Least squares symbol detection for multi antenna fh mfsk systems in the presence of follower jamming

ii CONTENTS ACKNOWLEDGEMENTS i CONTENTS ii SUMMARY v LIST OF FIGURES vi LIST OF ABBREVIATIONS vii LIST OF SYMBOLS ix CHAPTER 1 INTRODUCTION 1 1.1 FREQUENCY SHIFT KEYING 1 1.2 FAD

LEAST SQUARES SYMBOL DETECTION FOR MULTI ANTENNA SLOW FHSS/MFSK SYSTEMS IN THE

PRESENCE OF FOLLOWER JAMMING

ALAGUNARAYANAN NARAYANAN

NATIONAL UNIVERSITY OF SINGAPORE

2011

LEAST SQUARES SYMBOL DETECTION FOR MULTI

ANTENNA SLOW FHSS/MFSK SYSTEMS IN THE

PRESENCE OF FOLLOWER JAMMING

ALAGUNARAYANAN NARAYANAN

(B.E., ANNA University)

A THESIS SUBMITTED

FOR THE DEGREE OF MASTER OF ENGINEERING

DEPARTMENT OF ELECTRICAL AND COMPUTER

ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE

2011

i

ACKNOWLEDGEMENTS

First of all, I am grateful to God for giving me the strength and wisdom to finish this

thesis

My sincere thanks goes to my supervisor Professor Ko Chi Chung for his excellent

guidance, encouragement and insightful comments throughout the period of my research

work

I also wish to express my thanks to the staff and students in the communication

laboratory for their assistance and friendship Finally, I also wish to express my sincere

gratitude to my parents and family, who have always given me unconditional love and

great support

ii

CONTENTS

ACKNOWLEDGEMENTS i

CONTENTS ii

SUMMARY v

LIST OF FIGURES vi

LIST OF ABBREVIATIONS vii

LIST OF SYMBOLS ix

CHAPTER 1 INTRODUCTION 1

1.1 FREQUENCY SHIFT KEYING 1

1.2 FADING 3

1.3 AWGN 6

1.4 JAMMING 6

1.5 INTRODUCTION TO SPREAD SPECTRUM COMMUNICATIONS 7

1.6 FREQUENCY HOPPED SPREAD SPECTRUM SYSTEMS 9

1.5.1 SLOW FHSS SYSTEMS 11

1.5.2 FAST FHSS SYSTEMS 11

1.7 PERFORMANCE OF FHSS SYSTEMS IN A JAMMING ENVIRONMENT 12

1.7 RESEARCH OBJECTIVE and CONTRIBUTIONS 13

1.8 STRUCTURE OF THE THESIS 14

iii

CHAPTER 2

FHSS/MFSK SYSTEMS IN THE PRESENCE OF JAMMING 15

2.3 SUMMARY 20

CHAPTER 3

3.1 LS BASED SYMBOL DETECTION SCHEME 21

3.2 THEORITICAL ANALYSIS OF THE PROPOSED SCHEME 23

iv

APPENDIX-I 43 LIST OF PUBLICATIONS 47

v

SUMMARY

The focus of this thesis is the performance of frequency hopped M-ary frequency

shift keying (MFSK) systems in the presence of follower partial band jamming (PBJN)

over flat fading channels Thermal and other wideband Gaussian noises have been

modeled as additive white Gaussian noise (AWGN) at the receiver

Follower partial band jamming is a strong threat to the symbol error rate (SER)

performance of FHSS systems In order to overcome the effects of follower PBJN and

carry out symbol detection in slow FHSS/MFSK systems over quasi-static flat fading

channels, a least squares (LS) based method is proposed in this thesis Specifically, using

the principle of Least squares, the complex gain factor between the two jamming

components is estimated This estimate is then used to remove the jamming signal during

the symbol detection process

The effect of AWGN on the channel estimation and symbol detection are theoretically

analyzed The symbol error rate performances of the proposed algorithm are compared

with that of traditional maximum likelihood (ML) algorithm and the scheme proposed in

