ENHANCEMENT OF WI-FI COMMUNICATION SYSTEMS THROUGH

SYMBOL SHAPING AND INTERFERENCE MITIGATION

BY

TANIM MOHAMMED TAHER

Submitted in partial fulfillment of the requirements for the degree of

Master of Science in Electrical Engineering in the Graduate College of the Illinois Institute of Technology

Approved Advisor

Chicago, Illinois December 2007

iii

ACKNOWLEDGMENT

I am grateful to my advisors Dr. Joseph L. LoCicero, Professor at the Electrical

and Computer Engineering (ECE) department at the Illinois Institute of Technology (IIT),

and Dr. Donald R. Ucci, Associate Professor at the ECE department at IIT, who have

guided me through all the research work. They encouraged me to push the limits of my

abilities and were always there to answer my questions when I met with any obstacles

during my research.

I would like to give a special thanks to my colleague Dr. Ayham Z. Albanna who

served as my mentor. He also was involved in this research project with regards to the

development of a Microwave Oven signal model. I would also like to thank Matthew J.

Misurac, who served as my assistant in the Microwave Oven interference mitigation

project, and the Barker symbol shaping project and who always asked the right tough

questions that helped in our research path. I also thank my colleagues Roger Bacchus,

Ghaith Assaf and John T MacDonald.

My parents, Dr. Mohammed Abu Taher and Dr. Rowshan Ara Begum deserve the

greatest appreciation for guiding me all these years, for all the love, care and support they

provided me, and for encouraging me to always strive higher. I also thank my loving

sister, Dr. Tania Taher. Finally, I thank God Almighty for all his blessings and for

making any of this possible.

iv

TABLE OF CONTENTS

Page

ACKNOWLEDGEMENT . . . . . . . . . . . . . . . . . . . . . . . . . iii

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . vii

LIST OF NOMENCLATURE. . . . . . . . . . . . . . . . . . . . . . xii

LIST OF SYMBOLS. . . . . . . . . . . . . . . . . . . . . . . . . xiv

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. xvii

CHAPTER

1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1. IEEE 802.11 Communication Systems . . . . . . . . . . . . . . 1 1.2. Spectral Mask and IEEE 802.11 Channels. . . . . . . . . . . . . 2 1.3. Wireless Interference . . . . . . . . . . . . . . . . . . . . . . . 4 1.4. Inter-Symbol Interference . . . . . . . . . . . . . . . . . . . . 6 1.5. Barker Code and IEEE 802.11 1 Mbps Signal . . . . . . . . . . . . 8 1.6. IEEE 802.11 CCK 5.5 Mbps Signal . . . . . . . . . . . . . . . . 11 1.7. ComBlock Devices . . . . . . . . . . . . . . . . . . . . . . . . 13 1.8. Research Methodology . . . . . . . . . . . . . . . . . . . . . . . . 16

2. PULSE SHAPING FOR IEEE 1 MBPS BARKER SPREAD SIGNAL. . 18 2.1. Pulse Shaping Methodology . . . . . . . . . . . . . . . . . . . . 18 2.2. Sinusoidal Pulse Shaping . . . . . . . . . . . . . . . . . . . . . . 21 2.3. Logarithmic Pulse Shaping . . . . . . . . . . . . . . . . . . . . . . . . 26 2.4. Sincm Pulse Shaping. . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.5. BER Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.6. Comparison of Barker Symbol Shaped Systems . . . . . . . . . . . . 34

3. BUFFERED PULSE SHAPED BARKER SPREAD SYSTEMS . . . 36 3.1. Rational for using Buffer . . . . . . . . . . . . . . . . . . . . 36 3.2. Buffering 2 Bits. . . . . . . . . . . . . . . . . . . . . . . 37 3.3. Buffering of 3 Bits. . . . . . . . . . . . . . . . . . . . . . . . . 48

4. PULSE SHAPING FOR IEEE 5.5 MBPS CCK SIGNAL . . . . . . 54 4.1. CCK Pulse Shaping Methodology. . . . . . . . . . . . . . . . . . . . . 54 4.2. Sinusoidal Pulse Shaping . . . . . . . . . . . . . . . . . . . . . . 58 4.3. Sincm Pulse Shaping . . . . . . . . . . . . . . . . . . . . . . . . . . .59 4.4. BER Measurements. . . . . . . . . . . . . . . . . . . . . . . 61

v

CHAPTER Page

5. EXPERIMENTAL STUDY OF MICROWAVE OVEN SIGNAL . . . 65 5.1. Main Features of MWO Signal . . . . . . . . . . . . . . . . . 65 5.2. FM Signal . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5.3. Amplitude Variation . . . . . . . . . . . . . . . . . . . . . . . . 68 5.4. Transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.5. MWO PSD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

6. MODEL OF MICROWAVE OVEN SIGNAL . . . . . . . . . . . . 75 6.1. Necessity of MWO Model . . . . . . . . . . . . . . . . . . . . 75 6.2. Model #1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 6.3. Model #1 Simulation. . . . . . . . . . . . . . . . . . . . . . . . 78 6.4. Drawbacks of Model #1 . . . . . . . . . . . . . . . . . . . . 80 6.5. Model #2 . . . . . . . . . . . . . . . . . . . . . . . . . . 82 6.6. Model #2 Simulation . . . . . . . . . . . . . . . . . . . . . 85 6.7. Model #2 Experimental Emulation . . . . . . . . . . . . . . . . 86

7. MICROWAVE OVEN SIGNAL INTERFERENCE MITIGATION FOR IEEE 802.11 SYSTEMS. . . . . . . . . . . . . . . . . . . . . . . . 89 7.1. Interference Mitigation Technique . . . . . . . . . . . . . . . . . 89 7.2. Circuit Design and Description . . . . . . . . . . . . . . . . . 91 7.3. Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 95 7.4. BER Studies . . . . . . . . . . . . . . . . . . . . . . . . . 97

8. CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . 100 8.1. Pulse Shaping for 1 Mbps Signal . . . . . . . . . . . . . . . 100 8.2. Pulse Shaping for 5.5 Mbps Signal . . . . . . . . . . . . . . 101 8.3. MWO Signal Study . . . . . . . . . . . . . . . . . . . . . . . . 101 8.4. MWO Signal Modeling . . . . . . . . . . . . . . . . . . . . . 102 8.5. MWO Interference Mitigation . . . . . . . . . . . . . . . . . . 103 8.6. Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

INTERFERENCE SPECTROGRAMS. . . . . . . . . . . . . . . . . . 105

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

vi

LIST OF TABLES

Table Page

1.1 Differential QPSK encoding table used in CCK transmission . . . . . . . 11

1.2 5.5 Mbps CCK encoding table . . . . . . . . . . . . . . . . . . . . . 12

2.1 Simulated BER for Barker (no buffer) . . . . . . . . . . . . . . . . . 33

2.2 Experimental BER for Barker (no buffer) . . . . . . . . . . . . . . . . 33

2.3 Comparison of PSD sideband attenuations . . . . . . . . . . . . . . . . 34

2.4 Comparison of total power in each band . . . . . . . . . . . . . . . . 34

2.5 ISI after filtering operation . . . . . . . . . . . . . . . . . . . . . . 35

3.1. Simulated BER measurements for 2 bits buffered Barker spread system . . 48

3.2. Symbol mapping table for 3 bits buffered Barker spread system . . . . . . 51

3.3. Comparison of PSD sideband attenuations (3 bits buffered) . . . . . . . . 52

3.4. Simulated BER measurements for 3 bits buffered Barker spread system . . 53

4.1. Four possible vectors C . . . . . . . . . . .. . . . . . . . . . . . . . . . . . 55

4.2. Comparison of PSD sideband attenuations (unfiltered 5.5 Mbps data) . . 63

4.3. Comparison of total power in each band . . . . . . . . . . . . 63

4.4 ISI after filtering operation for CCK symbol Shaping . . . . . . . 64

7.1. BER for Case 1 (Wi-Fi at 2.46 GHz without interference mitigation) . . 98

7.2. BER for Case 2 (Wi-Fi at 2.46 GHz with interference mitigation) . . . 98

7.3. BER for Case 3 (Wi-Fi at 2.448 GHz without interference mitigation) . . 98

7.4. BER for Case 4 (Wi-Fi at 2.448 GHz with interference mitigation) . . 98

vii

LIST OF FIGURES

Figure Page

1.1 FCC Spectral Mask . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 IEEE 802.11 channels . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Symbol sequence without ISI . . . . . . . . . . . . . . . . . . . . . . 7

1.4 ISI distortion of a symbol sequence . . . . . . . . . . . . . . . . . . 7

1.5 Auto-correlation plot of 11-chip Barker sequence . . . . . . . . . . . 9

1.6 PSD of Barker spread 1 Mbps signal . . . . . . . . . . . . . . . . 10

1.7 PSD of 5.5 Mbps CCK signal . . . . . . . . . . . . . . . . . . . 13

1.8 ComBlock transmitter system . . . . . . . . . . . . . . . . . . . 14

1.9 ComBlock receiver system . . . . . . . . . . . . . . . . . . . . . 15

1.10 Block Diagram of ComBlock transmitter system . . . . . . . . . 15

1.11 Block Diagram of ComBlock receiver system . . . . . . . . . 15

2.1 Sinusoidally shaped pulse plot . . . . . . . . . . . . . . . . . . . . 21

2.2 Experimental Sinusoidally shaped pulse plot . . . . . . . . . . . . . . 22

2.3 Analytic PSD of sinusoidal pulse shape . . . . . . . . . . . . . . . 24

2.4 Simulated PSD of sinusoidal pulse shape . . . . . . . . . . . . . . . 25

2.5 Experimentally obtained PSD of sinusoidal pulse shape . . . . . . . . . 25

2.6 Auto-correlation plot of sinusoidal pulse shape . . . . . . . . . . 26

2.7 Logarithmically shaped pulse plot . . . . . . . . . . . . . . . . . . . . 27

2.8 Simulated PSD of logarithmic pulse shape . . . . . . . . . . . . . . . 27

2.9 Experimentally obtained PSD of logarithmic pulse shape . . . . . . . . . 28

2.10 Auto-correlation plot of logarithmic pulse shape . . . . . . . . . . 28

viii

Figure Page

2.11 Sinc shaped Barker pulse plot . . . . . . . . . . . . . . . . . . . . 29

2.12 Auto-correlation plot of sinc pulse shape . . . . . . . . . . . . 30

2.13 Simulated PSD of sinc Barker pulse shape . . . . . . . . . . . . . 30

2.14 Experimentally obtained PSD of sinc pulse shape . . . . . . . . . 31

2.15 MATLAB simulation methodology for each pulse shape . . . . . . . 32

2.16 Experimental methodology used for each pulse shape . . . . . . . 32

2.17 BER vs SNR study for pulse shaped Barker spread systems . . . . 33

3.1 State transition diagram for 2 bits buffered line code . . . . . . . . . 38

3.2 Block Diagram of 2 bit buffered Barker spread system . . . . . . . 39

3.3 State symbols for sinusoidal pulse shaping . . . . . . . . . . . . . 41

3.4 State symbols for sincm pulse shaping . . . . . . . . . . . . . . . 42

3.5 State symbols for logarithmic pulse shaping . . . . . . . . . . . . . 42

3.6 Simulated PSD of sinusoidal pulse shaping (2 bits buffered) . . . . . . 44

3.7 Simulated PSD of sincm pulse shaping (2 bits buffered) . . . . . . . . 44

3.8 Simulated PSD of logarithmic pulse shaping (2 bits buffered) . . . . . . 45

3.9 Experimental PSD of sinusoidal pulse shaping (2 bits buffered) . . . . . 45

3.10 Experimental PSD of logarithmic pulse shaping (2 bits buffered) . . . 46

3.11 Experimental PSD of rectangular pulse shaping (2 bits buffered) . . . . 46

3.12 Simulated PSD of rectangular pulse shaping (2 bits buffered) . . . . . 47

3.13 Cross-correlation plots for 4 states (3 bits buffered) . . . . . . . . . . 49

3.14 Symbols for the 8 states 3 bits buffered system . . . . . . . . . . . . 49

3.15 State transition diagram for 3 bits buffered system . . . . . . . . . . . . 51

ix

Figure Page

3.16 Simulated PSD of 3 bits buffered pulse shaped system . . . . . . . . 52

3.17 Experimental PSD of 3 bits buffered pulse shaped system . . . . . . 53

4.1 PSD of 5.5 Mbps CCK spread signal without symbol shaping . . . . . 57

4.2 Unmodified rectangular CCK . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.3 CCK symbols shaped by sinusoidal pulse shaping . . . . . . . . . . . . . 58

4.4 Simulated PSD of sinusoidally shaped 5.5 Mbps CCK spread signal . . . . 59

4.5 Experimental PSD of sinusoidally shaped 5.5 Mbps CCK spread signal . . 59

4.6 CCK symbols shaped by sincm pulse shaping . . . . . . . . . . . . . 60

4.7 Simulated PSD of sincm shaped 5.5 Mbps CCK spread signal . . . . . . 61

4.8 Experimental PSD of sincm shaped 5.5 Mbps CCK spread signal . . . . . 61

4.9 Simulated BER vs SNR measurements for CCK symbol shaping . . . 62

4.10 Composite Experimental PSD plots for CCK symbol shaping . . . . . . 64

5.1 Spectrogram showing key features of MWO signal . . . . . . . . . . . 67

5.2 Clean spectrogram of MWO signal . . . . . . . . . . . . . . . . . . 68

5.3 Time domain envelope of MWO signal . . . . . . . . . . . . . . . . . 69

5.4 Transient locations of MWO signal shown in ZSM . . . . . . . . . . . 70

5.5 Experimental spectrogram of MWO showing transients . . . . . . . . . . . . 71

5.6 MWO signal generation process . . . . . . . . . . . . . . . . . . . 72

5.7 PSD of experimental MWO #1 signal . . . . . . . . . . . . . . . . . . . 73

5.8 PSD of experimental MWO #2 signal . . . . . . . . . . . . . . . . . . . 73

5.9 PSD of experimental MWO #3 signal . . . . . . . . . . . . . . . . . . . 74

5.10 PSD of experimental MWO #4 signal . . . . . . . . . . . . . . . . . . . 74

x

Figure Page

6.1 Qualitative representation of MWO signal . . . . . . . . . . . . . . . . . . . 76

6.2 Simulated PSD of MWO based on model #1 (1 MHz range) . . . . . . . . . . 78

6.3 Simulated spectrogram of MWO based on model #1 (1 MHz range) . . . . 79

6.4 Simulated PSD of MWO based on model #1 (100 kHz range) . . . . . . . . . 79

6.5 Simulated spectrogram of MWO based on model #1 (100 kHz range) . . 80

6.6 Experimental spectrogram of an older MWO . . . . . . . . . . . . . . . . . . . 81

6.7 Remodeling the transients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

6.8 Qualitative representation of MWO signal model #2 . . . . . . . . . . . . . . . 83

6.9 Spectrogram of simulated MWO signal (model #2) . . . . . . . . . . . 86

6.10 Simulated PSD of MWO signal (model #2) . . . . . . . . . . . . . . . 86

6.11 Spectrogram of emulated MWO #2 signal . . . . . . . . . . . . . . . . . 87

6.12 PSD of emulated MWO signal measured by spectrum analyzer . . . . . . . 88

6.13 Experimental PSD of actual MWO . . . . . . . . . . . . . . . . . . . . . 88

7.1. Data transmission using 802.11 channel 1 . . . . . . . . . . . . . . . . . . . 91

7.2. Spectrogram of MWO signal & interference mitigation . . . . . . . . . . . . . 91

7.3 Block diagram for MWO interference mitigation system . . . . . . . . . 92

7.4. Photograph of Interference mitigation circuit . . . . . . . . . . . . . . . . 93

7.5. Cognitive Radio Citcuit diagram made in PSpice. . . . . . . . . . . . . 94

7.6 Case 1: No interference mitigation BER study (Wi-Fi at 2.46 GHz) . . 96

7.7 Case 2: Interference Mitigation (Wi-Fi at 2.46 GHz). . . . . . . . . . . . 96

7.8. Case 3: No interference mitigation BER study (Wi-Fi at 2.448 GHz) . 97

7.9. Case 4: Interference mitigation BER study (Wi-Fi at 2.448 GHz) . 97

xi

Figure Page

A.1 Spectrogram 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

A.2 Spectrogram 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

A.3 Spectrogram 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

xii

LIST OF NOMENCLATURE

Abbreviation Term

AC Alternating Current

ADC Analog to Digital Converter

AM Amplitude Modulation

AP Access Point

AWGN Additive White Gaussian Noise

BER Bit Error Rate

BPSK Binary Phase Shift Keying

CA Collision Avoidance

CCK Complementary Code Keying

CSMA Carrier Sense Multiple Access

DAC Digital to Analog Converter

FCC Federal Communications Commission

FM Frequency Modulation

IEEE Institute of Electrical and Electronics Engineers

I In phase

iid independent and identically distributed

IIR Infinite Impulse Response

IIT Illinois Institute of Technology

ISI Inter-Symbol Interference

ISM Industrial, Scientific and Medical

Mbps Mega Bits Per Second

xiii

mse mean squared error

Msps Mega Symbols Per Second

MWO Microwave Oven

OFDM Orthogonal Frequency Division Multiplexing

PBCC Packet Binary Convolutional Coding

PSD Power Spectral Density

Q Quadrature phase

QPSK Quadrature Phase Shift Keying

RF Radio frequency

SIR Signal-to-Interference Ratio

SNR Signal to Noise Ratio

Wi-Fi Wireless-Fidelity

WIL Wireless Interference Laboratory

WiNCom Wireless Networking and Interference Research Center

ZSM Zero Span Measurements

xiv

LIST OF SYMBOLS

Symbol Definition

B vector containing Barker sequence

Bm modified Barker sequence for 3 bits buffered system

π constant pi

j the complex number 1−

ƒ frequency variable in Hz

ω frequency variable in radians

ƒc signal carrier frequency

T time period of periodic signal

Tc time period of 1 chip

T(subscript) time duration constants

t time variable

n discrete time interval where time t=nT

nc number of chips

x(n) binary input data at time interval nT

σx2 variance of data x(n)

