos2f1t+Asin2f1t) (4.7)


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37

Table 4.2: Encoded sequence for Inphase channel of DQPSK transmitter

k 0 1 2 3 4 5

sk 1 1 0 1 0

ak 1 1 1 0 0 1

xI(t) tf12cos tf12cos tf12cos - tf12cos - tf12cos tf12cos

Table 4.3: Encoded sequence for Quadrature channel of DQPSK transmitter

k+1 0 1 2 3 4 5

sk+1 1 1 0 1 0

ak+1 1 1 1 0 0 1

xQ(t) tf12sin tf12sin tf12sin - tf12sin - tf12sin tf12sin

Table 4.4: DQPSK detected sequence for Inphase channel

k 0 1 2 3 4 5

xI(t) tf12cos tf12cos tf12cos - tf12cos - tf12cos tf12cos

k 0 0 0 0

Phasediff

+ + - + -

sk 1 1 0 1 0

Table 4.5: DQPSK detected sequence for Quadrature channel

k+1 0 1 2 3 4 5

xQ(t) tf1

2sin tf1

2sin tf1

2sin - tf1

2sin - tf1

2sin tf1

2sin

k 0 0 0 0

Phasediff

+ + - + -

sk+1 1 1 0 1 0


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38

Table 4.2 - 4.3 show the example of encoded sequence for Inphase and

Quadrature channel for DQPSK transmitted signals. The process for detecting the

transmitted sequence is shown in Table 4.4 - 4.5, respectively. The block diagram for

the DQPSK receiver is shown in Figure 4.6.

Figure 4.6 DQPSK receiver structure

It is assumed that two consecutive symbols 11 are transmitted and the phase

shift is zero. Using differential encoding, the demodulator signal for I channel is

)2cos(1tf . By/2 phase shifter, the demodulator signal for Q channel is )2sin(

1tf .

Input of the low pass filter is,

Inphase channel:

( ) )2cos(*)2sin()2cos()(111tftftftq

I +=

( )( ) )22sin(2

122cos1

2

1

)2sin()2cos()2(cos

11

111

2

tftf

tftftf

++=

+=

(4.8)


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39

The high frequency components are filtered by the low-pass filter, only the dc terms

remains and output of the low-pass filter is

2

1

)( =trI (4.9)

Quardrature channel:

( ) )2sin(*)2sin()2cos()(111tftftftq

Q +=

( )( ) )22sin(2122sin1

21

)2(sin)2sin()2cos(

11

1

2

11

tftf

tftftf

+=

+=

(4.10)

Since theqQ(t) is filtered, only the dc terms remains and output of the lowpass filter is

2

1)( =tr

Q(4.11)

The start bit from differential encoder is removed by correlating with the previous

signal at the output of the low-pass filter. The +dc levels from Inphase and Quadrature

channels representing the two parallel bit streams, are converted into a series bit stream

for detection.


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40

4.4.1 DQPSK BER Performance

BER performance for DQPSK detection scheme is evaluated using union bound

as discussed in previous section. The signal space plane for DQPSK union bound is

shown in Figure 4.7.

Figure 4.7 Union bound for DQPSK BER performance

Given that s=11. ErrorPe,11 will occur ifs=01 ors=10. The probability is written as

)

Q()

Q(22

P maxmaxe,11

+=

)

Q(2

2 max= (4.12)

The BER performance can be written as

)00()01()10()11(00,01,10,11,

=+=+=+== sPPsPPsPPsPPPeeeee

(4.13)


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41

SincePe,11 =Pe,10 =Pe,01=Pe,00, thenthe BER performance is

[ ])11(411,

== sPPPee

=

41

224 max )Q(

)

Q(2

2 max= (4.14)

The BER performance for DQPSK can be expressed as

=o

b

N

TAPe 4exp2

12

2

(4.15)

Therefore,

=

o

b

N

TAPe

4exp

2

(4.16)


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42


Differential 8 phase shift keying (D8PSK) uses eight different angles, which

every angle will represents one symbol of data in triplet bits. The constellation diagram

in Figure 4.8 shows the different eight angles used in D8PSK modulation technique.