[13] The proposed algorithm is found to outperform the other algorithms, when signal to

noise ratio (SNR) is greater than about 20dB

vi

LIST OF FIGURES

Fig 1.2 Block diagram of frequency hoped spread spectrum transmitter 9

Fig 1.3 Block diagram of frequency hopped spread spectrum receiver 10

Fig 4.1 Performance of various schemes against SNR for 0dB SJR, BFSK,

and four samples per symbol 30

Fig 4.2 Performance of various schemes against SNR for 0 dB SJR, 4-FSK

and four samples per symbol 31

Fig 4.3 Performance of various schemes against SNR for 0 dB SJR, 8-FSK

and eight samples per symbol 31

Fig 4.4 Performance of various schemes against SJR for 30dB SNR, 8-FSK

and twelve samples per symbol 32

Fig 4.5 Performance of the proposed LS based scheme with various number

of samples per symbol for 0 dB SJR and 8FSK 32

Fig 4.6 Performance of the proposed LS based scheme with various number

of samples per symbol at 0 dB SJR and 16 FSK 33

Fig 4.7 Plot of Mean percentage of absolute error between theoretical

and simulated values of x against SNR, with BFSK, -10 dB SJR and four samples per symbol 34

Fig 4.8 Performance of the theoretical and simulated SER of the proposed

scheme for BFSK,-10dB SJR and four samples per symbol 35

vii

LIST OF ABBREVIATIONS

AFSK Audio Frequency Shift Keying

ARMA Auto Regressive Moving Average

AWGN Additive White Gaussian Noise

BER Bit Error Rate

CDMA Code Division Multiple Access

DSSS Direct Sequence Spread Spectrum

FHSS Frequency Hopped Spread Spectrum

FSK Frequency Shift Keying

GMSK Gaussian Minimum Shift Keying

GSM Global System for Mobile communication

i.i.d independent and identically distributed

ISI Inter Symbol Interference

MAI Multiple Access Interference

MFSK M-ary Frequency Shift Keying

viii

OFDM Orthogonal Frequency Division Multiplexing

PBJN Partial Band Jamming Noise

SJR Signal to Jamming Power Ratio

SNR Signal to Noise Power Ratio

VSM Vector Similarity Metric

P theoretical bit error rate

T duration of one information bit

x

 

w n added white Gaussian noise

1

CHAPTER 1

INTRODUCTION

1.1 FREQUENCY SHIFT KEYING

Frequency shift keying (FSK) is a frequency modulation scheme in which digital

information is transmitted through changing the frequency of a carrier wave M-ary

frequency shift keying (MFSK) is a variation of FSK that uses more than two

frequencies MFSK is a form of M-ary orthogonal modulation, where each symbol

consists of one element from an alphabet of orthogonal waveforms M , the size of

the alphabet is usually a power of two, so that each symbol has log M bits An 2

example of Binary FSK is shown in fig 1.1

Minimum Shift keying (MSK) and audio frequency shift keying (AFSK) are two

other forms of FSK MSK is a particular form of coherent FSK, and it has better

spectrum usage when compared to FSK In MSK, the waveforms that are used to

represent the bits 0 and 1 will differ from each other by exactly half a carrier period

This is the smallest FSK modulation index that can be chosen such that the

waveforms for 0 and 1 are orthogonal Another form of MSK called Gaussian

minimum shift keying (GMSK), is used in the global system for mobile

communication (GSM) phone standard [30]

2

In Audio frequency-shift keying (AFSK) modulation technique, digital data is

represented by changes in the frequency (pitch) of an audio tone, yielding a signal

that has been encoded suitably for transmission via radio or telephone Normally, the

transmitted audio shuffles between two tones: "mark" and “space", representing

a binary one and a binary zero respectively In AFSK, modulation is done at baseband

frequencies This is the difference between regular frequency-shift keying methods

and AFSK

Even though Phase Shift Keying (PSK) modulation gives better performance than

FSK in an additive white Gaussian noise (AWGN) channel, it is difficult to maintain

phase coherence in the synthesis of the frequencies used in the hopping pattern

Therefore, FSK modulation with non coherent detection is used in frequency hopped

spread spectrum (FHSS) systems [2]

It is the deviation that a carrier modulated communication signal experiences when

it travels through certain propagation media In general, fading tends to vary with

time, geographical position and radio frequency, and it can be modelled as a random

process A channel that experiences fading is called as a fading channel The two

main reasons for fading in wireless systems are multipath propagation (referred to as

4

multipath fading) and shadowing from obstacles affecting the wave propagation

(referred to as shadow fading)

Multiple paths, in which a signal can traverse, are created by reflectors present in

the environment surrounding the transmitter and receiver Multipath propagation

results in the superposition of multiple copies of the transmitted signal at the receiver