θ arbitrary phase angle

k, i, m, s arbitrary indices for numbering, summation or power

k0 to ki constants

t0 to ti time constants with indices 0 to i

d0 to di data bits

c0 to ci chip sequence

xv

αn differential phase for the n’th data symbol

)(tw∠ phase at time t

vb(t) modulated analog transmission signal using Barker spread

y(t) analog baseband signal

Sy(f) PSD of y(t)

p(t) general pulse train

P(f) PSD of p(t)

s0 to si indices for numbering pulse waveforms psi(t)

psi(t) pulse train with an index si

Psi(f) PSD of psi(t)

ps(t) sinusoidally shaped Barker waveform

pL(t) Logarthmically shaped Barker waveform

pc(t) Barker waveform shaped by sinc function

b, b(subscript) constants determining time response and bandwidth of sinc pulse

b(t) reversed continuous time Barker pulse

a(t) continuous time Barker pulse

s(n) positivie/negative sign of pulses for n’th bit

vc(t) analog transmitted signal using CCK (at modulated frequency)

aI In phase part of CCK signal

aQ Quadrature part of CCK signal

x(n, k) I phase component of k’th chip for the n’th bit

y(n, k) Q phase component of k’th chip for the n’th bit

x I phase CCK vectors

xvi

y Q phase CCK vectors

c All possible CCK vectors

C CCK vectors where C=|c|

v(t) analog signal model for MWO signal at modulated frequency

x(t) Amplitude function of MWO signal

s(t) Frequency sweeping FM signal for MWO model

c(t) ON cycle waveform for one period of MWO signal model

fac AC line Frequency

f1, f(subscript) Carrier frequencies

β FM modulation index for MWO signal

A, A(subscript) Amplitude constants

t(subscript) time delays for shifting pulses

E( fn) MWO signal’s transient power at frequency fn

EO amplitude scale factor for MWO transient power

N total number of sinc pulses in MWO model

λn random variable for shifting sinc pulses in MWO model

Fc random variable for MWO’s carrier frequency offset

yT(t) threshold detector output for interference mitigation

xvii

ABSTRACT

This dissertation presents two methods to improve the performance of existing

Wireless Fidelity (Wi-Fi) networks. One method is symbol shaping, while the other is

interference mitigation via the use of cognitive radio.

The Federal Communications Commission mandates a spectral mask that governs

the spectral signatures and bandwidth of all IEEE 802.11 communication systems. Filters

are necessary to achieve this spectral mask but they introduce Inter-Symbol Interference

(ISI) that degrades the performance of the communications system. Symbol shaping is a

technique that shapes the transmitted digital information symbol to lower the sideband

amplitudes in the Power Spectral Density of the system. This method was applied to the

IEEE 802.11 Barker spread 1 Mbps signal, and the Complementary Code Keying

5.5 Mbps signals. The goal was to approximately achieve the spectral mask requirements

so that a low order filter would satisfy the spectral mask requirement, thereby, lowering

ISI and improving the wireless communication system. The resulting system was

extensively studied experimentally and via simulation.

The Microwave Oven (MWO) is a common appliance that interferes with

IEEE 802.11 Wi-Fi communication systems as it radiates in the same 2.4 GHz Industrial,

Scientific, Medical band. The nature of the MWO radiated signal is studied in detail and

an analytical model is developed that captures the key aspects of the radiation. This

knowledge is used to develop an interference mitigation technique using cognitive radio

that successfully mitigates MWO interference on Wi-Fi communications. This is

implemented and studied experimentally. This cognitive radio system is used to improve

Wi-Fi communications as it allows the mitigation of MWO interference.

1

CHAPTER 1

INTRODUCTION

1.1 IEEE 802.11 Communication Systems

Wireless digital data communications have become very popular and widespread

over the last decade. This is in step with the growth of the Internet as well as the price

reduction and widespread availability of portable devices like laptop computers and

wireless routers. Initially, there were several competing technologies employed in

wireless computer networks [TAN96] until the Institute of Electrical and Electronics

Engineers (IEEE) undertook to develop standards. The IEEE 802.11 protocols [IEE97]

were formulated to standardize wireless computer networks. These protocols played a

significant role in making wireless computer networks ubiquitous, as now a variety of

devices based on different platforms could communicate wirelessly as long as they

adhered to the IEEE 802.11 standards. Additionally the popularity of the IEEE 802.11

standards grew as the protocols evolved to include higher data rates. These rates

permitted high bandwidth applications like video and image streaming, thereby making

IEEE 802.11 communications desirable for most business, residential, and college

environments.

The IEEE 802.11 protocol has three common standards: IEEE 802.11a/b/g. The

2.4 GHz Industrial, Scientific and Medical (ISM) band has been allocated for the cost-

free operation ‘b’ and ‘g’ systems, while the ‘a’ systems function in the 5 GHz band. The

IEEE 802.11b [IEE99] permits data transmission at rates of up to 11 Mbps, while the

IEEE 802.11 ‘a’ and ‘g’ technologies support up to 54 Mbps data rate. In IEEE 802.11b

2

systems, data is transmitted at 1 and 2 Mbps by means of an 11 chip Barker spreading

code. In the 1 Mbps case, Binary Phase Shift Keying (BPSK) is used, while Quadrature

Phase Shift Keying (QPSK) [PRO94] is used to transmit the 2 Mbps signal. The 5.5

Mbps and 11 Mbps signals are transmitted by 8 chip Complementary Code Keying

(CCK) codes, and QPSK modulation is used. The IEEE 802.11a and IEEE 802.11g

systems use Orthogonal Frequency Division Multiplexing (OFDM) and Packet Binary

Convolutional Coding (PBCC) to transmit at higher data rates.

This research project aims to improve the performance of existing IEEE 802.11

wireless systems by symbol shaping and interference mitigation. The layout of this thesis

dissertation is as follows: chapters 2 and 3 apply symbol shaping to the 1 Mbps Barker

spread signal, chapter 4 applies symbol shaping to the 5.5 Mbps signal, while chapters 5

to 7 involve microwave oven studies, modeling, and interference mitigation.

1.2 Spectral Mask & IEEE 802.11 Channels

All wireless communication systems have bandwidth and power regulations set

by the Federal Communications Commission (FCC). These are the spectral mask

requirements. The spectral mask regulations have been formulated to minimize the

interference caused by the presence of wireless systems competing for the limited

spectral region. The bandwidth limitations allow multiple users to share the spectrum

using several Wireless-Fidelity (Wi-Fi) channels. The power limitation ensures that the

interference caused by a wireless system is confined to a limited spatial space the size of

which is proportional to the radiated power. For wireless computer networks adhering to

the IEEE 802.11 standards, the maximum allowable transmit power is 1 watt. The FCC

spectral mask is shown in Figure 1.1. The mask limits most of the radiated Radio

3

Frequency (RF) power within a bandwidth of 22 MHz by requiring the transmitted signal

Power Spectral Density (PSD) [PRO94] to be down by 30 dB at 11 MHz from the carrier

frequency, and down by 50 dB at 22 MHz from the carrier frequency.

In the 2.4 GHz ISM band, the IEEE 802.11b & g signals are allocated frequencies

from 2401 to 2473 MHz in the United States [LEU03]. Outside of this range, the PSD of

the signals is highly attenuated. This spectral space is further sub-divided into 11

channels as shown in Figure 1.2. Channel 1 has a center frequency of 2412 MHz and

channel 11 is centered at 2462 MHz. Channels 2 through 10 are centered between

channels 1 and 11 with adjacent channel spacing of 5 MHz each [MIS06]. However,

each channel has a 22 MHz bandwidth. This means each IEEE 802.11 channel overlaps

with adjacent ones as seen in Figure 1.2. In practice, most wireless Access Points (AP)

are assigned either channels 1, 6 or 11 as these channels are sufficiently far apart (25

MHz spacing) to avoid interference caused by spectral overlap [MAC07].

Figure 1.1. FCC spectral mask: The spectrum of an 11 Mbps rectangular pulse shaped signal is shown for comparison. (Source: IEEE 802.11 standards)

4

Figure 1.2. IEEE 802.11b & g channel allocations in the US

1.3 Wireless Interference

Officially, wireless interference is occurs when two or more Wi-Fi signals overlap

with each other at the same spatial, spectral, and temporal locations. Interference causes

degradation in the performance of the wireless system as the digital data is often

corrupted due to the overlapping signals. Such interference necessitates retransmission,

thereby data transmission. In addition, rates may need to be decreased. However, similar

loss in data throughput performance occurs due to the “listen-before-talk” paradigm that

is programmed into most wireless systems. This effect is often confused with wireless

interference and, hence, warrants some explanation.

Under normal conditions, all of the radios on a given channel share access to the

airwaves by means of a “listen-before-talk” mechanism. The technical term for this

mechanism is Carrier Sense Multiple Access/Collision Avoidance (CSMA/CA)

[GOL05]. Basically, the radios listen to determine if another device is transmitting. If

two or more physically close wireless data transmitters have PSDs that overlap, each

transmitter will wait and transmit only if the channel is available, i.e., no other device is

5

transmitting in at that time. For example, suppose there are two such devices, namely,

device A and device B. If device B wants to transmit data while device A is occupying

the wireless channel, device B has to wait until the channel has been cleared by device A.

Then, when device B takes over the channel, device A cannot transmit until the channel

is again clear. So clearly, the users of both devices A and B experience degradation in

the data communication performance, although wireless interference was avoided by

means of the CSMA/CA algorithm. This is often misconstrued as wireless interference.

Although the “listen-before-talk” mechanism helps prevent “wireless

interference,” since data throughput is adversely affected by it, people often confuse its

effect as wireless interference. Thus, the net effect and the cause are similar. The cause

is that several devices are competing for the same spectral space. The effect is that the

data throughput declines. However, there is one important difference. When “wireless

interference” occurs, data for some or all the interfering devices is corrupted. This may

make communication impossible. However, for the “listen-before-talk” mechanism, data

is not corrupted as wireless interference does not occur. So communication is still

possible, albeit, at a reduced throughput rate.

Wireless interference is now the single most disruptive factor for wireless

networks, in general. In a typical office building or multi-storied residential complex,

there are many APs that provide the wireless infrastructure for different computer

networks. The APs interfere as they compete for the limited number of IEEE 802.11

channels. At best, the range of each Wi-Fi network is reduced due to interference. At

worst, the problems caused by interference plus the “listen-before-talk” are so severe that

the wireless connection between some APs and their subscribers can be lost. Figures

6

A.1, A.2 and A.3 in Appendix A are spectrograms [RAP02] that visualize the invisible

phenomenon of interference. A spectrogram provides time, frequency and power

information, and so the spectral and temporal overlap characteristics of interference are

illustrated by the interference spectrograms.

Considerable research effort has been invested in studies that attempt to mitigate

interference or into the development of wireless communication systems that are more

robust to its interference. This includes cognitive radio and the application of adaptive

antennas [COM88]. In this research project, a wireless mitigation technique is developed

that allows Wi-Fi systems to avoid wireless interference caused by MicroWave Ovens

(MWOs) transmitting non-data carrying signals in the 2.4 GHz ISM band.

1.4 Inter-Symbol Interference

Inter-symbol interference (ISI) is a form of data signal distortion where the

previously transmitted symbols have an effect on the currently received symbol. In a

communication system free from ISI, the energy from each received symbol is confined

in the symbol interval. However, when ISI occurs, the time interval of each symbol is

“stretched”, that causes the current symbol to receive some energy from preceding

symbols. The energy from the previous symbols has a similar effect as noise, thus

making the communication less reliable. As a result, the current symbol received has a

greater probability of being decoded incorrectly.

ISI occurs when the frequency response of the transmission channel is not flat

and/or the channel’s bandwidth is less than the bandwidth of the data signal. The result

of transmission in such a channel is a filtering effect that introduces a filtering delay in

each symbol. This delay elongates the symbol causing ISI. For the same reason, using

7

filters to adjust the PSD characteristics of a signal also leads to ISI. This phenomenon of

ISI is clearly illustrated by Figures 1.3 and 1.4. Figure 1.3 shows a sequence of symbols

before ISI distortion. Fig 1.4 shows what the symbol sequence may look like after ISI

distortion. Notice how each symbol leaks into the following symbol.

Figure 1.3. Ideal symbol sequence without ISI

Figure 1.4. ISI distortion of a symbol sequence

The PSD of the IEEE 802.11b signals fails to meet the FCC spectral mask

requirements. Similar to the 11 Mbps rectangular pulse signal spectrum shown in

Figure 1.1, the IEEE 802.11b signals have sidelobes that are not sufficiently attenuated.

As a consequence, high order filters are required in the Wi-Fi transmitters to attenuate the

sidelobes enough to satisfy the spectral mask. The resulting transmitted signal inherently

suffers from ISI distortion. High ISI increases the Bit Error Rate (BER) of the

communication system. The objective of this work is to achieve the spectral mask

without using a high order filter, such that ISI is minimized.

8

ISI can be corrected either by increasing the signal’s symbol duration or by pulse

shaping. By increasing the symbol period, the time space between the data symbols is

increased and thus the “symbol stretching” caused by ISI now has lesser effect on the

data. However, increasing the symbol period means that the data transmission rate is

lowered, and this is highly undesirable in today’s high speed wireless networks. Symbol

shaping, also called pulse shaping, involves changing the shape of the data symbols.

Pulse shaping is done such that the new data signal possesses better PSD characteristics,

such that the amplitude of the sidelobes is lowered. As a result, the filtering requirement

necessary to meet the spectral mask is minimized, thus minimizing ISI.

1.5 Barker Code and IEEE 802.11 1 Mbps Signal

Generally speaking, a spreading code is a binary (uni-phase) or polyphase code

that expands the bandwidth of a digital signal by modulating each data symbol. Each

data symbol is transmitted by a sequence of nc chips, and the bandwidth is expanded by a

factor of nc. This nc is called the processing gain. By spreading a data signal over a

wider bandwidth, the signal becomes more resistant to narrowband interference. On the

receiver side, the data sequence is de-spread accomplished by using the same spreading

code to recover the original data.

The 11 chip Barker spreading code expands the bandwidth of a regular 1 MHz

bandwidth digital binary data signal by a factor of 11. The 1 Mbps data rate, however, of

the digital signal remains unchanged. This factor of 11 processing gain of the Barker

sequence makes the transmitted 1 Mbps wireless data signal highly robust to narrowband

interference. The Barker chip sequence used in the 802.11 standard is:

B = [+1,−1,+1,+1,−1,+1,+1,+1,−1,−1,−1]

9

This sequence has good auto-correlation [PRO94] properties that make the code

ideal for data transmission in wireless channels in indoor environments [SAL87]. In

these type of environments, wireless signals experience multiple reflections from walls

and furniture. Multipath fading [GOL05], therefore, is a significant problem that

threatens to make the wireless channel error-prone. However, for a Barker spread signal,

reflected and time-delayed multiple versions of the same signal are poorly correlated to

each other. This is because the correlation detector [PRO94] gives a high value only if

there is no time delay between the received symbol and the reference correlator symbol.

The correlation value is low for any delayed multipath version of the same signal. This is

demonstrated by a plot of the auto-correlation function of the 11 chip Barker sequence in

Figure 1.5.

The PSD of the Barker spread IEEE 802.11 signal is plotted in Figure 1.6. The

FCC spectral mask is shown by the dashed line. Clearly, it fails to meet the spectral

mask requirement [LEE05]. Consequently high attenuation output filters are needed to

satisfy the spectral mask requirement, which adds to the hardware cost and increases the

BER by introducing ISI.