1 1 1

1 1 0

1 0 0

1 0 10 0 1

0 0 0

0 1 0

0 1 1

Figure 4.8 D8PSK constellations diagram

From Equation (4.1 4.2), the transmitted signal of D8PSK is:

)2cos()( 1 itfAts =

8

)12( ii

+=

(4.17)

where index, i, takes on values from 0 to 7. The block diagram for the D8PSK receiver

is shown in Figure 4.9. The receiver consists of Inphase (I) channel, Quadrature (Q)

channel and Control (C) channel.


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43

Figure 4.9 Demodulation structure for D8PSK detection

BPF

x(t) - signal

Phase shifter /2

/4

BW=2/Tbc=f1 Inphase

signal

Quadraturesignal

Control signal

LPF

LPF

LPF

fcf1

fcf1

fcf1

Tb

Tb

Tb

s(t) - detection

It is assumed that consecutive symbols 110 are transmitted and the phase shift

is zero. The received signal is

( )8

2cos)(1

= tfAtx (4.18)

It is assume that A=1. Input of low-pass filter is:

Inphase channel:

( ) )2cos(*82cos)( 11 tftftqI =

( ) ( )8

cos2

18

22cos2

11

+= tf

( ) ( ) ( ) ( )[ ] 46.08

sin22sin8

cos22cos2

111

++= tftf (4.19)


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44

The high frequency components are removed by the low-pass filter, output of the low-

pass filter is only the dc term of the signal which it equals to

46.0)( =trI

(4.20)

Quadrature channel:

( ) )2sin(*8

2cos)(11 tftftqQ

=

( ) ( )8

sin2

18

22sin2

11

= tf

( ) ( ) ( ) ( )[ ] 19.08

sin22cos8

cos22sin2

111

+= tftf (4.21)

The high frequency components are removed by the low-pass filter, only the dc terms


19.0)( =trQ

(4.22)

Control channel:

Using/4 phase shifter differential encoder, two demodulator signals for control

channel are

)4

2sin()(

)42cos()(

1

1

2

1

=

=

tftx

tftx

c

c

(4.23)


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45

For c1channel, input of the low-pass filter is

42cos*

82cos)(

111

= tftftqC

( ) ( )8cos21

8322cos

21

1 += tf

( ) ( ) ( ) ( )[ ] 46.08

sin22sin8

cos22cos2

111

++= tftf (4.24)

For c2channel, input of the low-pass filter is

( ) ( )42sin*82cos)( 112 = tftftqC

( ) ( )8

sin2

18

322sin2

11

= tf

( ) ( ) ( ) ( )[ ] 19.08

sin22cos8

cos22sin2

111

= tftf (4.25)

Output of the control channel is the correlation of the output ofc1 andc2. The high

frequency components are filtered by the low-pass filter, only the dc terms remains and

output of the low-pass filter is

)(*)()(21

trtrtrCCC

=

(4.26)1.0=

The start bit from differential encoding is removed by correlating with the

previous signal at the output of the low-pass filter. The +dc levels from everychannels, representing the three parallel bit streams, are converted into a series bit

stream for detection.


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46

Table 4.6 shows the lookup table for D8PSK that expressed how the modulated

signals are demodulated at the detection part with the detected bits at the output of the

receiver.

Table 4.6: Lookup table for D8PSK detection

Demodulation signals

Bit 3Signal phases

x(t) Bit 1cos (2f1t)

Bit 2

sin (2f1t) cos (2f1t-/4) sin (2f1t-/4)Bits

cos (2f1t-/8) 1 1 1 0 110

sin (2f1t-/8) 1 1 1 1 111

cos (2f1t-3/8) 0 1 1 1 011

sin (2f1t-3/8) 0 1 0 1 010

-cos (2f1t-/8) 0 0 0 1 000

-sin (2f1t-/8) 0 0 0 0 001

-cos(2f1t-3/8) 1 0 0 0 101

-sin(2f1t-3/8) 1 0 1 0 100


BER performance for D8PSK detection scheme is evaluated using union bound,

as discussed in Section 4.3. The signal space plane for D8PSK union bound is shown in

Figure 4.10.