While travelling from the source to the receiver, each copy of the signal will be

experiencing differences in terms of attenuation, delay and phase shift, which will

lead to constructive and destructive interferences at the receiver end This can cause

amplification or attenuation of the signal power at the receiver Strong destructive

interference (also known as deep fades) can cause temporary failure of

communication due to a severe drop in the channel signal to noise ratio The effects

of fading can be overcome by using transmit diversity where the signal travels over

different channels that experience independent fading and then coherently combining

them at the receiver Now, the probability of experiencing a fade in this channel is

proportional to the probability that all the component channels simultaneously

experience a fade

Different types of fading are discussed below

 Slow fading – It arises when the coherence time of the channel is large when

compared to the delay constraint of the channel In this type of fading, the

amplitude and phase variations imposed by the channel can be considered as

constant with respect to the symbol period Slow fading can be caused when

there is a large obstruction such as a hill or large building, obscuring the main

5

signal path between the transmitter and the receiver Log normal

distribution is often used to model the amplitude change that is caused by

shadowing [30]

 Fast Fading – This occurs when the coherence time of the channel is small

compared to the delay constraint of the channel In this type of fading, the

amplitude and phase variations imposed by the channel vary considerably

with respect to the symbol period In a fast-fading channel, the transmitter

may use time diversity to take advantage of the variations in the channel

conditions, and thereby increase the robustness of the communication to a

temporary deep fade A deep fade may temporarily erase some of the

information that was transmitted By using an error-correcting code coupled

with successfully transmitted bits during other time instances (interleaving),

the erased bits can be recovered [30]

 Flat fading – In this type of fading, the coherence bandwidth of the channel is

larger than the bandwidth of the signal With flat fading all frequency

components will be affected in the same way

 Frequency selective fading – When the coherence bandwidth of the channel

is smaller than the bandwidth of the signal, frequency selective fading occurs

It is highly improbable that all parts of the signal will be simultaneously

affected by a deep fade because different frequency components of the signal

will be affected independently Frequency selective fading channels are

dispersive resulting delay spreads in the received signal As a result, the

transmitted symbols that are adjacent in time interfere with each other In such

6

channels equalizers can be used to compensate for the effects of the inter

symbol interference (ISI) Modulation schemes such as orthogonal frequency

division multiplexing (OFDM) and code division multiple access

(CDMA) use frequency diversity to provide robustness to frequency selective

fading In OFDM, the wideband signal is divided into many narrowband

modulated subcarriers with each of them being exposed to flat fading rather

than frequency selective fading [32] CDMA uses the Rake receiver to deal

with each echo separately [30]

1.3 AWGN

In additive white Gaussian noise model, the only impairment to proper

communication is the linear addition of wideband noise with a constant spectral

density and a Gaussian distribution of amplitude It produces simple and tractable

mathematical models which are useful for gaining insight into the underlying

behavior of the system Thermal vibrations of atoms in conductors, shot noise, black

body radiation from the earth and other warm objects are the main sources for

wideband Gaussian noise Background noise of the channel under study is normally

represented using AWGN

7

1.4 JAMMING

Jamming refers to the deliberate transmission of signals that disrupt

communications, by decreasing the signal to noise ratio at the receiver Generally, the

jammer sends out a signal at the same frequency as the transmitter and causes

interference to the received signal The purpose of jamming is to block out the

reception of transmitted signals Jamming models considered in frequency hopped

spread spectrum (FHSS) systems include partial band multi tone jamming and partial

band Gaussian noise jamming [31] A follower jammer has the capability to

determine which portion of the spread spectrum bandwidth is being used during some

time interval , and transmits its jamming signal in that portion of the spectrum

1.5 INTRODUCTION TO SPREAD SPECTRUM

COMMUNICATIONS

In this technique, a communication signal is transmitted in a bandwidth which is

significantly larger than the original frequency content of the signal The main feature

of this technique is that it decreases the probability of interference to other receivers

while maintaining the privacy Spread Spectrum generally uses a sequential noise like

signal structure to spread the narrowband information signal over a relatively

wideband of frequencies At the receiver, the received signal is given to a correlator

to retrieve the original information signal

8

Major features of spread spectrum communication are

 Resistance to jamming (interference) - The transmitted signal will have an

element of pseudo-randomness (unpredictability) associated with it This

randomness will be known only to the intended receiver and not to the jammer

As a result, the jammer will transmit an interfering signal without the

knowledge of the pseudo random pattern This reduces the vulnerability of the

transmitted signal to jamming

 Resistance to fading- Since spread spectrum signals occupy high bandwidth it

is unlikely that the signal will encounter multipath fading over its whole

bandwidth

 Multiple access capability- Multiple users can transmit simultaneously on the

same frequency (range) as long as they use different spreading codes.