-1 -0.5 0 0.5 1

x 10-6

0

0.2

0.4

0.6

0.8

1

Auto-correlation

Time Delay (sec)

Figure 1.5. Auto-correlation plot of 11-chip Barker sequence

10

Figure 1.6. PSD of Barker spread 1 Mbps signal

The IEEE 802.11 2 Mbps signal is also spread by the same 11 chip Barker code as

mentioned in Section 1.1. For the 2 Mbps case, QPSK is used. Two bits are taken at a

time: one for the in (I) phase and the other for the quadrature (Q) phase. Both the I and

Q phase bits are spread by corresponding I and Q phase Barker code waveforms.

Due to interference, channel noise, and decreased signal strength with distance, it

is quite common for the Wireless Local Area Networks (WLANs) to transmit at 1 or 2

Mbps between APs and laptops. Additionally, the Physical Layer Convergence Protocol

(PLCP) packet [CON00] is transmitted using the 1 Mbps signal. So although Wi-Fi data

rates have gone up tremendously, the 1 Mbps Barker spread signal still is crucial to IEEE

802.11 systems. Thus if the 1 Mbps signal can be improved, this will cause an overall

improvement of data transmission using IEEE 802.11 Wi-Fi at any data rate. In this

project, attempt is made to improve this 1 Mbps IEEE 802.11 signal by pulse shaping to

lower the signal’s ISI such that it gives improved performance in BER versus Signal to

Noise Ratio (SNR) studies.

Spectral Mask

11

1.6 IEEE 802.11 CCK 5.5 Mbps Signal

The 5.5 Mbps CCK signal uses an 8 chip polyphase spreading code to transmit 4

bits at a time. The symbol rate is 1.125 Msps, and since the processing gain is 8, the

baseband bandwidth of the CCK signal is 11 MHz. Unlike the real valued Barker

spreading sequence however, the CCK spreading sequence is complex. This complex

structure is what makes this spreading code a polyphase spreading code.

In quadrature phase 8-chip CCK, there are 65536 possible code words, and sets of

64 that are nearly orthogonal. This is because it takes 16 bits to define each code vector

(2 phases X 8 chips = 16 possible combinations). All the 64 nearly orthogonal code

words are used in 11 Mbps CCK signal. However, for the 5.5 Mbps data rate signal, a

subset of 4 of the 64 vectors having superior coding distance is used.

In the 5.5 Mbps CCK signal, the incoming data is grouped into 4 bits nibbles

where 2 of those bits select the spreading function out of the set of 4 while the remaining

2 bits modulate the symbol using QPSK. The 4 bit sequence is represented as [d0, d1, d2,

d3]. Bits [d0, d1] select the differential carrier phase as specified in Table 1.1. Notice,

that the “symbol number” affects this choice (even or odd). The 4 complex spreading

sequences are shown in Table 1.2 and are selected by [d2, d3].

Table 1.1. Differential QPSK encoding table used in CCK transmission Dibit pattern

(d0, d1) Even symbols Phase change

Odd symbols Phase change

00 0 π 01 π/2 3 π/2 (-π/2) 11 π 0 10 3 π/2 (-π/2) π/2

12

Table 1.2. 5.5 Mbps CCK encoding table d2, d3 c1 c2 c3 c4 c5 c6 c7 c8

00 1j 1 1j -1 1j 1 -1j 1 01 -1j -1 -1j 1 1j 1 -1j 1 10 -1j 1 -1j -1 -1j 1 1j 1 11 1j -1 1j 1 -1j 1 1j 1

When combined, the resulting transmitted analog signal, vc(t) is represent able as

( )θαπ +∠++= ),(2cos2)( knwtftv ncc , (1.1)

where αn is the differential phase for the nth data symbol (from Table 1.1), ),( knw∠ is

the phase of the nth data symbol’s kth chip determined from Table 1.2, θ is an arbitrary

phase angle, and cf is the carrier frequency of the signal [ALB06].

Cross coupling distortion occurs in M-ary phase shift keying for M > 2, where the

I and Q phase signal energies leak into each other. This commonly occurs in wireless

multipath environments because multipath signal components arriving with a delay are

shifted in phase. Thus, the later arriving multipath with a phase shift corrupts the I and Q

information from the primary signal ray. CCK that is used in the 802.11b standard is

quite resistant to multipath distortion in the form of cross coupling. This is because the

information in CCK is encoded directly onto complex chips, which cannot be cross-

couple corrupted by multipath. Thus 5.5 Mbps CCK signals are often utilized by APs

when channel conditions prohibit the use less robust higher data rate signals.

The PSD of the 5.5 Mbps CCK signal is shown in Figure 1.7. It is interesting to

note that this PSD has a simple sinc (sin x / x) shape that matches with the PSD of a

11 Mbps BPSK rectangular pulse shaped binary signal. The spectral mask is not

achieved by the unfiltered 5.5 Mbps CCK signal and this necessitates high order filtering.

Again, the filter introduces ISI that degrades the BER versus SNR performance of the

13

Wi-Fi system. Here also, the application of pulse shaping to reduce the ISI is a valid

option.

0 1 2 3

x 107

-90

-80

-70

-60

-50

-40

-30PSD plot

Frequency in Hz

Pow

er in

dB

m

Figure 1.7. PSD of 5.5 Mbps CCK signal

1.7 ComBlock Devices

ComBlocks [COM06] are modular communication chipsets that can be connected

as blocks to construct transmitters and receivers. Each module performs a specific task,

for example, modulation at 2.4 GHz. Modules are also swappable. In a transmit

configuration, for example, the 2.4 GHz modulator can be replaced by a 900 MHz one,

and the transmitter will function in a different frequency band.

A transmitter was constructed using five ComBlock chipsets connected in series:

a computer interface module, an arbitrary waveform generator, a high-speed baseband

Digital to Analog Converter (DAC), a modulator operating in the 2.4 GHz band, and an

amplifier. The transmitter is shown in Figure 1.8. Using this set up, any waveform with

a maximum double sideband bandwidth of 40 MHz can be transmitted. In order to

Spectral Mask

14

transmit the waveform, a digital version of the waveform is generated in a computer

using MATLAB software and this is saved in a data file. The data file is uploaded via the

computer interface module into the arbitrary waveform generator. The generator outputs

the digital waveform at up to 40 Msps, and the DAC converts this to a baseband analog

waveform consisting of I and Q phases. The 2.4 GHz modulator mixes this baseband

signal up to the ISM band, and the amplifier amplifies this for the transmit antenna.

A receiver was also constructed using ComBlock modules. The receiver,

displayed in Figure 1.9, consists of three chipsets. A 2.4 GHz receiver antenna receives

the Wi-Fi signal. At the RF end, one chipset demodulates the RF signal and mixes the

2.4 GHz received signal to baseband. The same chipset then samples the baseband

analog signal’s I and Q phases and digitizes the received waveform using a high-speed

Analog to Digital Converter (ADC). The digitized waveform is stored in the second

module, which is a memory storage unit. The third module is a computer interface chip.

The digital waveform is transferred from the memory storage unit to a computer via this

module for analysis using MATLAB.

Figure 1.8. ComBlock transmitter system

15

Figure 1.9. ComBlock receiver system

Block diagrams of the transmitter and receiver are shown by Figures 1.10 and

1.11, respectively. The diagrams show the flow of information and summarize the

chipsets’ operations. The blocks with dashed edges denote individual chipsets.

Figure 1.10. Block Diagram of ComBlock Transmitter

Figure 1.11. Block Diagram of ComBlock Receiver

Computer ComBlock LAN chip

Waveform storage

ADC conversion

20 MHz Lowpass filter

2.4 GHz QPSK demodulator

2.4 GHz Amplifier

BPF (2400-2500 MHz)

I

Q

Q I

Computer ComBlock USB chip

Waveform storage

DAC conversion

20 MHz LPF

2.4 GHz QPSK modulator

2.4 GHz Amplifier

BPF (2400-2500 MHz)

I

Q

Q I

16

In this research project, the ComBlock transmitter was used to experimentally

transmit novel pulse shaped versions of the 1 Mbps signal. The receiver was used to

capture the signal, demodulate the digital data, and obtain BER measurements to test the

performance of the experimental Wi-Fi systems. The ComBlock transmitter was also

used to emulate a MWO signal based on a model developed as part of this research.

Additionally, an interference mitigation experiment was conducted where the transmitter

and receiver both were used to test the efficacy of the interference mitigation system.

Furthermore, the ComBlock receiver was used to obtain Spectrogram plots, which were

instrumental in examining the phenomenon of wireless interference. Spectrograms were

also useful in studying the signal characteristics of MWOs.

1.8 Research Methodology

Research was conducted at the Wireless Interference Laboratory (WIL), which is

a part of the Wireless Networking and Communications (WiNCom) Research Center at

the Illinois Institute of Technology (IIT). Research undertaken at the WIL includes

studies examining the impact of wireless interference on computer networks, IEEE

802.11 signal characteristics and scope for signal improvement, characterization of

wireless transmission devices, and interference mitigation. The research undertaken in

this project falls under three of these categories: improvement of IEEE 802.11 signals,

characterization of a MWO, and mitigation of MWO interference.

To ensure the validity of the research results, a three-pronged approach was used

in addressing all the problems. Each problem was examined analytically, experimentally

and via simulation. The results obtained using the different approaches were compared to

obtain veritable conclusions. For example, when a sinusoidal pulse shaping function was

17

used for 1 Mbps Barker spread code, an analytical expression for the PSD was obtained

and plotted. This was then compared to the simulated and experimentally obtained PSD

plots. The three plots were in agreement and, thus, provided concrete support for the

results. The three-pronged approach was also useful in detecting and weeding out errors

and mistakes during the course of research. For example, when the experimentally

generated PSD for a buffered and pulse shaped 1 Mbps signal diverged from the

simulated PSD, an error in the simulation process was discovered and subsequently

corrected. However, due to high levels of complexity for some problems, the three-

pronged approach could not always be used. A case in point: effort was made to find the

analytical expression for the PSD of an MWO, but there was little success in this regard.

MATLAB software [MAT07] was used throughout the research project. PSpice

software was used to design the interference mitigation circuit and simple logic chips

were used for its construction. For experimental work, ComBlocks were used. A

spectrum analyzer was used for important measurements. Several measurement devices

including oscilloscopes, voltmeters, etc. were used during the research.

18

CHAPTER 2

PULSE SHAPING FOR IEEE 1 MBPS BARKER SPREAD SIGNAL

2.1 Pulse Shaping Methodology

For the case of the 1 Mbps Barker spread signal without any pulse shaping, each

data bit is transmitted as a sequence of 11 Barker chips with chip interval, Tc = T / 11,

where T is the bit duration (1 µs). The chips are unit amplitude rectangular pulses, and

the PSD for the unfiltered data signal modulated by this Barker wave shape does not

satisfy the FCC spectral mask. Figure 1.6 shows that the second lobe must be filtered by

at least 17 dB and the third lobe by at least 32 dB to be below the mask. In our

simulation studies, a fifth order Butterworth filter with a cutoff frequency of 9.5 MHz

was required to satisfy the mask requirements. This introduced considerable ISI.

The Barker waveform was modified by smoothing the rectangular pulse shapes in

the original Barker symbol. The modified pulse shapes still adhered to the general

Barker sequence and maintained good autocorrelation properties. Several smoothing

functions were applied to the Barker waveform of which three shapes that provided best

results were examined thoroughly. Sinusoidal, logarithmic and a sincm functions were

used to smooth individual chips in these three cases. Regardless of the exact form of the

Barker symbol shape, the baseband data signal can be represented as:

∑∞

−∞=

−⋅=n

nTtpnxty )()()( , (2.1)

where x(n) ∈ {–1, 1} is random binary data, that is independent and identically

distributed, and p(t) is the pulse shaped Barker waveform. The signal, y(t), is a zero-

mean cyclostationary [PRO94] random process with PSD given as (2.2):

19

22( ) ( ) ,x

yS f P fTσ

= (2.2)

where σx2 is the variance of x(n) and P(f) is the Fourier transform of the pulse shaped

Barker symbol, p(t).

For each symbol shape, the resulting communication system was analyzed via

simulation and experimentation. The PSD was of key interest in order to observe spectral

improvements. The amount of sideband attenuation achieved was observed to check the

degree to which the spectral mask was satisfied. However, the spectral mask could not

be completely satisfied by symbol shaping alone and filtering was still required.

However, for the novel signals, only low order filters are necessary to achieve the

spectral mask. Thus, ISI is considerably reduced. This theoretically should translate to

better system performance in BER versus SNR studies. In order to investigate this theory

further, more simulations and experiments were conducted.

An auto-correlation plot of each pulse shape was obtained and compared with that

of the unmodified Barker waveform. A good similarity between the two implies that the

new signal should have good multipath robustness. Beyond the auto-correlation plot

itself, in order to further validate the performance of the communication systems, BER

simulation studies were performed for each of pulse shaped Barker waveforms in

MATLAB. In these studies, random binary data was Barker spread using each symbol

shape to obtain a simulated transmit signal. A minimum order Infinite Impulse Response

(IIR) filter [PRO96] was used to filter the baseband information signal such that the PSD

satisfied the spectral mask without introducing excess ISI. This signal was applied to an

Additive White Gaussian Noise (AWGN) channel and the SNR of the output noisy signal

was recorded. After transmission through this simulated AWGN channel, a correlation

20

detector [PRO94] was used to decode the received bits. The decoded bits were compared

to the transmitted bits to obtain a BER value for the channel at the recorded SNR level.

Keeping true to the three-pronged approach described in Section 1.8, the

communication systems with the various symbol shapes were emulated by the ComBlock

transmitter and receiver. Experimentation was done to cross-check the simulation results.

A Rohde & Schwarz™ spectrum analyzer (model no. FSP 38) was used to obtain the

experimental PSD. Experimental BER studies were conducted where Barker spread data

signals (using the novel pulse shapes) were transmitted over the air. The data signals

were captured by the ComBlock receiver, the signals were demodulated and the received

bit streams were decoded to obtain BER measurements. The ComBlock receiver,

however, did not do the BER analysis. In each experimental run, the digitized waveform

captured by the ComBlock was downloaded to a computer where a MATLAB program

analyzed the waveform to decode the received bits using a correlation detector and an

experimental BER value was obtained.

For the experimental communication system, however, a 1 Mbps data rate could

not be used. Due to hardware speed limitations, a 4 MHz chip-rate was used

corresponding to a bit-rate of 363 kbps with the 11 chip Barker code. Using

4 Mchips/second, the main-lobe bandwidth in the experimental PSD is expected to be

4 MHz. The baseband modulated signal was viewed with a 400 MHz oscilloscope to

provide a temporal domain representation. All these experimental plots were compared

to the simulated and analytically expected results as based on the three-pronged research

approach.

21

The implementation of complex pulse shaping in a transceiver system is feasible,

where the system hardware can be constructed inexpensively by replacing the high-speed

DAC with a discrete-time analog storage device. Such a device stores the modulator’s

signal level values as analog voltages. During each bit interval, the analog voltages will

be output at discrete sub-time intervals to construct the complete pulse shape. Typically,

a communication system requires a small finite set of pulse shapes. Thus, only a limited

number of the analog storage cells are needed, thereby eliminating the need for complex

digital logic circuits and DACs. Recently, a topic of promising research has been the

integration of such analog waveform generators with digital communication systems

[CHA05].

2.2 Sinusoidal Pulse Shaping

Figure 2.1. Plot of Sinusoidally shaped Barker waveform

Sinusoidal pulse shaping was employed to shape sequences of Barker chips. The

resulting wave shape is shown in Figure 2.1, where the energy per symbol is equal to that

22

of the original Barker wave shape. The sinusoidal pulse shape can be expressed

analytically as

4

1( ) 2 ( )

Ks Sk

p t p t=

= ∑ , (2.3)

where the compound parts are given as

1

2

3

4

( ) sin(2 / 2 ), 5 3( ) cos(2 / 4 ), 3( ) sin(2 / 2 ), 0( ) sin(2 / 6 ), 0 6

S C C C

S C C C

S C C

S C C

p t t T T t Tp t t T T t Tp t t T T tp t t T t T

ππ

ππ

= − − ≤ ≤ −

= − − ≤ ≤ −= − ≤ ≤

= ≤ ≤

. (2.4)

The waveform based on these equations was used to spread random digital data in

a MATLAB program. A digitally represented waveform was obtained and the data file

was uploaded to the ComBlock transmitter. The ComBlock’s arbitrary waveform

generator generated the analog waveform using this data. The experimental analog

waveform was examined with an oscilloscope as is shown in Figure 2.2. It matches with

Figure 2.1.

Figure 2.2. Oscilloscope plot of sinusoidally shaped Barker waveform

23

The PSD of the sinusoidally shaped Barker waveform lends itself to an analytic

study. Using rectangularly windowed and shifted sinusoids, as defined in (2.4), the

Fourier spectrum of ps(t) is found to be

∑= ⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥⎦

⎤

⎢⎢⎣

⎡

−=

2

122 )2/()(

)cos()2/()(2

k c

Tfjkc

cs TfkeTfkkTfP

c

ππππ

(2.5)

Using (2.2) and (2.7) the PSD can be computed. The analytic PSD is displayed in

Figure 2.3, and the MATLAB simulated PSD (with 5000 bits) is plotted in Figure 2.4.