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47

Figure 4.10 D8PSK union bound signal space plane

Using trigonometric function, error distance, dcan be expressed as,

8sinAd= (4.27)

From Equation 4.4, error distance, dj for a given symbol,sj is written as

=

8sin

2

MAXj

Qd (4.28)

Given that s=111. ErrorPe,111 will occur ifs=011 ors=110. The probability is written

as

)

Q()

Q(8

sin28

sin2

P maxmaxe,111

+=


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48

)

Q(8

sin2

2 max

= (4.29)


)100()101()110()111(100,101,110,111,

=+=+=+== sPPsPPsPPsPPPeeeee

)000()001()010()011(000,001,010,011,

=+=+=+=+ sPPsPPsPPsPPeeee

(4.30)

SincePe,111 =Pe,101 =Pe,101=Pe,100 =Pe,011 =Pe,001 =Pe,001=Pe,000, thenthe BER

performance is

[ ])111(8111,

== sPPPee

=

8

1

8sin

228 max )

Q(

)

Q(8

sin2

2 max

= (4.29)

The BER performance for D8PSK can be expressed as

=

8sin

4exp

2

12

2

o

b

N

TAPe (4.30)

Therefore,

= 8sin4exp

2

o

b

N

TA

Pe (4.31)


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49


Differential 16PSK uses sixteen different angles, which every angle represents

four bits per symbol of information. D16PSK technique can transmits four bits per

symbol for every transmission. Similar to D8PSK, D16PSK uses differential coding at

the modulation part to overcome phase synchronization error at the receiver side. The

constellation diagram in Figure 4.11 shows the different angles used in D16PSK

modulation technique.

1100

1110

11110111

0110

0100

0101

0001

0000

0010

0011 1011

1010

1000

1101

1001

Figure 4.11 D16PSK constellations diagram

The transmitted signal of D16PSK can be written as

)2cos()(1 itfAtx =

( )16

12 ii

+=

(4.32)


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50

where index, i, takes on values from 0 to 15. The block diagram for the D16PSK

receiver is shown in Figure 4.12.

Figure 4.12 D16PSK receiver structure

It is assumed that consecutive symbols 1101 are transmitted with assumption

that the phase shift is zero. The received signal is

)16

2cos()(1

= tfAtx (4.33)


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51

It is assume that A=1. Input of the low-pass filter is

Inphase channel:

( ) )2cos(*16

2cos)(11tftftq

I =

( ) ( )16

cos2

116

22cos2

11

+= tf

( ) ( ) ( ) ( )[ 49.08

sin22sin8

cos22cos2

111

++= tftf ] (4.34)



49.0)( =trI

(4.35)

Quadrature channel:

( ) )2sin(*8

2cos)(11tftftq

Q =

( ) ( )8

sin2

18

22sin2

11

= tf

( ) ( ) ( ) ( )[ ] 1.08

sin22cos8

cos22sin2

111

+= tftf (4.36)



1.0)( =trQ

(4.37)


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52

Control channel for 3rdbit, using/4 phase shifter, two demodulator signals are shown

as below

)4

2sin()(

)4

2cos()(

1

1

2

1

=

=

tftx

tftx

c

c (4.38)

c1channel:

( ) ( )4

2cos*16

2cos)(111

= tftftc

( ) ( )163cos

2

1

16

522cos2

1

1

+= tf

( ) ( ) ( ) ( )[ ] 42.016

5sin22sin16

5cos22cos2

111

++= tftf (4.39)

c2channel:

( ) ( )4

2sin*16

2cos)(112

= tftftc

( ) ( )163sin21

16522sin

21

1 = tf

( ) 28.016

522sin2

11

= tf

( ) ( ) ( ) ( )[ ] 28.016

5sin22cos16

5cos22sin2

111

= tftf (4.40)

