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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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