The agreement is excellent and we observe that there is an 11 dB attenuation

improvement over the rectangular Barker PSD. To satisfy the FCC mask requirement a

simple second order Butterworth filter with a 9.5 MHz cutoff frequency is needed.

An experimentally measured PSD using a sinusoidally shaped Barker waveform,

modulated at 2.420 GHz, is given in Figure 2.5, along with the FCC spectral mask

(dashed lines). The analytic and simulated PSD, in Figs. 2.3 and 2.4, respectively, match

very closely with the experimental PSD. Note that the experimentally emulated PSD in

Figure 2.5 has a mask with transitions at 4 MHz and 8 MHz away from the carrier

frequency since the chip rate is 4 MHz.

With equal energy per shaped symbol, the peak of the autocorrelation function

should be the same for the sinusoidal and rectangular pulse shaped Barker waveforms.

Plotted in Figure 2.6 is the autocorrelation function of the rectangular Barker waveform

(dashed line), and the sinusoidally shaped Barker waveform (solid line). The Barker

code’s autocorrelation property dictates that the autocorrelation function is bounded by

.))24(())24sin(()24(

22

)210()1(

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥⎦

⎤

⎢⎢⎣

⎡

−−−−

−−−−

ππ c

Tfkjc

TfkeTfkkj

ck

24

one-eleventh of its peak for time shifts of 1 chip or more. This property is largely

preserved with the sinusoidally shaped Barker waveform, and is strictly preserved for

time shifts of 3 chips or more. Consequently, the shaped Barker communication system

should be robust to multipath distortion and noise. The mean square error (mse) between

the two auto-correlation plots in Figure 2.6 is 0.7477. For comparison purposes, the

power of the rectangular Barker’s auto-correlation waveform is 4.1178.

0 0.5 1 1.5 2 2.5 3

x 107

-110

-100

-90

-80

-70

-60

-50

-40

-30

Frequency (Hz)

Pow

er in

dB

m

Analytical PSD of Sinusoidally Pulse shaped Barker waveform

Figure 2.3. Analytic PSD of sinusoidal pulse shaped Barker waveform.

25

0 0.5 1 1.5 2 2.5 3

x 107

-110

-100

-90

-80

-70

-60

-50

-40

-30Baseband Transmitted signal PSD

Frequency in Hz

Pow

er in

dB

m

Figure 2.4. Simulated PSD of sinusoidal pulse shaped Barker waveform.

Figure 2.5. Experimental PSD of sinusoidal pulse shaped Barker spread system emulated at a 4MHz chip rate.

26

0 0.5 1 1.5 2

x 10-6

-5

0

5

10

15Time Auto Correlation

Time (s)

Aut

o-co

rrela

tion

Figure 2.6. Auto-correlation function of sine-shaped Barker

2.3 Logarithmic Pulse Shaping

A logarithmic smoothing function was used for the leading and trailing transitions

of the Barker chip sequence. The general form of this function was

)log()( 0210 ttkkktpL ++= , (2.6)

where k0, k1, k2, and t0 are constants.

Plotted in Figure 2.7 is the logarithmically shaped Barker symbol and the

(original) rectangularly shaped Barker waveform. The amplitude of the log-shaped

waveform has been adjusted so that the energy per symbol is the same in both cases.

A closed form analytic expression cannot be obtained for the PSD of the

logarithmically shaped Barker symbol. Its PSD was found with a MATLAB simulation

using the Welch PSD [PRO96]. This PSD result is plotted in Figure 2.8 using 5,000 data

bits. This PSD shows an improvement in spectral characteristics, where the sidebands

are attenuated 8 dB more than the rectangular Barker PSD shown in Figure 1.6. A third

27

order Butterworth filter with a 9.5 MHz cutoff frequency is needed to satisfy the spectral

mask, compared to a fifth order filter when pulse shaping is not used. The single

sideband PSD of the experimentally emulated logarithmically pulse shaped Barker signal

is shown in Figure 2.9. The auto-correlation plot of the logarithmically shaped pulse is

shown in Figure 2.10 and compared to the ideal, the mse value is only 0.267.

Figure 2.7. Logarithmic and rectangular shaped Barker symbol with equal energies.

0 0.5 1 1.5 2 2.5 3

x 107

-110

-100

-90

-80

-70

-60

-50

-40

-30Baseband Transmitted signal PSD

Frequency in Hz

Pow

er in

dB

m

Figure 2.8. Simulated PSD of the logarithmic Barker waveform.

28

Figure 2.9. Experimentally emulated PSD of the logarithmic Barker waveform.

0 0.5 1 1.5 2

x 10-6

-5

0

5

10

15Time Auto Correlation

Time (s)

Aut

o-co

rrela

tion

Figure 2.10. Auto-correlation function of log-shaped Barker

2.4 Sincm Pulse Shaping

A third shaping method was studied employing sinc-functions of the form

[ ]mc tbtAtp )(sinc)( 1+= , (2.7)

29

where 0 < m < 1. The best PSD, relative to the FCC mask, was obtained with two values

for m, where m1 = 0.55 for the 1-chip segments, and m2 = 0.83 for the 2- and 3-chip

segments, e.g., +1 +1 +1. Simulation was used to find these optimal m1 and m2 values for

the best spectral characteristics. The plot of this pulse shape is shown in Figure 2.11. Its

auto-correlation function is plotted in Figure 2.12 and the mse compared to that of

rectangularly shaped Barker’s auto-correlation is 0.825.

As with the log-shaped Barker symbol, the sinc-function shaped symbol does not

lend itself to a closed form analytic expression for the PSD. The simulated PSD is

plotted in Figure 2.13, while Figure 2.14 shows the experimentally obtained PSD.

Observe that the first sideband is attenuated by 12 dB compared to the rectangular Barker

pulse, but there is also less influence on the third sideband. A second order Butterworth

filter with 9.5 MHz cutoff frequency was adequate to meet the spectral mask in this case

-4 -2 0 2 4

x 10-7

-1.5

-1

-0.5

0

0.5

1

1.5

Time (s)

p(t)

in V

olts

The sincm shaped waveform

Figure 2.11. Plot of sinc-function shaped Barker waveform.

30

0 0.5 1 1.5 2

x 10-6

-5

0

5

10

15Time Auto Correlation

Time (s)

Aut

o-co

rrela

tion

Figure 2.12. Auto-correlation of sinc-function shaped Barker waveform.

0 0.5 1 1.5 2 2.5 3

x 107

-110

-100

-90

-80

-70

-60

-50

-40

-30Baseband Transmitted signal PSD

Frequency in Hz

Pow

er in

dB

m

Figure 2.13. Simulated PSD of sinc-function shaped Barker waveform.

31

Figure 2.14. Experimental PSD of sinc-function shaped Barker waveform.

2.5 BER Measurements

As previously mentioned, BER simulation studies were performed for each of the

four Barker pulse shaped waveforms in MATLAB at various SNR levels. A synchronous

demodulator and correlation detector were used in all cases. The BER simulation

methodology has been described in words in Section 2.1. Figure 2.15 provides a visual

summary. The BER study results are shown in Table 2.1 using 50,000 random test bits

each time. The unmodified rectangular Barker waveform signal was also used in the

BER study as the control case. This table also indicates the filter order used to achieve

the FCC spectral mask requirement after pulse shaping. With low order filters, ISI is

minimized; but ISI will increase as the filter order grows. High noise levels were chosen

32

to obtain meaningful BER results with the available computing resources. A BER vs

SNR plot is shown in Figure 2.17 showing the performance of the various pulse shaped

systems. This plot shows that the sinusoidally shaped system performs about 0.5 dB

better than its unmodified rectangular shaped counterpart.

MATLAB Simulation Methodology used for each Pulse Shape

1) Design Pulse Shape adhering to Barker Sequence.

2) Examine its Auto-correlation properties.

Generate random bit sequence and spread each bit by pulse shape to obtain data waveform.

Add Additive White Gaussian Noise (AWGN).

Obtain the PSD of data waveform using the Welch method.

Use Correlator to obtain timing information from the “received signal”

Use Correlatorto decode the received bits.

Examine Bit Error Rate

10010110111010

10010110101010 Figure 2.15. Diagram illustrating BER simulation study

Experimentation Methodology used for each Pulse Shape

Design Pulse Shape adhering to Barker Sequence in Matlab.

Generate random bit sequence and spread each bit by pulse shape to obtain data waveform. Transmit over the Air.

Upload the data waveform to the Comblock transmitter.

Use Correlator to obtain timing information

Use Correlatorto decode the received bits.

Examine Bit Error Rate

Comblock receiver captures the received data waveform for computer download.

10010110111010

10010110101010

Figure 2.16. Diagram illustrating experimental BER study

33

Figure 2.17. BER vs SNR study for pulse shaped Barker spread systems

In Section 2.1, the experimental BER method used to test each communication

system was described. Figure 2.16 illustrates this diagrammatically. The experimental

BER results, obtained using the experimental ComBlock test bed, are shown in Table 2.2.

Table. 2.1. Simulated BER measurements for Barker pulse shape (no buffer).

Bit Error Rate at SNR levels: Pulse Shape Used

Filter Order –11.5 dB –11 dB –10 dB

Rectangular 5 3.70E-03 2.74E-03 9.00E-04 Logarithmic 3 2.48E-03 1.40E-03 5.60E-04 Sinusoidal 2 2.62E-03 1.36E-03 3.80E-04

Sinc-function 2 2.80E-03 1.98E-03 3.80E-04

Table 2.2. Experimental BER measurements at receiver-to-transmitter distance of

1 meter for Barker pulse shape (no buffer).

Pulse Shape Used Experimental BER

Rectangular 9.99E-03 Logarithmic 6.22E-03 Sinusoidal 3.71E-03

Sinc-function 5.84E-03

34

2.6 Comparison of Barker Symbol Shaped Systems

In general, the sinusoidally shaped system performed the best both in simulation

and experimental emulation. This system experienced little ISI due to the low order filter

used. The rectangular Barker system required the highest order filter and thus

experienced more ISI that degraded the performance. The improvements in the unfiltered

spectral characteristics are summarized in Table 2.3, where the rectangular pulse shape

forms the unmodified control system with no symbol shaping. The table shows the

attenuation in peak lobe powers. Additionally, Table 2.4 shows the total amount of

sideband energy leakage in the PSD of the various signals. For lower sideband powers,

there is lesser interference caused to nearby Wi-Fi channels.

Table. 2.3. Comparison of PSD peak sideband attenuations

Pulse Shape Used Second Lobe drop Third Lobe drop

Rectangular 13.1 dB 17.2 dB Logarithmic 18.2 dB 20.8 dB Sinusoidal 24.0 dB 35.9 dB

Sinc-function 24.7 dB 30.5 dB

Table. 2.4. Comparison of total power in each band

Pulse Shape Main Lobe

Power %

Second Lobe

power %

Third Lobe

power %

Second Lobe drop

(dB)

Third Lobe drop (dB)

Rectangular 90.6 5.08 2.03 12.5 16.5 Logarithmic 98.6 0.954 0.264 20.1 25.7 Sinusoidal 99.7 0.257 0.023 25.9 36.4

Sinc-function 99.6 0.316 0.071 25.0 31.4

Table 2.5 quantifies the amount of ISI occurring in each system, where the metric

is the amount of energy in one symbol that leaks into the next symbol interval. We notice

that the rectangular system has almost 5% energy leakage due to ISI compared to only

35

0.2% for the sinusoidal case. The value of symbol shaping versus output filtering to

satisfy the FCC spectral mask has thus been firmly established [TAH07].

Table. 2.5. ISI after filtering operation

Pulse Shape Power within Bit Interval (%)

Power leakage outside Bit Interval (%)

Rectangular 94.7 5.3 Logarithmic 97.5 2.5 Sinusoidal 99.8 0.2

Sinc-function 99 1

At the end of the chapter, it is worth mentioning that the pulse shaped systems

functioned as novel Wi-Fi setups that performed better than the common IEEE 802.11

1 Mbps system in several respects. These were better spectral characteristics, lower order

filter requirement, and improved BER performance. Again, the best performance was

obtained with sinusoidal pulse shaping. These conclusions were verified by matching

results obtained by analytic, simulation, and experimental studies. One principle goal of

this research project is to improve IEEE 802.11 Wi-Fi systems. This goal has been partly

achieved as it has been shown that the IEEE 802.11b 1 Mbps signal can be improved by

applying the results of this pulse shaping study.

36

CHAPTER 3

BUFFERED PULSE SHAPED BARKER SPREAD SYSTEMS

3.1 Rational for using Buffer

The research in Chapter 2 showed that the sinusoidal Barker waveform shaping

was able to reduce the PSD considerably compared to the rectangular shaped Barker

symbol. To achieve FCC mask compliance, however, a second order output filter was

still needed. The dominant feature of the PSD of the original Barker waveform comes

from the abrupt transitions after just one bit interval, that is, after 1 μs. This feature is

also seen with the shaped Barker symbols, and is illustrated in the experimentally

recorded oscilloscope plot in Figure 2.2, where sinusoidal shaping has been used. The

sudden discontinuity in the time domain raises the power of the higher frequency

components in the spectral domain. Thus, to eliminate the need for an output filter to

satisfy the FCC spectral mask, it is necessary to eliminate these discontinuities.

It is possible to introduce special line codes for the Barker waveform that will not

have the discontinuity seen in Figure 2.2. The line code would examine the current data

bit and the next bit. If a chip transition from +1 to –1 (or vice versa) is about to occur,

the line code alters the pulse shape of the next Barker spread waveform in such a way to

guarantee a smooth transition from the current bit to the next bit. Thus, the

discontinuities would be removed resulting in better spectral characteristics relative to the

FCC spectral mask. In this case it is necessary to buffer two or three bits before the

appropriate pulse shaped Barker symbol is output for information transmission.

37

Two line codes were studied to test this hypothesis. One line code buffered 2 bits,

while the other dealt with 3 bits at a time. The two methods described here combine both

line coding and pulse shaping in an effort to attain the spectral mask. The results are

detailed herein.

3.2 Buffering 2 Bits

In this system, we use two Barker waveforms to form a line code: the original

Barker waveform, and its time reversed version. Section 3.2.1 develops this signal,

mathematically, where two bits are buffered at a time. Section 3.2.2 shows all the

possible symbols.

3.2.1 Mathematical Foundation of 2 Bit Buffered Barker System. Let x(n) be

binary random iid data from a set {-1,1}, with zero mean and unity variance. A

waveform, a(t), is defined for 0 ≤ t < T, that is a symbol pulse based on the Barker

sequence B (+++---+--+-). Another waveform, b(t), is defined for the interval 0 ≤ t < T,

that is a symbol pulse based on the reversed Barker pulse (-+--+---+++), such that

b(t) = a(T-t). (3.1)

The +1 bit is to be represented by the symbol a(t), and the bit -1 is assigned the symbol

b(t). Continuing with the definitions, s(n) is defined as the sign (+ or –) for the

information symbol, y(t) at time interval nT. Combining all, during time nT < t < (n+1)T:

y(t) = s(n)·a(t-nT), (3.2a)

if x(n) = 1. However, if x(n) = -1, then

y(t) = s(n)·b(t-nT). (3.2b)

38

Since s(n) can take on two possible values, there are a total of four possible

symbol states. These states, namely 1 through 4 are given as follows:

State 1 = +a(t-nT) State 2 = –a(t-nT) State 3 = +b(t-nT) State 4 = –b(t-nT).

The line code permits state transitions such that no discontinuities occur at the end

of a bit interval. The line code thus selects the appropriate bit symbol, a(t) or b(t), and

the sign s(n) in order to avoid discontinuities of the type shown in Figure 2.2. The state

transition diagram for the line code is shown in Figure 3.1.

Figure 3.1. State transition diagram for 2 bit buffered Barker system

In this line code, (3.4) is used to generate the sign value, s(n):

s(n) = –x(n)·x(n–1)·s(n–1). (3.4)

Taking the initial condition, x(–1).s(–1) = –1, (3.4) can be further simplified for n ≥ 0, to:

s(n) = (-1)n·x(n) . (3.5a)

For a different initial condition, x(-1)·s(-1) = +1, and we obtain (3.5b).

s(n) = (-1)n+1·s(n) . (3.5b)

State 1

State 2

State 3

State 4

x(n) = +1

+1 +1 +1

–1

–1

–1 –1

(3.3)

39

With these definitions and equation (3.5a), the block diagram of the system is

constructed. Figure 3.2 shows the structure that is used to generate the information signal

based on the 2 bit buffered line code.