The different types of spread spectrum communications are

1 Direct Sequence (DS) – A sine wave is pseudo randomly phase modulated

with a string of pseudo noise code symbols called chips The duration of the

chip is shorter than that of the information bit

2 Frequency hopping (FH) - The carrier frequency is pseudo randomly

changed over a wide range of frequency for transmitting radio signals A

detailed description of frequency hopping system is given in the next section

3 Time hopping – In this technique, the carrier is turned on and off by a pseudo

random sequence

9

4 Chirp Spread – Here, wideband frequency modulated chirp pulses are used

to encode information A chirp is a sinusoidal signal whose frequency

increases or decreased over a certain amount of time

1.6 FREQUENCY HOPPED SPREAD SPECTRUM

SYSTEMS

In this system, each carrier frequency is chosen from a set of 2h(where his a positive integer) frequencies that are placed over the width of the available data

modulation spectrum The pseudo-random code is used to control the sequence of

carrier frequencies A block diagram of a frequency hopped spread spectrum system

transmitter and receiver are given in fig 1.2 and 1.3

Figure 1.2 Block diagram of frequency hopped spread spectrum transmitter

10

Figure 1.3 Block diagram of frequency hopped spread spectrum receiver

Normally binary or M-ary FSK mosulation schemes are used in FHSS Based on

the symbol transmitted , any one of the M frequencies will be used The output signal

from the modulator will be translated in frequency by an amount that is determined

by the pseudo noise (PN) sequence, which in turn , is used to selsct a frequency that

is synthesized by the frequency synthesizer The frequency translated signal is mixed

with the output from the FSK modulator and transmitted If the PN generator output

has m bits then 2m  1 frequency translations are possible

In the receiver , an identical PN generator, that is synchronised with the received

signal, is used to control the output of the frequency synthesizer [19] By mixing the

synthesizer output with the received signal, the frequency translation introduced at the

transmitter can be removed The resultant signal is demodulated by means of an FSK

11

demodulator A signal for maintaining synchronism of the PN generator with the

frequency translated received signal is usually extracted from the received signal

FHSS systems are mainly used in miltary communication [3], wireless personal

communications [20] and satellite communications [21-23] Two different types of

frequency hopped spread spectrum systems are discussed below

1.6.1 SLOW FHSS SYSTEMS

When MFSK data modulation is used with FHSS systems, the data modulator

output is one of the 2h tones, each lasting hT seconds, where Tis the duration of the information bit Each of these tones will be orthogonal with respect to the other tones

Hence, the frequency spacing between two tones should be at least 1

hT Assume that,

in each T (chip duration) seconds the modulated data output is transmitted in a new c

frequency by the frequency hop modulator WhenT c hT , the FHSS system is called

a slow frequency hopping system

1.6.2 FAST FHSS SYSTEMS

In fast FHSS systems, the hopping frequency band changes many times per

symbol That is T c hT A major advantage of fast FHSS systems is that frequency

12

diversity gain can be achieved in each transmitted symbol, which is particularly

beneficial in a partial jamming environment

1.7 PERFORMANCE OF FHSS SYSTEMS IN A

JAMMING ENVIRONMENT

FHSS systems are known to be robust against interference However, their

performance will be severely affected by multi tone jamming (MTJ) and partial band

jamming Among the two, MTJ can cause more damage to the FHSS signal In partial

band jamming, the frequency that is currently assigned to the receiver is measured by

the jammer and then a jamming signal is transmitted in the frequency slot used The

jamming signal will be sent as soon as possible, once the current frequency slot is

determined [4]

Fast frequency hopping may be seen as a viable solution to overcome the

detrimental effects of partial band jamming, because of the fact that hopping

frequency changes at a very high rate, making it difficult for the jammer to find out

the current frequency slot used But when fast frequency hopping is used the

synchronization requirements will become more stringent as hopping rate is increased

and it may be impossible to decrease the dwell interval of the hop Due to such

practical limitations fast hopping is difficult to be implemented in some applications

and scenarios The effect of the jammer causes the interference component in the

received signal to be very high So, symbol detection at the receiver end gets complex