Input of low-pass filter is the correlation ofc1(t) and c2(t) of the channel and can be

shown as

)(*)()(21

tctctqc

= (4.41)


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53



1 (4.42).0)( =trC

Control channel for 4th bit, using/4 phase shifter, the demodulator signals for the

channel are

)8

2cos()(11

= tftxd

)82sin()( 12 = tftxd

)8

32cos()(

13

= tftx

d

)8

32sin()(

14

= tftx

d(4.43)

d1channel:

( ) ( )8

2cos*16

2cos)(111

= tftftd

( ) ( )16

cos2

116

322cos2

11

+= tf

( ) ( ) ( ) ( )[ ] 49.016

3sin22sin16

3cos22cos2

111

++= tftf (4.44)


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54

d2channel:

82sin*

162cos)(

112 = tftftd

( ) ( )16sin21

16322sin

21

1 = tf

( ) ( ) ( ) ( )[ ] 1.016

3sin22cos16

3cos22sin2

111

= tftf (4.45)

d3channel:

( ) ( )832cos*162cos)( 113 = tftftd ( ) ( )

165cos

2

116

722cos2

11

+= tf

( ) ( ) ( ) ( )[ ] 28.016

7sin22sin16

7cos22cos2

111

++= tftf (4.46)

d4channel:

( ) ( )8

32sin*16

2cos)(114

= tftftd

( ) ( )16

5sin2

116

722sin2

11

= tf

( ) ( ) ( ) ( )[ ] 42.016

7sin22cos16

7cos22sin2

111

= tftf (4.47)


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55

Input of low-pass filter for 4th bit channel is the correlation ofd1(t), d2(t), d3(t) andd4(t).

It can be expressed by:

)(*)(*)(*)()( 4321 tdtdtdtdtqd =

The high frequency components are filtered by the low-pass filter, only the dc term will

remain at the output of the filter. The output is

006.0)( =trd

The start bit from the differential encoding is removed by correlating with

previous signal at the output of low-pass filter. The +dc levels from every channel,

representing the four parallel bit streams are converted into a series bit stream for

detection.

Table 4.7 shows the lookup table for D16PSK that expressed how the modulated

signals are demodulated at the detection part of the receiver.


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Table 4.7: Lookup table for D16PSK detection

100101010101cos (2f1t-31/16)

100000010101cos (2f1t-29/16)

101000010001cos (2f1t-27/16)

101100000001cos (2f1t-25/16)

001100000000cos (2f1t-23/16)

001010000000cos (2f1t-21/16)

000010001000cos (2f1t-19/16)

000110101000cos (2f1t-17/16)

010110101010cos (2f1t-15/16)

010011101010cos (2f1t-13/16)

011011101110cos (2f1t-11/16)

011111111110cos (2f1t-9/16)

111111111111cos (2f1t-7/16)

111001111111cos (2f1t-5/16)

110001110111cos (2f1t-3/16)

110101010111cos (2f1t-/16)

sin (2f1t-3/8)cos (2f1t-3/8)sin (2f1t-/8)cos (2f1t-/8)sin (2f1t-/4)cos (2f1t-/4)

Bit 4Bit 3Bit 2

sin (2f1t)

Bit 1

cos (2f1t)

BitsDemodulation signalsSignal phases

x(t)


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BER performance for D16PSK detection scheme is evaluated using union

bound, as discussed in Section 4.3. From D16PSK constellation diagram in Figure 4.8,

error distance, dis evaluated using trigonometric function, and can be expressed as,

16sinAd = (4.50)

From Equation (4.4), error distance, dj for a given symbol,sj is written as

=

16sin

2

MAXj

Qd (4.51)

Given that s=1111. ErrorPe,1111 will occur ifs=0111 ors=1110. The probability is

written as

)

Q()

Q( 16sin216sin2P

maxmax

e,1111

+=

)