Figure 3.2. Block Diagram of 2 bit buffered Barker spread system

In Figure 3.2, the sign block, s(n), is selected by the line code according to (3.5),

and this selection helps remove the discontinuities of the type shown in Figure 2.2. The

system in Figure 3.2 works as follows:

1. If x(n) = +1, the top path produces a waveform y(t)= s(n)·a(t-nT). In this case, the

lower path produces a zero since +1–1=0.

2. If x(n) = -1, the lower path produces a waveform y(t)= s(n)·b(t-nT). In this case,

the top path produces a zero since –1+1=0.

Thus, over the time interval nT ≤ t <(n+1)T, y(t) is expressed as

y(t) = 0.5[x(n) + 1]·s(n)·a(t-nT) – 0.5[x(n) – 1]·s(n)·b(t-nT). (3.6)

From (3.5a), s(n) = (–1)n· x(n). Thus, (3.6) simplifies to:

y(t) = 0.5(–1)n·{[1+x(n)]·a(t-nT) – [1 – x(n)]·b(t-nT)} . (3.7)

40

From (3.1), we know that b(t) = a(T-t). Thus, further simplifying, over the interval time

nT ≤ t <(n+1)T,

y(t) = 0.5 (-1)n·{[1+x(n)]·a(t-nT) – [1 – x(n)]·a(-t + T + nT)} . (3.8)

Finally, for all t ≥ 0, based on (3.8) and factoring in the initial conditions (3.5), we get

[ ]{ [ ] } )1()1()()(1)()(1)1(5.0)( 1

0−⋅−⋅++−⋅−−−⋅+−= +

∞

=∑ sxnTTtanxnTtanxty n

n. (3.9)

Note that (3.9) completely defines the line coding performed using the 2 bit line

code system. Close examination of (3.9) reveals that only one pulse shaped Barker

waveform is required to be designed, i.e., a(t). This simplifies the effort involved in

pulse shaping. Indeed, the methods for symbol design used for this pulse shaped line

code are similar to the pulse shaping effort where no line code is used. For the systems in

Chapter 2, only one pulse shape waveform is required to be made each time, analogous to

this 2 bit buffered system. Figure 3.1 and (3.9) also reveal an interesting property of the

line code: strictly speaking, there is no real need to have a buffer register as y(nT) really

just depends on x(n). However, the principle for the line code is based on buffering two

bits, hence, the nomenclature of “2 bit buffered Barker system”.

3.2.2 Symbols Shapes Tested. According to Figure 3.1, it is clear that 4 symbols are

necessary, one for each state. However, we noted that all four pulse shaped symbols can

be obtained from just one pulse shape. This is obvious from (3.1) and the state equations

(3.3). Once the symbol for a(t) has been designed, it corresponds to the state 1 symbol.

State 2 can be obtained simply as –a(t). States 3 and 4 can be obtained by time reversing

the symbols for states 1 and 2 respectively. So the key is the shaping function used for

the waveform a(t).

41

Several functions were used to shape the chips for a(t). This included sinusoidal,

logarithmic and sincm functions. Figures 3.3 through 3.5 show the state symbol plots for

each of these pulse shaping methods. It should be noted that using this system, there is

increased complexity at the receiver side. Two correlation detectors are required: one to

detect states 1 and 2, and another correlation detector to detect states 3 and 4.

0 0.5 1

x 10-6

-1

-0.5

0

0.5

1Plot of bit +1; state 1

Time in s0 0.5 1

x 10-6

-1

-0.5

0

0.5

1Plot of bit +1; state 2

Time in s

0 0.5 1

x 10-6

-1

-0.5

0

0.5

1Plot of bit -1; state 3

Time in s0 0.5 1

x 10-6

-1

-0.5

0

0.5

1Plot of bit -1; state 4;

Time in s

Figure 3.3. State symbols for sinusoidal pulse shaping (2 bits buffered)

42

0 0.5 1

x 10-6

-1

-0.5

0

0.5

1Plot of bit +1; state 1

Time in s0 0.5 1

x 10-6

-1

-0.5

0

0.5

1Plot of bit +1; state 2

Time in s

0 0.5 1

x 10-6

-1

-0.5

0

0.5

1Plot of bit -1; state 3

Time in s0 0.5 1

x 10-6

-1

-0.5

0

0.5

1Plot of bit -1; state 4;

Time in s

Figure 3.4. State symbols for sincm pulse shaping (2 bits buffered)

0 0.5 1

x 10-6

-2

0

2Plot of bit +1; state 1

Time in s0 0.5 1

x 10-6

-2

0

2Plot of bit +1; state 2

Time in s

0 0.5 1

x 10-6

-2

0

2Plot of bit -1; state 3

Time in s0 0.5 1

x 10-6

-2

0

2Plot of bit -1; state 4;

Time in s

Figure 3.5. State symbols for logarithmic pulse shaping (2 bits buffered)

43

3.2.3 PSD Plots. A random bit stream was applied to the system described in

Section 3.2.1 using each of the pulse shaped state symbols shown in Section 3.2.2. The

simulated PSD was obtained in MATLAB. Initially, promising results were obtained.

The spectral mask seemed to have been satisfied without using any filter according to the

simulations results, where the maximum power in the sidelobes was much attenuated

compared to the mainlobe power. However, the experimentally measured PSD varied

from the simulation results, and the sideband attenuations were not that promising. It was

then realized that the parameters for MATLAB’s Welch function used to estimate the

simulated PSD needed calibration. This was one situation where the three-pronged

approach came in handy, whereby error in the simulation process was discovered and

rectified as there was discrepancy between the simulated and experimental results. After

this correction was made, the simulated and experimental PSDs matched.

Unfortunately, these PSD results showed that the line code introduced many tones

in the power spectrum that made the system unviable for Wi-Fi communications. The

tones made it impossible for any of the pulse shaped systems designed using this line

code (2 bits buffered) to meet the requirements of the spectral mask.

For the various pulse shaping functions, the PSDs obtained using simulation are

shown in Figures 3.6 to 3.8. The matching experimentally obtained PSDs are shown in

Figures 3.9 to 3.11. Note the presence of tones in all cases. The FCC spectral mask is

not applicable here due to the presence of the tones.

It is surmised that the tones are a result of the line coding process as opposed to

the particular pulse shaping functions used. Even when no pulse shaping is used, the

44

tones are still observed as is shown in Figure 3.12, which is the PSD of the 2-bit buffered

system when a(t) is chosen to equal the unmodified rectangular Barker waveform.

0 0.5 1 1.5 2 2.5 3

x 107

-110

-100

-90

-80

-70

-60

-50

-40

-302 bit buffer signal PSD

Frequency in Hz

Pow

er in

dB

m

Figure 3.6. Simulated PSD of sinusoidal pulse shaping with 2 bits buffered system

0 0.5 1 1.5 2 2.5 3

x 107

-110

-100

-90

-80

-70

-60

-50

-40

-302 bit buffer signal PSD

Frequency in Hz

Pow

er in

dB

m

Figure 3.7. Simulated PSD of sincm pulse shaping with 2 bits buffered system

45

0 0.5 1 1.5 2 2.5 3

x 107

-110

-100

-90

-80

-70

-60

-50

-40

-302 bit buffer signal PSD

Frequency in Hz

Pow

er in

dB

m

Figure 3.8. Simulated PSD of logarithmic pulse shaping with 2 bits buffered system

Figure 3.9. PSD of experimental sinusoidal pulse shaping with 2 bits buffered system

46

Figure 3.10. PSD of experimental logarithmic pulse shaping

Figure 3.11. PSD of experimental rectangular pulse shaping with 2 bits buffered system

47

0 0.5 1 1.5 2 2.5 3

x 107

-110

-100

-90

-80

-70

-60

-50

-40

-302 bit buffer signal PSD

Frequency in Hz

Pow

er in

dB

m

Figure 3.12. Simulated PSD of rectangular 2 bits buffered Barker system

3.2.4 BER Measurements. Although this symbol shaping research using 2 buffered

bits is not practically viable, the performance of the system was still studied to see if it is

viable in alternate communication systems. The system was simulated using the line

code and the various pulse shapes. Data was transmitted using the simulated

communication system over an AWGN channel at various SNR levels. Correlation

detection was used in the simulated receiver side and a BER value obtained. No filters

were used in the simulations, as the spectral mask could not be applied to these systems

due to the presence of tones in the PSD plots. The results are shown in Table 3.1. The

results are poorer than the systems described in Chapter 2. Therefore, this avenue of

research was not met with adequate success. Nevertheless, knowledge was gained in

alternative symbol shaping techniques and line coding.

48

Table. 3.1. Simulated BER measurements for 2 bits buffered Barker spread system.

Bit Error Rate at SNR levels: Pulse Shape Used –4.5 dB –4 dB –3 dB

Rectangular 0.40E-04 0.00E-04 0.00E-04 Logarithmic 2.80E-04 2.20E-04 0.20E-04 Sinusoidal 2.96E-03 1.58E-03 4.40E-04

Sinc-function 2.46E-03 1.38E-03 3.60E-04

3.3 Buffering 3 Bits

In this system sinusoidal pulse shaping was used as the results from Chapter 2 and

Section 3.2.3 showed that sideband attenuation was best achieved by sinusoidal shaping.

A line code was utilized that buffered 3 bits: the previously transmitted bit, the current

bit to be transmitted, and the next bit. Based on this set of 3 bits, one of 8 possible

symbol states is selected for transmission such that all discontinuities are eliminated. A

modified Barker sequence was used for the symbol shaping, Bm (- - - + - + + - + + +), as

this provides the smoothest possible bit possible transitions. Symbols 1 through 4

transmit the +1 bit and were based on +Bm, while symbols 5 through 8 transmit the -1 bit

and followed –Bm. The difference between symbol 1 and symbol 2/3/4 is in how the

symbol’s first 3 and last 3 chips are shaped. Thus, how the bit begins and ends is

different such that there is a smooth transition. However, Barker sequence’s auto-

correlation function is no longer preserved as shown in Figure 3.13.

49

0 50 100 150 200-5

0

5

10

15Cross correlation state1 to state1

0 50 100 150 200-5

0

5

10

15Cross correlation state1 to state2

0 50 100 150 200-5

0

5

10

15Cross correlation state1 to state3

0 50 100 150 200-5

0

5

10

15Cross correlation state1 to state4

Figure 3.13. Cross-correlation between state 1 and other states

The principle idea behind this line code is that based on the previous and the next

state symbols, the current symbol can be chosen such that there is no discontinuity at the

beginning and end of the current bit interval. Thus, the discontinuities such as those seen

in Figure 2.2 that are characteristic of the non-buffered Barker spread wireless signal are

completely eliminated by this 3 bits buffered system. As a result, the sidebands in the

PSD are expected to be attenuated since the high frequency components that arise as a

result of any signal discontinuity are removed. The 8 state symbols used in this study are

shown in Figure 3.14.

50

0 0.5 1

x 10-6

-2

0

2Plot of bit +1; state 1

Time in s0 0.5 1

x 10-6

-2

0

2Plot of bit +1; state 2

Time in s

0 0.5 1

x 10-6

-2

0

2Plot of bit +1; state 3

Time in s0 0.5 1

x 10-6

-2

0

2Plot of bit +1; state 4

Time in s

0 0.5 1

x 10-6

-2

0

2Plot of bit -1; state 5

Time in s0 0.5 1

x 10-6

-2

0

2Plot of bit -1; state 6

Time in s

0 0.5 1

x 10-6

-2

0

2Plot of bit -1; state 7

Time in s0 0.5 1

x 10-6

-2

0

2Plot of bit -1; state 8

Time in s

Figure 3.14. Symbols for the 8 state 3 bits buffered system

The 3 bit sequence used in the line code can be represented as d-1, d0, d1, where d-1

is the previous bit, d0 is current bit to be sent, and d1 is the next bit. Table 3.2 shows the

symbol mapping employed by the line code based on this 3 bit sequence and Figure 3.15

shows the state transition diagram. Applying this map to Figure 3.14, it is possible to

51

check that there is always a smooth signal transition from the previous bit to the present

bit, and then onto the next.

Table. 3.2. Symbol mapping table for 3 bits buffered Barker spread system.

Bit stream d-1 d0 d1

State symbol transmitted

0 1 0 State #4 0 1 1 State #3 1 1 0 State #2 1 1 1 State #1 0 0 0 State #5 0 0 1 State #6 1 0 0 State #7 1 0 1 State #8

Figure 3.15. State transition diagram for 3 bits buffered Barker system

State 1

State 2

State 3

State 4

00 State 5

State 6

State 7

State 8

11

10

1011

01

0100

1011

00 01 10

11

00

01

52

This line coded system using sinusoidal pulse shaping system was simulated to

obtain the PSD shown in Figure 3.16. For result verification, the experimentally

generated PSD for this system is shown in Figure 3.17. The PSD of this system shows

the best spectral characteristics observed while dealing with Barker spread signals. The

sidebands were more attenuated than any of the other systems investigated in this study.

Table 3.3 shows the sideband attenuation achieved in comparison with the unmodified

rectangular Barker spread signal. As a result, a simple second order filter with a cutoff

frequency of 10 MHz is all that is needed to satisfy the spectral mask.

Table. 3.3. Comparison of PSD sideband attenuations (unfiltered 1 Mbps data signals)

Pulse Shape Used Second Lobe drop Third Lobe drop

Rectangular (No Buffer)

13.1 dB 17.2 dB

Sine-shaping (3 bits buffered)

26.0 dB 38.7 dB

0 0.5 1 1.5 2 2.5 3

x 107

-110

-100

-90

-80

-70

-60

-50

-40

-30Unfiltered signal PSD

Frequency in Hz

Pow

er in

dB

m

Figure 3.16. PSD of 3 bits buffered system with sinusoidal shaping

53

Figure 3.17. PSD of experimental 3 bits buffered system with sinusoidal shaping

The performance of this 3 bits buffered system was studied to see its BER versus

SNR performance. The system was simulated using random binary data, and the signal

was transmitted over an AWGN channel at various SNR levels. Correlation detection

using four correlators (states 1 to 4) was used in the simulated receiver side, and the BER

value was recorded. The results are shown in Table 3.4. The results show improved

performance compared to the control case (unmodified IEEE 802.11 1 Mbps Barker

spread system). However, compared to the systems described in Chapter 2, the

improvement is less significant as the correlation function (Figure 3.13) is less than ideal.

Table. 3.4. Simulated BER measurements for 3 bits buffered Barker spread system.

Bit Error Rate at SNR levels: Pulse Shape Used

Filter Order –11.5 dB –11 dB –10 dB

Rectangular (No Buffer) 5 3.70E-03 2.74E-03 9.00E-04

Sinusoidal 2 3.14E-03 2.14E-03 5.40E-04

54

CHAPTER 4

PULSE SHAPING FOR IEEE 5.5 MBPS CCK SIGNAL

4.1 CCK Pulse Shaping Methodology

In Section 1.6, we observed how the CCK time domain signal can be represented.

To recap, the transmitted signal, vc(t) can be represented as

( )θαπ +∠++= ),(2cos2)( knwtftv ncc , (4.1)

where αn is the differential phase for the n’th data symbol (from Table 1.1), ),( knw∠ is

the phase of the n’th data symbol’s k’th chip determined from Table 1.2, θ is an arbitrary

phase angle, and cf is the carrier frequency of the signal.

The 5.5 Mbps 802.11b signal in (4.1) can be expressed as

( ) ( )( ) cos 2 ( , ) sin 2 ( , )c I c Q cv t a f t w n k a f t w n kπ θ π θ= + ∠ + + + ∠ + , (4.2)

where, 2 cos( )I na α= , (4.3a)

and, 2 sin( )Q na α= − . (4.3b)

The implementation of the CCK spread signal uses αn ∈ {±π/4, ±3π/4} resulting in binary

(±1) sequences for aI and aQ at the chip rate. The signal in (4.2) can be rewritten as

( ) ( )( ) ( , )cos 2 ( , )sin 2c c cv t x n k f t y n k f tπ θ π θ= + + + , (4.4)

where, ( )( ) ( )( )( , ) cos , sin ,I Qx n k a w n k a w n k= ∠ + ∠ , (4.5a)

and, ( )( ) ( )( )( , ) sin , cos ,I Qy n k a w n k a w n k= − ∠ + ∠ , (4.5b)

with the index n representing the symbol number and the index k representing its kth

chip.

55

In this development, there are a total of 16 x vectors and 16 y vectors,

corresponding to the 16 c vectors for the CCK code used in 5.5 Mbps signal. The group

of 16 y vectors is exactly the same as the 16 x vectors but in different order. It is

important to note that this set of 16 vectors contains 8 groups with 2 identical vectors

each. Additionally, it was observed that for any vector C, there exists the negative of that

vector in another group. Therefore, we see that there are only 4 possible vectors C.

Table 4.1 shows the 4 possible vectors C.

Table. 4.1. Four possible vectors C.