Many anti-jamming algorithms have been proposed for slow FHSS system to

reduce the effect of jamming But the focus of most of these algorithms is the

13

elimination of partial band jamming [5-11], with the problem of follower jamming

addressed to a smaller extent in [12-13] and [24] In [12], an antenna array using the

sample matrix inversion algorithm is exploited to separate the desired signal and the

jamming signal But, in this case the antennas have been assumed to be having equal

gains These assumptions will not hold good in a quasi static flat fading channel

The technique proposed in [24] performs better in a jamming dominant scenario

But in this technique, the received jamming signals are treated as deterministic

quantities to be estimated So this algorithm will produce less accurate jamming

estimates at lower jamming power regions This causes deterioration in the

performance of the algorithm

Even though vector similarity based symbol detection scheme proposed in [1]

gives good symbol detection performance in the presence of follower jamming in a

quasi static flat fading channel, it assumes that the receiver has complete knowledge

about the channel parameters This places a restraint on the system

1.8 RESEARCH OBJECTIVE and CONTRIBUTION

Least squares (LS) method is a standard way of estimating the unknown

parameters from the received data set In this thesis, we investigate how a least

squares based approach can be formulated for carrying out symbol detection in the

presence of jamming and AWGN in FHSS communication systems Specifically, the

proposed approach uses a two element array to reject single follower jamming signal

interference and carry out symbol detection in slow FHSS/MFSK systems over quasi

static flat fading channels Using the principle of Least squares, the complex gain

14

factor between the two jamming components is estimated This estimate is used to

remove the jamming signal during the symbol detection process

The effect of AWGN on the channel estimation and symbol detection are

theoretically analyzed The SER performances of the proposed algorithm are

compared with that of traditional maximum likelihood (ML) algorithm and the

scheme proposed in [13] The proposed algorithm has been found to outperform the

other algorithms, when signal to noise ratio (SNR) is greater than about 20dB

1.9 STRUCTURE OF THE THESIS

In CHAPTER 2, the transmitted signal model and the received signal model are

discussed

The proposed LS based algorithm and the associated theoretical calculations are

given in CHAPTER 3

Performance of the proposed scheme is discussed in CHAPTER 4

CHAPTER 5 concludes this thesis and suggests some future work

In this thesis an MFSK modulated slow FHSS system is considered In order to

reduce the harmful effects of follower partial band jamming in a flat fading

environment, a simple two-element receiver array, where the signal from each

element is down converted and sampled at N times the symbol rate is used Using the samples collected from the two elements the relative gain between the jamming

components in the two elements can be determined, and this in turn can be used to for

symbol detection In CHAPTER 3, the process of symbol detection will be discussed

in detail

2.1.1 TRANSMITTED SIGNAL MODEL

Without loss of generality symbols are taken to be transmitted in hops each

consisting of ksymbols The first symbol in each hop is a pilot symbol, while the remaining ones are data symbols Consider the detection of the symbol in a hop over

where f is the hopping frequency,u0,1, ,M1 represents the pilot symbol that

is known at the receiver and f denotes the frequency spacing between two MFSK d

tones Similarly the complex envelope of the transmitted data signal is

s t  j  f df t, (2) where d0,1, M1 represents the data symbol

2.1.2 PARTIAL BAND JAMMING MODEL

As shown in [14], the follower jammer first measures the hopping frequency

and the spectrum of the desired hop and then directs the available transmitting power

to the currently used frequency slot With just the knowledge of the hopping

frequency of the desired signal ,this jammer will transmit a noise like signal which

will cover the entire band of the desired signal The complex envelope of the

follower partial band jamming signal is therefore

where n t is the baseband equivalent band-limited signal which can be modeled as j 

a zero mean band-limited Gaussian random process In equation (3) n t is j 

17

multiplied by an exponential term, so as to up convert the baseband signal to the

frequency slot occupied by the desired signal

2.1.3 RECEIVED SIGNAL MODEL

It is assumed that the desired signal and the follower jamming signal

experience a quasi-static flat fading channel The received pilot signal at the l th

antenna element is therefore given by

where l1, 2, w t represents the complex additive white gaussian noise (AWGN) l 

in the receiver, and the complex coefficients  l, l account for the overall effects of phase shifts , fading and antenna response on the desired signal and the jamming

signal at the l thantenna element respectively As discussed in [15] and [16], the fading

gains can be taken to be non-selective and remain unchanged within hop duration in

slow FH systems As mentioned earlier, the first symbol in each hop is a pilot symbol,

while the remaining ones are data symbols Following (4), the received data signal at

the l thantenna element is given by

At the l th antenna element the received signal is sampled at N times the symbol

Using (1), (3) and (4), the nthsample of the received pilot signal is