Q(16

sin2

2 max

= (4.52)


)0000(....)1110()1111(0000,1110,1111, =++=+== sPPsPPsPPP eeee (4.53)


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Since the priory probability is same, thenthe BER performance can be written as

)111(16111,

== sPPPee

=

161

16sin

2216 max )Q(

)

Q(16

sin2

2 max

=

=

16sin

4exp

2

12

2

o

b

N

TA(4.55)

Therefore, the BER performance of D16PSK detection is

=

16sin

4exp

2

o

b

N

TAPe (4.56)

4.7 Robustness to Phase Synchronization Error in Differential Multiple PSK

Detection

This section will display the effect of phase delay presented in received signal

for differential multiple PSK modulations. It is to show that the phase is not present in

the detection, and differential phase modulation is robust to phase synchronization

error.


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4.7.1 Case for DQPSK Detection

Given that a received signal,x(t) is

( ) ( )1111

2sin2cos)( +++= tfAtfAtx b

Tt0 (4.57)

where1 is the phase delay present in the signal. It is assume that A=1. Input of low-

pass filter is the correlation of the received signal and the previous signal from

differential encoding. Input of the low-pass filter is presents as

Inphase channel:

( ) )2cos(*)2sin()2cos()(111111

++++= tftftftqI

)2sin()2cos()2(cos111111

2 ++++= tftftf

( ) )222sin(2

1222cos

2

1

2

11111

++++= tftf (4.58)

Since the high frequency component is filtered, the output of low-pass filter is only the

dc term of the signal. Output of the low-pass filter is

2

1)( =tr

I(4.59)

Quadrature channel:

( ) )2sin(*)2sin()2cos()(111111

++++= tftftftqQ

)2(sin)2sin()2cos(11

2

1111 ++++= tftftf


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60

( ) )222sin(2

1222sin

2

1

2

11111

+++= tftf (4.60)

High frequency component of the signal is removed by the low-pass filter. Only the dc

term of the signal remains at the output. Output of the low-pass filter is

2

1)( =tr

Q(4.61)

The result proofs that the phase is not presented in the detection, and the DQPSK

detection is robust to phase error.

4.7.2 Case for Differential Multiple Phase Detection

For multiple phase detection, the example of D8PSK will be used to calculate

the effect of phase delay. The result of phase effect in any differential M-ary PSK is

same, since it uses the same method to demodulate the data.

The received signal is given by

( )11 8

2cos)( ++= tfAtx b

Tt0 (4.62)


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where1 is the phase delay present in the signal. It is assume that A=1. By using

differential encoding from the previous start bit signal, and by using phase shifter, the

demodulators can be shown as

( )11

2cos)( += tftxI

( )11

2sin)( += tftxQ

( )111 4

2cos)( ++= tftxc

( )112 4

2sin)( ++= tftxc

(4.62)

Input of low-pass filter is the correlation of the received signal and the demodulator of

channels. Input of the low-pass filter is calculated as below.

Inphase channel:

( ) )2cos(*8

2cos)(1111

++= tftftqI

( ) ( )8

cos2

12

822cos

2

111

++= tf

( 46.028

22cos2

111 ++=

tf ) (4.63)

The high frequency component in the signal is filtered by the low-pass filter. Then the

output signal is only the dc term of the signal.

(4.64)46.0)( =trI


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Quadrature channel:

( ) )2sin(*8

2cos)(1111

++= tftftqQ

( ) ( )8sin21

2822sin2

111 += tf

( 19.028

22sin2

111++= tf ) (4.65)

Since theqQ(t) is filtered, only the dc terms remains and output of the low-pass filter is

19.0)( =trQ

(4.66)

C channel:

( ) ( )11111 4

2cos*8

2cos)( ++= tftftc

( ) ( )8

cos2

12

8322cos

2

111

++= tf

( 46.028322cos21

11 ++= tf ) (4.67)

( ) ( )11112 4

2sin*8

2cos)( ++= tftftc

( ) ( )8

sin2

12

8322sin

2

111

+= tf

( 19.028322sin21 11 += tf ) (4.68)

Input of low-pass filter for C channel is

)(*)()(21tctctq

c= (4.69)


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Since theqQ(t) is filtered, only the dc terms remains and output of the lowpass filter is

1.0)( =trc

The result proofs that the phase is not presented in the detection. Thus, the differential

multiple phase detection is robust to phase synchronization error.