Chip # 1 2 3 4 5 6 7 8 vector 1 –1 1 –1 –1 –1 1 1 1 vector 2 1 –1 1 1 –1 1 1 1 vector 3 1 1 1 –1 1 1 –1 1 vector 4 1 1 –1 –1 –1 1 1 –1

Furthermore, we notice that vector 2 can be obtained by simply reversing vector 3

and vice versa. Similarly, vector 1 can be obtained by reversing vector 4. Thus, there are

only two truly unique set of vectors in the 5.5 Mbps system, that is vectors 1 and 2. For

pulse shaping using the 5.5 Mbps system, these two vectors 1 and 2 only need to be

designed, thereby simplifying the effort considerably.

Several shaping functions like sinusoidal and sincm were used to shape the chips

in vectors 1 and 2. The resulting pulse shaped symbols still adhered to general shape of

the CCK code vectors. Then the two symbol vectors 1 and 2 were reversed to obtain the

pulse shaped symbols for vectors 3 and 4, completing the symbol set for vector C. Then

from C, the complete symbol set was obtained for all possible x and y vectors.

For each type of pulse shaping that was performed for vectors 1 and 2 as

described above, the communication system was simulated. Binary random data at a rate

56

of 5.5 Mbps was spread using the pulse shaped CCK symbols and the Welch method was

used to obtain the simulated PSD. The PSDs of the pulse shaped CCK systems were

compared to the PSD of the unmodified CCK system shown in Figure 1.7. Of particular

interest was the improvement in sideband attenuation. The pulse shaped CCK signals

showed marked improvement in spectral characteristics.

The PSDs of the pulse shaped CCK signals were also examined experimentally.

For the experimental PSD, however, a 5.5 Mbps data rate could not be used. Due to

hardware speed limitations, a 4 MHz chip-rate was used corresponding to a bit-rate of

2 Mbps with the 8 chip CCK code. Using 4 Mchips/second, the main-lobe bandwidth in

the experimental PSD comes out as 4 MHz. The experimental PSDs were compared to

the simulated ones to check if the results were in agreement.

The spectral mask could not be completely satisfied by symbol shaping alone and

filtering was still required. However, for the novel signals, only low order filters are

necessary to achieve the spectral mask and, thus, ISI is considerably reduced.

In order to examine the performance of the communication systems, BER

simulation studies were performed for each of the pulse shaped CCK systems in

MATLAB. In these studies, random binary data was CCK spread using the shape symbol

vectors to obtain a simulated transmit signal. A minimum order IIR filter was used to

filter the baseband information signal such that the PSD satisfied the spectral mask

without introducing excess ISI. AWGN noise was added to simulate the channel and the

SNR was recorded. After transmission through this simulated AWGN channel, a

synchronous correlation was used to decode the received bits. A total of eight correlators

were needed: one each for the four possible I and Q phase vectors. The decoded bits

57

were compared to the transmitted bits to obtain a BER value for the channel at the

recorded SNR level.

For purposes of easy comparison, the PSD of the 5.5 Mbps signal spread using the

unmodified rectangular chip CCK is repeated in Figure 4.1. A fourth order Butterworth

filter with a 9.0 MHz cutoff frequency is required to make this signal meet the spectral

mask requirement. The symbols representing the four vectors C are shown in Figure 4.2.

0 0.5 1 1.5 2 2.5 3

x 107

-90

-80

-70

-60

-50

-40

-30PSD plot

Frequency in Hz

Pow

er in

dB

m

Figure 4.1. Simulated PSD of 5.5 Mbps CCK signal with no pulse shaping

0 2 4 6

x 10-7

-1

0

1Plot of vector 1

Time in s0 2 4 6

x 10-7

-1

0

1Plot of vector 2

Time in s

0 2 4 6

x 10-7

-1

0

1Plot of vector 3

Time in s0 2 4 6

x 10-7

-1

0

1Plot of vector 4

Time in s Figure 4.2. Unmodified CCK symbols

58

4.2 Sinusoidal Pulse Shaping

Sinusoidal functions were used to shape the chips in the CCK vectors. The

sinusoidally symbol shaped vectors are displayed in Figure 4.3. Comparing with

Figure 4.2, notice that the pulse shaped CCK vector waveforms still follow the CCK

vectors’ chip values. The simulated PSD obtained by this shaping method is shown in

Figure 4.4. The experimentally obtained PSD is shown in Figure 4.5. An improvement

of 10 dB is obtained for attenuation of the first sideband, while the second sideband is

attenuated by 15 dB more than the system without any pulse shaping. As a consequence,

the spectral mask is met by using a second order Butterworth filter with a 8.75 MHz

cutoff frequency.

0 2 4 6

x 10-7

-1

0

1

Plot of vector 1

Time in s0 2 4 6

x 10-7

-1

0

1

Plot of vector 2

Time in s

0 2 4 6

x 10-7

-1

0

1

Plot of vector 3

Time in s0 2 4 6

x 10-7

-1

0

1

Plot of vector 4

Time in s

Figure 4.3. CCK symbols shaped by sinusoidal functions

59

0 0.5 1 1.5 2 2.5 3

x 107

-90

-80

-70

-60

-50

-40

-30PSD plot

Frequency in Hz

Pow

er in

dB

m

Figure 4.4. Simulated PSD for CCK symbols shaped by sinusoidal functions

Figure 4.5. Experimentally obtained PSD for CCK symbols shaped by sinusoidal

functions

4.3 Sincm Pulse Shaping

Functions of the form sincm were used to shape the chips in the CCK vectors. The

symbol shaped vectors designed in such away are displayed in Figure 4.6. The simulated

60

PSD obtained by this shaping method is shown in Figure 4.7, and the experimentally

obtained PSD in Figure 4.8. An improvement of 7 dB is obtained for attenuation of the

first sideband, while the second sideband is attenuated by 7 dB more than the system

without any pulse shaping. Filtering by a third order lowpass filter (cutoff frequency 9.5

MHz) is necessary here also.

With sincm pulse shaping for the CCK spread 5.5 Mbps signal, the spectral

improvements are not as good compared to the application of sincm for shaping the

Barker spread 1 Mbps signal. Nevertheless, spectral improvement is observed.

0 2 4 6

x 10-7

-1

0

1

Plot of vector 1

Time in s0 2 4 6

x 10-7

-1

0

1

Plot of vector 2

Time in s

0 2 4 6

x 10-7

-1

0

1

Plot of vector 3

Time in s0 2 4 6

x 10-7

-1

0

1

Plot of vector 4

Time in s

Figure 4.6. CCK symbols shaped by sincm functions

61

0 0.5 1 1.5 2 2.5 3

x 107

-90

-80

-70

-60

-50

-40

-30PSD plot

Frequency in Hz

Pow

er in

dB

m

Figure 4.7. Simulated PSD for CCK symbols shaped by sincm functions

Figure 4.8. Experimentally obtained PSD for CCK symbols shaped by sincm functions

4.4 BER Measurements

The BER vs SNR simulation study for the CCK signals was mentioned in

Section 4.1. Each of the pulse shaped systems, including the unmodified rectangularly

62

shaped CCK waveform was subjected to this study using 200,000 random bits in order to

test the system performance. The results of the BER versus SNR studies are shown in

Figure 4.9. The specifications for the Butterworth filter used to satisfy the spectral mask

are included in the table. The filter order is indicative of the amount of ISI introduced,

and the system performance is indicated by the BER values.

Figure 4.9. Simulated BER vs SNR measurements for CCK symbol shaping

The simulated BER results show that the sincm function pulse shaped 5.5 Mbps

CCK system has lesser ISI and performs about 1 dB better (in terms of BER versus SNR)

than the rectangular system. Compared to the Barker spread signal, there is somewhat

greater improvement (about 0.5dB) in the system performance for the CCK spread signal

through pulse shaping. The Barker signal is BPSK, but the CCK spread signal is QPSK.

By filtering any signal, ISI occurs in both the I and Q phases. However, for the Barker

spread system this is no issue as it is a BPSK signal and Q phase ISI has no effect.

However, for the QPSK CCK signals, this effect has a greater impact leading to signal

63

distortion. Since filtering adversely affects CCK signals more, reducing the spectral

mask filter’s order provides increased gain in performance for CCK spread.

The spectral improvements for using the pulse shaped CCK systems are

summarized in Table 4.2. The table shows the attenuation in peak lobe powers.

Additionally, Table 4.3 shows the total amount of sideband energy leakage in the PSD of

the various signals. For lower sideband powers, there is lesser interference caused to

nearby Wi-Fi channels.

The composite PSD plot showing the PSD of the different CCK systems is shown

in Figure 4.10. Notice that the sinusoidal system performed the best both in terms of

spectral improvement and in terms of the better system performance with respect to the

BER vs SNR study. The rectangular unmodified 5.5 Mbps CCK signal performed worst

in both aspects. Thus, the results show that the IEEE 802.11 5.5 Mbps CCK signal can

be considerably improved by symbol shaping.

Table. 4.2. Comparison of PSD peak sideband drops (unfiltered 5.5 Mbps data signals)

Pulse Shape Used Second Lobe drop Third Lobe drop

Rectangular 13.3 dB 17.4 dB Sinusoidal 23.0 dB 32.9 dB

Sinc-function 19.8 dB 24.2 dB

Table. 4.3. Comparison of total power in each band (unfiltered 5.5 Mbps CCK signals)

Pulse Shape Main Lobe

Power %

Second Lobe

power %

Third Lobe

power %

Second Lobe drop

(dB)

Third Lobe drop (dB)

Rectangular 90.6 5.08 2.02 12.5 16.5 Sinusoidal 99.4 0.417 0.075 23.8 31.2

Sinc-function 98.6 0.91 0.301 20.3 25.1

64

Table 4.4 quantifies the amount of ISI occurring in each system, where the metric

is the amount of energy in one symbol that leaks into the next symbol interval. We notice

that the rectangular system has almost 5% energy leakage due to ISI compared to only

2.4% for the sinc case.

Table. 4.4. ISI after filtering operation for CCK symvol shaping

Pulse Shape Power within Bit Interval (%)

Power leakage outside Bit Interval (%)

Rectangular 93.8 6.2 Sinusoidal 97.6 2.4

Sinc-function 97.2 2.8

Figure 4.10. Experimentally obtained composite PSD plots for CCK symbol shaping

Sincm pulses

Rectangular pulses

Sinusoidal pulses

65

CHAPTER 5

EXPERIMENTAL STUDY OF MICROWAVE OVEN SIGNAL

5.1 Main Features of MWO Signal

As mentioned in Chapter 1, the 2.4 GHz band is dominated by high-speed data

communications and Wi-Fi. Access points, wireless laptops, Personal Digital Assistants,

Bluetooth [GUI04] devices, and cordless phones [BAT01] all intentionally operate in this

band for the purpose of communicating. On the other hand, various commercial devices

not intended for Wi-Fi communications, such as microwave ovens and other residential

and industrial products, also radiate in the 2.4 GHz band. The emitted electromagnetic

RF signals they produce act as interference to Wi-Fi users. The composite interference

from intentional Wi-Fi transceivers and unintentional emitters results in reduced network

performance, and even connectivity loss. The microwave oven is one of the most

common unintentional interference device [KAM97].

There are two types of MWOs: residential and commercial MWOs. The

residential MWO contains a single magnetron that periodically turns on and off as the

60 Hz AC line voltage changes from positive to negative [GAW94]. Thus, the MWO

signal goes through ON and OFF cycles characterized by the respective presence and

absence of RF radiation. A commercial MWO has two magnetrons that operate 180

degrees out of phase such that energy is always radiated into the MWO cavity. RF

energy leaking from the MWO cavity causes interference in the 2.4 GHz ISM band. In

this research project, the interference signal from the residential MWO was studied in

detail [TAH06].

66

In this chapter, an overview of MWO operation is provided, as well as

experimental signal characteristics. In particular, we explore the frequency-sweeping

phenomenon of the MWO signal, the envelope of the MWO signal in the time domain,

and the transient signals that exist in the MWO signal but have been often overlooked in

prior MWO studies.

5.2 FM Signal

The residential MWO signal, in the ON mode, is similar to a Frequency

Modulated (FM) signal [PRO94], with a fixed carrier frequency, and an instantaneous

frequency that changes with time. The MWO center frequency varies with the

manufacturer and model, but for the models tested, it was in the 2.45 GHz range. The

MWO signal is repetitive in nature with a period of 16.67 ms, which is the inverse of the

60 Hz frequency of the AC supply line powering the MWO. However, the frequency-

sweep in the MWO signal is less than half of the 60 Hz time period, typically 5-6 ms.

This is shown in the spectrogram in Figure 5.1, where the sweep of the MWO signal is

clearly seen. Figure 5.2 repeats the same spectrogram image but without any markings

for visual clarity. This figure also shows transients before and after the frequency-sweep.

The spectrogram is particularly useful in developing a model for MWO emissions

because it experimentally reveals the characteristics of the frequency-sweeping and

transient aspects of the MWO signal. All the spectrogram plots were obtained using the

ComBlock receiver described in Section 1.7. The spectrogram’s bandwidth is 20 MHz.

This is because the digital sampling rate of the ComBlock is 40 MHz, and, according to

the Nyquist criterion [PRO96], a maximum 20 MHz bandwidth of spectral information

can be obtained from this digitally sampled data. MATLAB’s “spectrogram” function

67

[MAT07] was used to obtain the plots from the data. The function compartmentalizes the

signal versus time data, and for each such subset of data, it estimates the frequency

spectrum using algorithms based on the fast Fourier transform [PRO96].

During the frequency-sweeping part of the ON cycle, the radiated signal does not

behave like conventional FM where the power level is constant. However, the signal can

be characterized as an FM signal with varying power levels. The latter property lends

itself to an Amplitude Modulated (AM) mode [PRO94]. Thus, a combined AM-FM

waveform will serve as a basis for the frequency-sweeping part of the signal [TAH06].

The approximate sinusoidal shape in Figure 5.1 represents the FM signal that sweeps the

spectrum over 15 MHz for approximately one half of the 60 Hz AC cycle. A thorough

investigation for the amplitude of the MWO signal is detailed in Section 5.3.

Figure 5.1. Spectrogram of MWO signal with key features labeled

Transients

AM-FM Signal

A B

68

Figure 5.2. Clean Spectrogram of MWO signal

5.3 Amplitude Variation

The envelope of the MWO signal varies significantly during the ON cycle. To

study the characteristics of the actual envelope of the MWO signal, measurements were

carried out in the WIL. The Zero-Span Mode (ZSM) of a Rohde & Schwarz Spectrum

Analyzer (model no. FSP 38) was used to capture the envelope of the RF MWO signal.

The spectrum analyzer’s Resolution Bandwidth (RBW) was set to 10 MHz and the center

frequency to 2.455 GHz. The time domain MWO signal captured by the spectrum

analyzer is shown in Figure 5.3. Observe that the oven is on about half of the 60 Hz

cycle. The amplitude of the MWO signal can be approximated by a sinusoidal waveform

when the microwave oven is on. Careful observation of Figure 5.1 also gives support of

this approximation. The increase in shading indicates that the power of the AM-FM

signal increases during the ON cycle and then decreases as it approaches the OFF cycle;

the power depends on the amplitude and, hence, the amplitude change is also observable

in the spectrogram.

69

Figure 5.3. The envelope of the MWO signal over two 60 Hz cycles (3.33 ms/div)

It is important to notice the transient signals at the beginning and end of each ON

cycle in Figure 5.3. These transient signals, together with the frequency-sweeping signal,

comprise the radiated MWO signal. The transient signals are studied in detail in

Section 2.4.

5.4 Transients

The transient part of the MWO was observed in Figures 5.1 to 5.3. In each period

of the MWO signal, there are two transient signals, one occurring at the beginning and

another occurring at the end of the ON cycle of the MWO. The characteristics of the

transient signals in the time and frequency domains are further investigated here.

Numerous ZSM measurements were taken to estimate the bandwidth of the transient

signal as well as its duty cycle. The ZSM captures were obtained at different frequencies

across the ISM band, using a narrow resolution bandwidth of 10 kHz. If a periodic

transient signal was detected at that ZSM center frequency, then its power and duty cycle

were measured.

70

To synchronize all the ZSM captures of the transient signal at different

frequencies, a 60 Hz line trigger was used. With this experimental setup, the zero-span

captures of the transient signals at different frequencies are aligned. This is illustrated in

Figure 5.4 where the periodic transient signals are at the same time locations, even

though the capturing frequencies are different (2.46 GHz and 2.44 GHz). Observe that

the width of these transient signals is approximately 1 ms at both the frequencies in

Figure 5.4, with the turn-on transient slightly longer than the turn-off transient.

Figure 5.4. Zero-span measurements at 2.46 GHz and 2.44 GHz over two 60 Hz cycles (3.33 ms/div)

A programmed spectrum analyzer captured a series of ZSM measurements at

uniformly spaced frequencies over the 85 MHz ISM band to estimate the bandwidth of

the turn-on and turn-off transients. Measuring the periodic time-varying power

signatures of the transient signal over the 2.4 GHz ISM band and combining all the zero-

span captures, an experimental spectrogram was generated showing the transient signals.

The contour plot of the spectrogram is shown in Figure 5.5 over one power cycle with the

Transients

Transients

Turn-on Turn-off Turn-on Turn-off

71

low-level noise suppressed. The transient signals are broadband, extending over 60 MHz

in bandwidth. Also, the power of the transient signals is concentrated at frequencies

where the sweeping part of the MWO signal meets the transient part in the spectrogram

plot (see points A and B in Figure 5.1).

The spectrogram obtained using this method has a bandwidth of 80 MHz, that is,

four times the ComBlock spectrogram’s bandwidth. Hence, this ZSM based spectrogram

method was utilized to study the very wideband MWO transient signals. The limitation

of this ZSM based spectrogram method is that it can be used to obtain power versus

frequency and time plots only for periodic signals. The advantage of this method is that

large bandwidth spectrograms are obtainable.

It is useful to understand why the transients occur in the MWO. The MWO

magnetron needs a minimum threshold voltage (Volt A, Figure 5.6) to operate, i.e., to

emit microwave energy. Since Volt A is positive, the time duration for the ON cycle is

less than that of the OFF cycle. This is observable in Figures 5.1 to 5.3.

Figure 5.5. An experimental spectrogram for transient signals over one 60 Hz cycle (2 transient signals)

72

Figure 5.6. MWO signal generation process

The minimum threshold voltage (Volt A) is inadequate for sustained operation of

the magnetron. A second threshold (Volt B > Volt A) is required for the MWO to

generate a frequency-sweeping signal. Between the two thresholds, the MWO emits

wideband transient pulses. The transient areas are shown shaded in Figure 5.6. The

threshold values and the transient times are manufacturer dependant, with a nominal

transient duration of 1 ms. Obviously, transients are periodic and synchronized to the AC

line signal.

5.5 MWO PSD

Figure 5.7 shows the PSD of an actual MWO, experimentally measured in the

WIL. The maximum power is concentrated at the higher frequencies, that is near the

frequency-swept region shown in Figure 5.1 (points A and B). The power in the lower

frequencies comes from the transients shown in the spectrogram of Figure 5.5 and is

Time (s)

Threshold Volt A

Threshold Volt B

ON OFF

Transients

73

25 dB weaker in strength. Similar characteristics were observed for other MWOs

(Figures 5.8 to 5.10) whose spectra were measured.

Figure 5.7. Experimental PSD for MWO 1 (center 2.42 GHz, 12 MHz / division)

Figure 5.8. Experimental PSD for MWO 2 (center 2.45 GHz, 10 MHz / division)

74

Figure 5.9. Experimental PSD for MWO 3 (center 2.45 GHz, 10 MHz / division)

Figure 5.10. Experimental PSD for MWO 4 (center 2.43 GHz, 10 MHz / division)

75

CHAPTER 6

MODEL OF MICROWAVE OVEN SIGNAL

6.1 Necessity of MWO Model

An analytical model is highly useful in wireless network simulation studies. For

example, simulations that study wireless network throughput and performance must

account for RF interference from other radiating sources. If this interference is a

microwave oven, a model of the device becomes necessary [TRA04]. In this chapter,

two MWO analytical models have been developed. A good analytical model can be

utilized in wireless network simulation as one of the wireless interferers operating in the

simulated physical layer [JER92]. Also, a proper model allows better understanding of

the RF signal from a MWO, which is important in understanding the nature of wireless

interference caused by MWO and in developing interference mitigation techniques.

Indeed, the model is used in Chapter 7 to develop an interference mitigation technique.

6.2 MWO Model #1

From the experimental data and analysis presented in Chapter 5, an analytical

model was developed [TAH06]. The MWO signal can be expressed as the sum of two

wideband transient signals and a frequency-swept signal during the ON cycle, and zero

during the OFF cycle. The frequency-swept signal is modeled as an AM-FM signal.

Based on the shapes of the MWO signals in Figures 5.1 and 5.3, the frequency-swept

signal, s(t), is modeled as a sinusoidally modulated FM signal with a sinusoidally shaped

amplitude, x(t). Here, both the modulations are at the 60 Hz line frequency.

76

The 1 ms (approximate) transient signal pulse was modeled as the sum of two sinc

waveforms modulated at different carrier frequencies. The two sinc pulses also have

different main lobe widths in the time domain and thus different bandwidths in the

frequency domain. One sinc waveform has a wide spectral bandwidth to provide power

across the entire ISM band, while the other sinc waveform has a narrower bandwidth

with power concentrated in the frequency-swept band. The transient bandwidths are 40-

80 MHz and the main lobe of each sinc waveform is in the order of nano-seconds.

Figure 6.1 shows a qualitative plot of the time domain locations of these signals for each

ON cycle.

Figure 6.1. Qualitative representation of MWO signal model

The complete MWO signal, v(t), can be expressed as the sum of ON cycle wave-

shapes, c(t), that is,

( ) ( )n

v t c t nT∞

=−∞

= −∑ , (6.1)

where T = 1/fac and fac = 60 Hz.

Using the structure shown in Figure 6.1 and the signal description above, the ON

cycle wave-shape can be written as,

The two transient signals are centered in each of these locations

The frequency sweeping FM and

AM modulated signal. The cosine shape shows the AM modulating envelope used.

Time (ms)

77

1 1 1

2 2 2

1 1 1

2 2 2

( ) ( ; ) cos(2 )( ; )cos(2 )

( )( ; ) cos(2 )( ; ) cos(2 ) ,

a

a

a

a

c t A p t t b f tA p t t b f ts tA p t t b f tA p t t b f t

ππ

ππ

= +

+ +

++ −

+ −

(6.2)

where the pulse waveform, p(t), is,

( ; ) sinc ( ) , 0.5 ,pp t b bt t T= < (6.3)

The power in the transient pulses is dictated by the amplitudes, A1 and A2, and the

center of their spectra is determined by the carrier frequencies, f1 and f2. The time

locations of the transient pulses are at ± ta and their duration is Tp. The bandwidths of the

two transients are determined by b1 and b2.

The AM-FM signal, with sinusoidal modulation, can be written as,

( )( ) ( ) cos 2 sin(2 ) , 0.5 ,c ac ss t A x t f t f t t Tπ β π= + < (6.4)

where the amplitude variation is given by,

( ) cos(2 ).acx t f tπ= (6.5)

The power in s(t) is dictated by the amplitude A and the sweep time, Ts. The peak

frequency deviation is determined by the modulation index, β, while Ts and β determine

the frequency-swept band. The center frequency of the magnetron is given by fc.

Using the model, any MWO signal can be represented by a total of 12 parameters.

It is, of course, possible to refine the model with different pulse widths for the turn-on

and turn-off transients, non-symmetric pulse locations, and other pulse shapes. However,

the 12 parameter model, when simulated, provides reasonable agreement to experimental

measurements as detailed in the next section.

78

6.3 MWO Model #1 Simulation

The analytical model presented in the previous section was simulated using

MATLAB. The simulations were carried out in the MHz and kHz ranges for

computational convenience. Our simulations have shown that this analytical model is

scalable to all frequencies and bandwidths as the general characteristics of the PSD and

the spectrogram are preserved. Figure 6.2 shows the Welch PSD estimate for one

simulation run, and Figure 6.3 shows its spectrogram. Here, the FM carrier frequency

was set to 1 MHz and the FM sweep bandwidth was set to 0.05 MHz. In this simulation,

the transient bandwidths are each 0.05 MHz, and the transient carrier frequencies, f1 and

f2, are chosen so that the combined transient spectra span a 0.1 MHz range.

Figure 6.2. Simulated PSD of the MWO signal (carrier frequency in 1 MHz range)

Frequency (MHz)

79

Figure 6.3. Simulated spectrogram MWO signal (carrier frequency in 1 MHz range)

In a second simulation, the FM carrier frequency was set to 100 kHz, the sweep

bandwidth was fixed at 10 kHz and the total transient bandwidth was set at 20 kHz. The

PSD and the spectrogram are displayed in Figures 6.4 and 6.5, respectively. In this case,

the lower power wide transient bandwidth was 20 kHz and the higher power narrow

transient bandwidth was 10 kHz. Here, f2 was set so that the narrow transient signal’s

spectrum overlapped with frequency-swept band.

Figure 6.4. Simulated PSD of the MWO signal (carrier frequency in 100 kHz range)

Frequency (kHz)

Frequency (MHz)

80

Figure 6.5. Simulated spectrogram of MWO signal (carrier frequency in 100 kHz range)

We see that the simulation results, for the analytical model introduced in

Section 6.1, capture the main features of the actual MWO PSD. The maximum power is

concentrated at the higher frequencies in the frequency-swept region. The power in the

lower frequencies comes from the transients and is 25 dB weaker in strength. This

reduced PSD level is seen both in experimental and simulated results. The simulated

spectrograms in Figures 6.4 and 6.5 compare quite well with the experimental

spectrogram shown in Figure 5.1. However, greater similarity between the simulated

model and experimental measurements from actual MWO devices is desired.

6.4 Drawbacks of Model #1

The model developed in Section 6.2 (model #1) has three major drawbacks.

These limitations with model #1 necessitate modifications in order to obtain an analytical

model that better captures the characteristics of MWO ovens in general.

The first problem with model #1 is that for a bandwidth of 50 MHz, the transient

durations come out to be in the order of nanoseconds as opposed to milliseconds. This is

Frequency (kHz)

81

because for the sinc pulse used in the model, the time domain duration of the main lobe

of the pulse is inversely proportional to the signal’s frequency domain bandwidth. Thus,

for a signal bandwidth in the MHz range, the transient duration comes out only in the

order of hundreds of nanoseconds. However, we know from Chapter 5 that the transients

last for about a millisecond: a discrepancy of fourth order magnitude between the model

and actual MWO signals.

Second, the FM carrier frequency of a MWO is not constant but varies. This is

dramatically illustrated by the spectrogram of an old 1980s MWO in Figure 6.6.

Although the newer MWO devices do not have such highly fluctuating characteristics,

the carrier frequencies are not stationery either. Careful observation of the spectrogram

in Figure 5.2 reveals that the AM-FM signal carriers on adjacent ON cycles differ.

Figure 6.6. Experimental spectrogram of an older MWO

Finally, we notice from Figures 5.2 and 5.5 that the transient power PSD is not

flat. However, model #1 treated the transient power PSD essentially as flat PSD, albeit

Time(s)

Freq

uenc

y (H

z)

82

with two discrete power levels. From Figures 5.2 and 5.5, the varying transient power

level can be approximated by means a bell curve, but with a short tail on the high

frequency curve.

A second analytical model, MWO model #2 was thus developed [TAH08a] in

order to address these issues. This is described in the following sections.

6.5 MWO Model #2

In model #2, the transient duration problem was corrected and the carrier

frequency from one ON cycle to the next was made random. The transients were

formulated as a sum of sinc pulses modulated at uniformly spaced frequencies, where the

sinc pulse power was a function of the frequency following a modified Rayleigh

distribution shown by the left sub-plot in Figure 6.7. If in the frequency and power axes,

this distribution (left sub-plot) is compared with the transient spectrogram (right sub-plot

in Figure 6.8), satisfactory correlation is obtained.

Figure 6.7. Remodeling the transients. Left sub-plot shows the plot of function used to

control the frequency domain power of the transients. Right sub-plot shows experimentally measured transient powers for an MWO.

Frequency (GHz)

Tim

e (m

s)

2.4 2.41 2.42 2.43 2.44 2.45 2.46 2.470

2

4

6

8

10

12

14

16

2.4 2.42 2.44 2.46 2.48 2.5

x 109

0

0.2

0.4

0.6

0.8

1

Frequency (GHz)

Nor

mal

ized

Am

plitu

de

Transient Power vs frequency in model

83

Based on these three modifications, analytical model #2 of the MWO signal was

developed as a derivative of the earlier model #1. During each period, the signal can be

expressed as a sum of two transients and an AM-FM signal to represent the frequency

swept signal. As in the previous model #1, the modeled AM-FM signal, s(t), consists of a

sinusoidally modulated FM signal with a sinusoidally shaped amplitude, x(t). The AM

and FM modulations are both sinusoidal in nature at the 60 Hz line frequency.

The large bandwidth of the transient signals was modeled as the sum of sinc

pulses modulated at different subcarrier frequencies. Figure 6.8 shows a qualitative plot

of the time domain locations of these signals for each ON cycle.

Figure 6.8. Qualitative representation of MWO #2 signal model

The complete MWO signal, v(t), can be expressed as the sum of ON cycle wave-

shapes, c(t), that is,

( ) ( )n

v t c t nT∞

=−∞

= −∑ , (6.6)

where T = 1/fac and fac = 60 Hz.

Using the structure shown in Figure 6.8 and the signal description above, the ON

cycle wave-shape can be written as

Time (ms)

The two transient signals are centered in these locations

The frequency swept AM-FM modulated signal.

Ts

TP TP

td td

84

( ) ( ) ( )

( ) ( ) ( )

1

1

( ) cos 2

cos 2

( ),

N

n d nn

N

n d nn

c t E f p t t f t

E f p t t f t

s t

π

π

=

=

= −

+ +

+

∑

∑ (6.7)

where the transient pulse waveform is given by

( )( ) sinc ( + ) , 0.5 ,n pp t b t t Tλ= < (6.8)

with b a bandwidth parameter (usually 4 kHz), TP the width of the transient pulse

centered at ± td , and λn a random variable uniformly distributed over ± 0.5Tp to provide a

time offset for each sinc pulse in the transient signal summation.

The transient signal is the sum of N sinc pulses modulated by subcarriers, fn ,

uniformly spaced from f1 to fN . Here, f1 and fN are the minimum and maximum values of

fn , respectively, such that (N – 1)b = fN – f1 . The energy in each sinc pulse is determined

by the function E( fn). Several curve fitt ing functions were tested for E( fn)

but best results were obtained with a modified Rayleigh function [RAP02]

defined as

( )2

2( )

22

( ) ,N n

h

f ffN n

n Oh

f fE f E ef

−−−

= (6.9)

where ,h N pkf f f= − (6.10)

EO is an amplitude scale factor, and fpk is the subcarrier frequency with the maximum

transient energy.

The AM-FM signal, with sinusoidal modulation, can be written as

( )( ) ( )cos 2 sin(2 ) , 0.5 ;c ac ss t A x t F t f t t Tπ β π= + < (6.11)

where the amplitude variation is given by

85

( ) cos(2 )acx t f tπ= , (6.12)

and the power in s(t) is dictated by the amplitude, A, with the sweep time given by Ts.

The peak frequency deviation is determined by the modulation index, β. The carrier

frequency of the AM-FM signal is a random variable, Fc, that is uniformly distributed

between frequencies fa and fb. During any given period, Fc is fixed, but it varies from one

ON cycle to the next. The operating range of Fc, that is fb – fa, is typically 5 MHz.

Using the model, any MWO signal can be represented by appropriately choosing

a set of 13 independent parameters. This model, when simulated and emulated, provides

very good agreement to experimental measurements as detailed in the next section.

6.6 MWO Model #2 Simulation

The model described in the previous section was studied by experimentation and

via simulation to examine its accuracy. The model #2 described was simulated in

MATLAB software. Simulations were performed in the megahertz range for

computational convenience. Simulations at higher and lower frequency ranges have

shown that the model is scalable to all frequencies and bandwidths without altering the

general signal characteristics. Figure 6.9 shows a spectrogram obtained using the

simulated model. Figure 6.10 shows the PSD computed over 100 cycles. The parameters

were chosen such that the PSD in Figure 6.10 closely matched the characteristics of the

MWO PSD shown in Figure 5.7. For computational feasibility, however, the MWO total

bandwidth was limited in simulation to 1.5 MHz compared to the 60 MHz bandwidth of

the experimental MWO in Figure 5.7.

86

Figure 6.9. Spectrogram of simulated MWO signal

Figure 6.10 Simulated PSD of MWO signal

6.7 Model #2 Experimental Emulation

To verify the simulation studies and to further validate the model, the MWO

model was emulated experimentally such that the model parameters matched with a

different MWO whose PSD is shown in Figure 6.13. This experimentation was done as

87

part of the three pronged approach to check if the simulation results could be verified

independently by emulation. For this purpose, a ComBlock transmitter unit operating in

the 2.4 GHz range was used to emulate the MWO signal based on the model equations.

Figure 6.11 shows the experimentally emulated spectrogram. Figure 6.12 is the PSD of

this emulated signal obtained with a spectrum analyzer. Due to experimental limitations,

the emulated MWO model’s bandwidth was limited to 1.5 MHz as opposed to 50 MHz

for the actual MWO PSD in Figure 6.13. The simulation and emulation studies show that

the model is a good approximation to the MWO signal. Furthermore, they demonstrate

that the model’s parameters are readily adjustable to approximately match the

characteristics of different MWOs.