4.8 Signal Representation in Time and Frequency Domain

Figure 4.13 shows the example of 8-bit data sequence {1 0 1 1 0 1 0 0} have been

transmitted using all DPSK, DQPSK, D8PSK and D16PSK techniques discussed in this

chapter. The signals are shown in time and frequency domain. The frequency

representation shows the data is placed at the carrier frequency of 1000Hz, and the time

domain representation observe the modulated signals that carry symbol of data for 100baud transmission rate.


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(a) (b)

(c) (d)

Figure 4.13 Signals representation in time and frequency domain. (a) DPSK

modulated signal (b) DQPSK modulated signal (c) D8PSK modulated signal (d)

D16PSK modulated signal


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CHAPTER V

RESULTS AND DISCUSSIONS

5.1 Introduction

The chapter will display the results of the BER and PER performance analysis

by using four modulation techniques in differential phase modulation. The results are

discussed on the theoretical and simulation value to compare the performance of DPSK,

DQPSK, D8PSK and D16PSK detection. Simulation is performed in the present of

additive white Gaussian noise based on Equation (3.1) in chapter III. A random phase

terms is included in the simulation that is based on a uniform distribution where the

phase range is 2/50 . This is to determine the effect of phase synchronization

error on the detection method.


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5.2 Analysis of BER Performance

The BER performance of DPSK, DQPSK, D8PSK and D16PSK detection has

been analyzed theoretically and by simulation. It is proved theoretically and also by

simulation that, as the number of phases increases, the SNR ratio also increases for a

fixed bit error rate.

Figure 5.1 Theoretical BER performance

The theoretical BER performance for DPSK, DQPSK, D8PSK and D16PSK

detection are shown in Figure 5.1. The result shows that the DPSK detection gives the

best performance amongst the other detection techniques. For a given BER of 10-4, the

performance of DQPSK detection downgrades by only 0.4 dB compared to DPSK


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detection. For d8PSK detection, the reduction of performance is 4 dB compared to

DQPSK detection and better than D16PSK detection by 3dB. The theoretical BER

performance for each of the modulation is summarized in Table 5.1.

Table 5.1: Theoretical BER Performancefor a fixed BER of 10-4

Type of detection BER SNR (dB)

DPSK 0.0001 12.2

DQPSK 0.0001 12.6

D8PSK 0.0001 16.8

D16PSK 0.0001 19.7

The result is also true by simulation. It shows that the DPSK detection gives the

best performance. The reduction in performance for DQPSK detection in terms of the

fixed BER of 10-4 is about 2dB. Beyond D8PSK detection, the performance

downgrades 6dB for every doubling of phases. Figure 5.2 shows the simulation result

of DPSK, DQPSK, D8PK and D16PSK detection. The value of SNR for BER

performance of 10-4

for every type of the simulation is shown in Table 5.2.


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Figure 5.2 Simulation result of BER performance

Table 5.2: BER performance of simulation result for a fixed BER of 10

-4


DPSK 0.0001 13.8

DQPSK 0.0001 16.3

D8PSK 0.0001 22.0

D16PSK 0.0001 27.7


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5.3 Analysis of PER Performance

The PER performance are analyzed theoretically and also by simulation. The

results of the performance are shown in Figure 5.3 - 5.4, respectively.