Figure 6.11. Spectrogram of emulated MWO #2 signal

88

Figure 6.12. PSD of emulated MWO signal measured by spectrum analyzer

Figure 6.13. Experimental PSD of actual MWO

89

CHAPTER 7

MICROWAVE OVEN SIGNAL INTERFERENCE MITIGATION FOR IEEE 802.11 SYSTEMS

7.1 Interference Mitigation Technique

While the CSMA protocol is effective in Wi-Fi collision avoidance, the MWO is

oblivious to this type of interference avoidance. Hence, an alternate interference

mitigation mechanism needs to be developed. In this section, a technique that allows

Wi-Fi devices to avoid interference caused by MWO signals is outlined. From Chapter 5,

it was seen that the frequency-swept part of the MWO signal spans a relatively narrow

bandwidth (approximately 15 MHz). The transient signal bandwidths are much larger

(60 MHz or more) and they occupy the entire ISM band. Due to this relatively large

bandwidth, the MWO affects data communications in all IEEE 802.11 channels [AVA02]

[INT98] [ZHA05]. However, the transient bursts are periodic. Thus, if the transient time

locations are known, then MWO interference can be avoided by simply stopping data

transmission during those time intervals.

Consider the case in which an IEEE 802.11 signal is being transmitted at

channel 1, centered at 2.412 GHz, with a main-lobe bandwidth of 22 MHz. The MWO

frequency-swept spectrum does not impinge on channel 1, so we can freely operate in

this channel during the OFF cycle and during the time interval when the MWO emits the

AM-FM signal. Since the transient signals exist for only 2 ms out of the 16.67 ms period,

then in theory, 88% of the time, MWO interference can be avoided in channel 1.

Now, consider the case when another common IEEE 802.11 channel is being

used, that is, channel 11, which is centered at 2.462 GHz. The MWO frequency-swept

90

signal and the transient pulses both interfere with this channel. However, during the OFF

cycle, that is 50-60% of the time, the MWO signal interference can be avoided while

transmitting in channel 11. For each IEEE 802.11 channel and MWO spectral signature,

an effective interference mitigation paradigm can be formulated.

For MWO interference mitigation, the Wi-Fi transmitter must be synchronized

with the AC line signal. For Wi-Fi devices with AC power, the synchronization is

relatively easy to achieve. Once synchronized, the position of the transient pulses can be

estimated from the zero crossings of the AC voltage, the average duration of the transient

pulses, and the average frequency-sweep time. For the Wi-Fi devices that are battery-

powered, synchronization can be done by using the 60 Hz periodic transient bursts of the

MWO signal that are detectable throughout the ISM band. To implement MWO

emission mitigation, the Wi-Fi device simply requires a detector that uses the signature of

the MWO interference signal to identify when a MWO is operating. The MWO

model #2 developed in Chapter 6 can be used as a reference MWO signature that is

compared to receive RF signals to detect when MWO interference is present.

The MWO interferer is present when there is a 60 Hz periodic signal in the ISM

band, synchronized with the AC line voltage. If the Wi-Fi device is using channel 11, it

can switch to a channel outside the frequency-swept band, like channel 1, or employ a

mitigation mode where it only transmits during the OFF cycle duration. Any Wi-Fi

device operating on channel 1 (or on other channels outside the frequency-swept region)

can transmit data in the manner shown in Figure 7.1, i.e., it transmits at all times other

than when the transients are present. For data transmission in IEEE 802.11 channel 11

can be achieved by the scheme shown in Figure 7.2. As part of this research project, the

91

interference mitigation technique illustrated by Figure 7.2 was implemented [TAH08b]

using a cognitive radio [GOL05] circuit and is described in this chapter.

Figure 7.1. Data transmission using 802.11 channel 1 (shaded areas are transient locations)

Figure 7.2. Spectrogram of MWO signal & interference mitigation

7.2 Circuit Design and Description

Figure 7.3 shows the block diagram for the interference mitigation circuit

developed in this research project. The mitigation principle is based on Figure 7.2. For

DATADATA DATA DATAThreshold Volt B

Threshold Volt A

Time (ms)

Experimental MWO #1 Spectrogram

Frequency Sweep/AM-FM Transients

Data Data Data

Transmit Data Packets during OFF cycles

92

successful interference mitigation, it is necessary to detect the presence of MWO

interference signals and synchronize the data transmitter with the MWO’s ON-OFF

cycles. The signature of a radiating MWO signal is detected and a Wi Fi transceiver is

controlled to communicate only during the OFF cycles. The function of each system

block is described in the following paragraph.

Figure 7.3. Block diagram for MWO interference mitigation system

The 2.4 GHz ISM band signal received by the antenna is down-converted by the

baseband converter in Figure 7.3. The threshold detector senses any received signal

above the background noise threshold. The transient detector compares the threshold

detector output, yT (t), with the AC line reference signal. If the timing of yT (t) matches

the expected MWO transient time location, then the cognitive radio records the detection

of a transient. The expected transient time locations are 2 ms time durations before or

after the zero voltage crossings of the sinusoidal AC line reference. If the transient

detector records the presence of several transient pulses over consecutive AC line cycles,

the cognitive radio circuit concludes that a MWO interference signal is present. This

smart radio system ignores all Wi-Fi signals and only triggers when a MWO signal is

present.

Baseband Converter

Threshold Detector

Transient Detector

Transmit Controller (50

/ 100 %)

60 Hz AC Line Reference

yT (t)

Baseband Logic Circuit

93

If a MWO signal is present, the transmit controller instructs the Wi-Fi transmitter

to synchronize with the AC line cycle and operate only during the MWO OFF cycles. If

the MWO signal is not detected, the Wi-Fi transmitter is instructed by the transmit

controller to operate normally. A circuit was constructed that successfully implements

the interference mitigation function [TAH08b]. The circuit was constructed and was

tested to work properly. Figure 7.4 is a photograph of the baseband logic circuit. Figure

7.5 shows its PSpice [PSP07] circuit diagram.

Figure 7.4. Photograph of Interference mitigation circuit (left) showing digital logic chips. The ComBlock transmitter (right) is being controlled by this circuit.

94

Figu

re 7

.5.

Bas

eban

d lo

gic

cont

rol c

ircui

t dia

gram

mad

e in

PSp

ice

95

7.3 Experimental Setup

An experimental Wi-Fi communication system was used to transmit and receive

digital data in the presence of MWO interference. The Wi-Fi signal was transmitted by

the ComBlock transmitter at a rate of 363 kbps with the 11 chip Barker spreading code.

This data signal’s bandwidth is 8 MHz. This signal was chosen because it is very similar

to the 1 Mbps data rate IEEE 802.11 signal that is used to transmit the physical layer

convergence protocol [CON00] and often data for wireless local area networks. Thus,

the results of this interference mitigation study applied to the 8 MHz Wi-Fi signal are

well applicable to IEEE 802.11 Wi-Fi systems in general.

The data is transmitted in 128 bit packets by the ComBlock transmitter. The

ComBlock receiver captures and decodes the data packets. The transmitted and received

packets are compared to get the experimental BER. In all experiments, the receiver was

placed in a position equidistant from the Wi-Fi transmitter and an interfering MWO.

Three different MWOs were used in the BER study. Four experimental scenarios were

tested for each MWO and the BER was recorded each time. Case 1 is shown by the

spectrogram in Figure 7.6. Here, the Wi-Fi transmitter operates at 2.46 GHz without any

interference mitigation. In this frequency range the AM-FM signal of the MWO exists

and hence there is high interference. Case 2 is shown in Figure 7.7, where the

interference is mitigated and the Wi-Fi transmitter frequency is still at 2.46 GHz. In

Case 3 and Case 4, the Wi-Fi transmitter carrier frequency is at 2.448 GHz, where there

is less interference as only low duty-cycle MWO transients exist. Interference is not

mitigated in Case 3 but it is mitigated in Case 4 by the cognitive radio system. The

spectrograms for cases 3 and 4 are shown in Figures 7.8 and 7.9 respectively.

96

Figure 7.6. Case 1: No interference mitigation BER study (Wi-Fi at 2.46 GHz)

Figure 7.7. Case 2: Interference mitigation (Wi-Fi at 2.46 GHz)

97

Figure 7.8. Case 3: No interference mitigation BER study (Wi-Fi at 2.448 GHz)

Figure 7.9. Case 4: interference mitigation BER study (Wi-Fi at 2.448 GHz)

7.4 BER Studies

Tables 7.1 through 7.4 show the experimentally recorded BERs for each of the

scenarios described in Section 7.3. The results vary depending on the MWO used as the

interference source acting on the experimental ComBlock wireless system.

Freq

uenc

y (H

z)

Time(s)

98

Table 7.1. BER for Case 1 (Wi-Fi at 2.46 GHz without interference mitigation)

MWO # Data Rate BER 1 363.3 kbps 0.016610 2 363.3 kbps 0.112900 3 363.3 kbps 0.007315

Table 7.2. BER for Case 2 (Wi-Fi at 2.46 GHz with interference mitigation)

MWO # Data Rate BER 1 181.7 kbps 0.000000 2 181.7 kbps 0.000000 3 181.7 kbps 0.000000

Table 7.3. BER for Case 3 (Wi-Fi at 2.448 GHz without interference mitigation)

MWO # Data Rate BER 1 363.3 kbps 0.002008 2 363.3 kbps 0.000165 3 363.3 kbps 0.000523

Table 7.4. BER for Case 4 (Wi-Fi at 2.448 GHz with interference mitigation)

MWO # Data Rate BER 1 181.7 kbps 0.000000 2 181.7 kbps 0.000000 3 181.7 kbps 0.000000

Although the data rate drops to 50% in the interference mitigated case, the BER is

minimized. This means that data packets will be reliably transmitted by a Wi-Fi device

even when a MWO is operating. In the case where this interference mitigation is not

used, the data rate remains at 100% but the BER is much higher, as shown in Table 7.1.

This means that many data packets are likely to be dropped as a result of interference and

the actual throughput may be much less than the mitigated case even though the data

transmission rate is higher. At high BER and high packet drop rates, the Wi-Fi

connection may be severed [AVA02]. The MWO interference mitigation technique

solves this problem completely.

99

It should be noted that the Barker spread IEEE 802.11 signal is the most resistant

to interference and noise effects. For other IEEE 802.11 signals the BER is likely to be

higher in similar experimental settings. Also, the BER greatly depends on the relative

received signal strengths of the data signal and the MWO signal, that is, the Signal-to-

Interference Ratio (SIR) [PAU06]. Due to this effect, the BER varies considerably if the

distances between the receiver, transmitter, and the MWO are changed. Therefore,

Tables 7.1 to 7.4 are meant only for comparative purposes to demonstrate the

performance of the experimental Wi-Fi system in the different scenarios, particularly

with or without interference mitigation. Tables 7.1 and 7.3 also show that MWO

interference significantly degrades the wireless communication system performance

making interference mitigation valuable. Furthermore, this method is practically

realizable on consumer access points and other Wi-Fi devices.

100

CHAPTER 8

CONCLUSION

8.1 Pulse Shaping for 1 Mbps Signal

This research was described in Chapter 2. A new Barker spread modulation

scheme was investigated that incorporated pulse shaping techniques with an 11-chip

Barker code. Four pulse shapes were studied and their PSDs determined. In all cases the

PSD was compared to the FCC spectral mask. The sinusoidally shaped Barker waveform

required the least output filtering in order to satisfy the spectral mask. The BER

performance was also studied. The pulse shaped systems performed better in several

respects: better spectral characteristics, lower order filter requirement, and improved

BER performance. The conclusions were verified by matching results obtained by

analytic, simulation, and experimental studies.

Two novel line coding techniques were employed in conjunction with pulse

shaping as an effort to further boost performance. Both the two systems were tested via

simulation and experimental study. One system employed the buffering 2 of bits at a

time. However, the spectral characteristics of this line coded Barker spread system were

observed to be poor. The second line code system utilized the buffering of 3 bits at a

time. The spectral characteristics of this system were the best observed, such that the

FCC spectral mask was nearly achieved without using any filtering. Simulated BER

results for this system showed that its performance was better than the rectangular pulse

Barker spread system with no buffering.

101

8.2 Pulse Shaping for 5.5 Mbps Signal

This research direction was the result of logical progression of applying symbol

shaping to the Barker spread 1 Mbps signal and onto the CCK spread 5.5 Mbps signal,

and the work has been described in this dissertation in Chapter 4. A new CCK spread

modulation scheme was investigated that incorporated pulse shaping techniques to

modulate the four possible I and Q phase vectors. Several shapes were studied and their

PSDs determined. In all cases the PSD was compared to the FCC spectral mask. The

sinusoidally shaped CCK waveform required the least output filtering in order to satisfy

the spectral mask. The BER performance was also studied by simulation. The pulse

shaped systems performed better in several respects: better spectral characteristics, lower

order filter requirement, and improved BER performance. The results of this research

work can be used to improve the performance of the existing IEEE 802.11 5.5 Mbps

CCK based wireless signal.

8.3 MWO Signal Study

Chapter 5 described the research undertaken here. The MWO signal was

meticulously studied as part of this research project. In particular, key features of the

MWO signal: the ON-OFF duty cycle, the AM-FM frequency sweeping nature of the

signal, and the transients were thoroughly investigated. Prior MWO signal studies have

often neglected the short duration transients, but our research has shown conclusively that

the transients are important and have critical interference impacts on Wi-Fi

communication on account of their high bandwidth.

102

As a result of this signal study, valuable insights were attained that made it

possible to accurately model the MWO signal and develop an interference mitigation

technique. The results of this experimental signal are valuable to engineers studying

MWO leakage and its interference on Wi-Fi systems.

8.4 MWO Signal Modeling

In this work, described in Chapter 6, analytical models were developed for the

MWO signal based on its experimental characteristics. Model #1 was developed that

expressed the major features of the MWO signal: ON-OFF duty cycle, the AM-FM

frequency sweeping nature of the signal, and the transients. This model was simulated

and compared with the actual experimental MWO measurements. Although there was

some degree of correlation between the two, more accuracy was desired in the model.

As a result, model #2 was formulated and was carefully designed to cover more

details of an actual MWO. This analytical model was simulated and emulated.

Emulation was done to support of the model. The emulation also sheds light on our

three-pronged research approach. The spectrogram and PSD plots obtained by simulation

and emulation matched extremely well with actual experimental plots of the MWO

signal.

Model #2 is more refined and can be utilized in wireless network simulation

studies that aim to improve IEEE 802.11 Wi-Fi transmission. Thus, the modeling

research aims to improve Wi-Fi communications indirectly by aiding network simulation

engineers in their quest to optimize wireless networks.

103

8.5 MWO Interference Mitigation

The interference mitigation research presented in Chapter 7 provides the single

biggest improvement to Wi-Fi communication. An interference mitigation technique was

formally proposed and implemented. The implemented circuit performed fully in line

with its expected function. Thus, interference on Wi-Fi systems due to MWOs can now

be eliminated, thereby improving Wi-Fi communication system performance in certain

interference rich environments.

The interference mitigation technique was practically implemented and BER

results were obtained via an experimental Wi-Fi communication system. Promising

results were obtained, thereby validating the research results and effort. This novel

system is practically realizable on consumer wireless APs in order to improve the

performance of wireless computer networks based on AP infrastructure.

8.6 Future Work

As part of ongoing and future work, pulse shaping to improve spectral

characteristics will be extended to other IEEE 802.11 signals; particularly the higher data

rate signals transmitted using PBCC. It is this researcher’s goal to study the pulse

shaping systems via simulation and experimental emulation and, wherever possible, by

analytical means.

It has been shown that the existing IEEE 802.11 1 Mbps data signal can be

improved through symbol shaping. Although not investigated in this research project, it

is expected that the same pulse shaping techniques are applicable to shape the I and Q

104

phase symbols of the QPSK IEEE 802.11 2 Mbps data signal, and similar results are

expected. For future work, this hypothesis needs to be tested.

The RF signal and interference from a residential MWO has been thoroughly

studied. In the future, we intend to look at RF leakage from the other types of MWOs:

commercial and switching MWOs. As part of future work, interference mitigation based

on the technique shown in Figure 7.1 will be practically implemented.

Interference mitigation using cognitive radio has proved valuable for MWO

interference mitigation. It is hoped that similar cognitive radio algorithms will be applied

to mitigate interference on IEEE 802.11 systems from other wireless devices like the

cordless telephone.

105

APPENDIX

INTERFERENCE SPECTROGRAMS

106

In this appendix several interference spectrograms are plotted. The figure titles

describe which devices are interfering.

Figure A.1. Spectrogram 1: interference between MWO, AP, ComBlock transmitter, and DSSS cordless phone.

ComBlock transmitter signal

Cordless phone’s data packet

MWO signal

AP data packet

107

Figure A.2. Spectrogram 2: interference between MWO, ComBlock transmitter, and

DSSS cordless phone.

Figure A.3. Spectrogram 3: interference between ComBlock transmitter, and DSSS

cordless phone.

ComBlock transmitter data packet

MWO signal

Cordless phone signal

108

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