Figure 5.3 Theoretical PER performance

Figure 5.3 shows the theoretical PER performance of DPSK, DQPSK, D8PSKand D16PSK derived in previous chapter. The result shows that for a given PER of 10-2

the performance based on SNR is almost the same with the theoretical BER

performance discussed in Section 5.2. DPSK gives the lowest packet error rate,

followed by DQPSK, which the reduction in performance is only 0.4 dB. The

performance of D8PSK detection reduced 4 dB than DQPSK detection, and is better


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than D16PSK detection by 3dB. Table 5.3 illustrates the theoretical performance for a

fixed PER of 10-2. Note that, the SNR value is almost the same with BER performance

of 10-4 discussed in previous section.

Table 5.3: Theoretical PER Performancefor a fixed PER of 10-2


DPSK 0.01 12.2

DQPSK 0.01 12.6

D8PSK 0.01 16.7

D16PSK 0.01 19.6

Figure 5.4 shows the PER performance of the simulation result. In the

simulation, the packet size is 80 bits, which the data is transmitted using PACTOR

format as discussed in previous chapter. For a fixed PER of 10-2, DPSK gives the

lowest PER, followed by DQPSK, D8PSK and D16PSK. The reduction in performance

for DQPSK detection is 2dB. Beyond D8PSK detection, the performance downgrades

6dB for every doubling of phases. For the simulation of PER, it is also follow the resultof BER performance for a fixed BER of 10-4. Table 5.4 shows that it gives similar SNR

value with the simulation of BER performance.


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71

Figure 5.4 Simulation result of PER performance

Table 5.4: Simulation PER Performancefor a fixed PER of 10-2


DPSK 0.01 12.2

DQPSK 0.01 12.6

D8PSK 0.01 16.7

D16PSK 0.01 19.6

From the results, it is shown that for every doubling of phases, the BER

performance decreases, but the main important thing is the capability to increase the

performance of data transmission rate. It is also shown that even the random phase

delay is applied in the simulations, the error performance is not effected by this phase


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72

delay. This is because the differential encoding is used in the modulation, so the phase

synchronization is not critical such in coherent PSK detection.

From the comparison of the simulation and the theoretical results, it is clearly

shows that the BER and PER of the simulation is higher than the theoretical result. It is

also shows that, as the SNR increases, the performance of simulation degrade faster

than the theoretical performance. This is expected since the theoretical performance is

calculated in ideal case. By simulation, the performance of modulations are depending

on the design of filters and detection structures, carrier frequency and the number of

samples used in modulation, and also how big the random noise power will effect the

change in phases. All these factors are contributing bigger error in the detection. The

graph of BER and PER comparison performances for DPSK, DQPSK, D8PSK and

D16PSK detections are shown inAppendixA-B, respectively.


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CHAPTER VI

CONCLUSIONS

6.1 Conclusions

In this study, the differential multiple PSK modulation techniques are evaluated

to analyze the performance of the modulation in term of the BER and PER. Differential

multiple PSK modulation techniques proofs to be the suitable method because of it

capability of achieving higher data transmission rate, its robustness to phase

synchronization error and it also capable in providing lower error rate compared to

many other possible advance modulation techniques.

Modulation techniques based on DPSK is proofed in capability to provide lower

error rate than modulation based on FSK techniques [Martin, 1988]. In addition,

DQPSK modulation technique provides better performance than noncoherent FSK, and

the transmission rate is two times faster than the FSK technique [Shaameri-Jaswar,

2003] (Appendix C).


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In general, the BER and PER performance for differential multiple phase

detection decrease for every doubling of phases, but the main advantage is the

capability in achieving higher transmission rate, and implementation can be made

simpler compared to coherent PSK detection since the phase synchronization error is

not critical.

6.2 Suggestions

The suggestions of this study are as follow:

1. For future study, it is suggested to implement the error control mechanism in

differential multiple PSK detection to detect errors that occur in packets of data

transmission.

2. Since the performance analysis of this study was limited in presence of additive

white Gaussian noise and phase delay, it is suggested to analyze the

performance of differential multiple PSK in presence of multipath fading, such

as Rayleigh and Rician fading channel.

3. The complexity of differential multiple PSK is simple and reliable, so it is

suggested to implement the design of modulation technique on hardware for

transmission using HF.

4. To have more accurate performance results, it is suggested to explore other

advance modulation techniques in PSK, such as differential in Quadrature

Amplitude Modulation (QAM). QAM possesses the potential for providing


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better performance since the symbol is separated as widely as possible in the

signal space diagram [Roden, 1988].


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REFERENCES

[Abdullah-Husni et al, 2003] Abdullah, M.A.; Husni, E.M.; S. Hassan, S.I.,

Investigation of a Rural Telecommunication System using VSAT Technology

in Malaysia. 9th Asia Pacific Conference on Communications, 2003 (APCC),

Penang, 21-24 September 2003.

[Charles-Tri, 2003] Charles, W.V.; Tri, T.H., Performance Analysis of Direct

Sequence Differential Phase Shift Keying (DS-DPSK) with Self-Normalization

and L-Fold Diversity in a Fading Channel. California: Naval Postgraduate

School, 2003.

[Couch, 1997] Couch, L.W. II, Digital and Analog Communication Systems.

Prentice-Hall International, Inc. 5th edition, 1997.

[Goodman, 1992] Goodman, J.M., HF Communications Science and Technology,

Van Nostrand Reinhold, 1992.

[Haykin, 1988] Haykin, S., Digital Communications. John Wiley and Sons,

Inc., 1988

[Jaswar-Shaameri, 2003] Jaswar, F.D.; Shaameri, A.Z., FPGA Implementation of

CPFSK Modulation Techniques for HF Data Communication. Malaysia:

Faculty of Elect. Engr., Univ. Teknologi Malaysia, 2003.

[John-Mohamed et al, 2002] John, D.B.; Mohamed, K.N.; Mary, E.D., Data

Recovery in Differentially Encoded Quadrature Phase Shift Keying

(DEQPSK). Mnemonics, Inc., 2002.


94/100

77

[Kasser, 1991] Kasser, J.E., Applied digital communications via HF radio.

Fifth International Conference on HF Radio Systems and Techniques, 1991,pp.

44 47.

[Kolimbiris, 2000] Kolimbiris, H., Digital Communications Systems with Satellite

and Fiber Optics Applications. New Jersey: Prentice Hall, Inc., 2000.

[McNamara, 1991] McNamara, L.F., Ionosphere: Communications, Surveillence,

and Direction Finding. Krieger Publishing Company, Malabar, Florida, 1991.

[NATO] NATO Standardization Agreement: Profile For High Frequency (HF)

Radio Data Communicatios STANAG 5066.

[Nilsson-Giles, 1997] Nilsson, J.E.M.; Giles, T.C., Wideband multi-carrier

transmission for military HF communication, MILCOM 97 Proceedings ,Volume: 2,

pp.1046 1051, 1997.

[Proakis, 1995] Proakis, J .G., Digital Communications. Mc Graw-Hill, Inc., 3rd

Edition, 1995.

[Henry, 1992] Bill Henry, K9GWT. Getting Started in Digital Communications-Part

4-AMTOR. American Radio Relay, Inc. QST June 1992, pp. 34-35, 1992.

[Raos et al, 2003] Raos; Del Cacho, A.; Perez-Alvarez, I.; Zazo, S.; Mendieta-

Otero, E.; Santana-Sosa, H.; Paez-Borralo, J.M., Advanced OFDM-CDMA HF

Modem With Self-interference Cancellation. Spain: Universidad de Las Palmas

de Gran Canaria, 2003.

[Reynolds-Gillespie, 1997] Reynolds, P.D.; Gillespie, A.F.R., Interim Profile For

Maritime HF Data Communications. IEE 7th Int. Conf. on HF Radio Systems

and Techniques, 1997, pp. 265-270, 1997.


95/100

78

[Roden, 1988] Roden, M.S., Digital Communication Systems Design.

Prentice-Hall International Inc., 1988.

[Rodger, 2000] Rodger, E.Z.;

performance analysis of differential phase modulation. for hf communication

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