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Chapter 3
Digital Communication Fundamentals for Cognitive Radio
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
2
Outline Fundamental of Data Transmission Digital Modulation Techniques Probability of Bit Error Multicarrier Modulation Multicarrier Equlization Intersymbol Interference Pulse Shaping
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
3
Data Transmission
Anatomy of a wireless Digital Comm Sys
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
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Data Transmission
Fundamental Limits Shannon–Hartley theorem
S is the total received signal power over the bandwidth (in case of a modulated signal, often denoted C, i.e. modulated carrier), measured in watt or volt;
N is the total noise or interference power over the bandwidth, measured in watt or volt; and
S/N is the signal-to-noise ratio (SNR) or the carrier-to-noise ratio (CNR) of the communication signal to the Gaussian noise interference expressed as a linear power ratio (not as logarithmic decibels).
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
5
Data Transmission
Source of Transmission Error
The linear filter channel with additive noise
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
6
Data Transmission
Additive White Gaussian Noise (AWGN) White noise assumption in most situations Gaussian pdf
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
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Data Transmission
Additive White Gaussian Noise (AWGN)
Histogram of AWGN superimposed onthe probability density function for aGaussian random variable of N(0,0.25)
Power spectral density of AWGNwith N(0,0.25)
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
8
Data Transmission
Nearest neighbor detection
AWGN N(0,0.01) AWGN N(0,0.25)
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
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Digital Modulation Techniques
Representation of Signals Euclidean Distance between Signals Decision Rule Power Efficiency M-ary Phase Shift Keying M-ary Quadrature Amplitude
Modulation
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
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Representation of Signals
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
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Euclidean Distance between Signals For any two signals and , the
Euclidean Distance between them is defined as
Vector form
)(tsi )(ts j
dttstsd jiij22 )()(
jiij ssd
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
12
Decision Rule
Nearest neighbor rule: Determine is if is the closest to
rewritten as
waveform representation
r is
ijsrsr ji ,is
r
ijsrsr ji ,
T
j
T
i dttstrdttstr00
)()()()(
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
13
Power Efficiency
Measures the largest minimum signal distance achieved given lowest transmit power Energy per symbol
Energy per bit
dttsPEM
ii
is
1
0
2 )(
MEE s
b2log
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
14
Power Efficiency
Power efficiency
bP E
d 2min
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
15
M-ary Phase Shift Keying
1,,1,0),2cos()(
Mmm
ttAts ci
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
16
M-ary Quadrature Amplitude Modulation
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
17
M-ary Quadrature Amplitude Modulation
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
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M-ary Quadrature Amplitude Modulation Receiver
Simple receiver structure makes M-QAM popular in digital communication systems.
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
19
Probability of Bit Error
Also known as bit error rate Starting from the modulation scheme
with two signal waveforms, and Assuming the noise term has a
Gaussian distribution
)(1 ts )(2 ts
);0(~)( Ntn
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
20
Derivation of BER
Assuming was transmitted, then an error event occurs if
where
)(1 ts
dttstrdttstrTT
)()()()( 2010
)()()( 1 tntstr
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
21
Derivation of BER
P(error)=
is the noise densityis the correlation between and
Q-function defines the area under the tail of a Gaussian pdf
x
y dyexQ 2/2
21)(
0
12
NEQ
0N
12 )(1 ts )(2 ts
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
22
Derivation of BER
When ,
and therefore
0
1221
22
NEEQ
21 ss EE
2min1221 2 dEE
0
2min
2NdQPe
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
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Upper Bound on BER
At least one error occurs
Therefore
j
m
j
m
12
1141312
m
j
ije N
dQP
2 0
2
2
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
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Lower Bound on BER
The smaller , the more likely an error happens.
Therefore
0
2min
2NdQPe
2ijd
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
25
Multicarrier modulation
Advantages:•Transmission agility•High datarate•Immunity to non-flat fading response.•“divide-and-conquer” channel distortion•Adaptive bit loading
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
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Multicarrier modulation
Disadvantages:•Sensitive to narrowband noise•Sensitive to amplitude clipping•Sensitive to timing jitter, delay
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
27
Multicarrier Modulation
Transmitter
Receiver
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
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Comparison between single carrier and multicarrier tt
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
29
OFDM
Orthogonal Frequency Division Multiplexing
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
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FB-OFDM
Orthogonal Frequency Division Multiplexing with Filterbank
FB-MC subcarrier spectrum employing a seuqre-root raised cosine prototype lowpass filter with a rolloff of 0.25
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
31
OFDM
Transmitter
Receiver
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
32
Multicarrier Equalization
Interference in multicarrier systems
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
33
Distortion Reduction
Channel coding•Add redundancy to improve recovering
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
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Distortion Reduction
Channel equalization
Before equalization
After equalization
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
35
Distortion Reduction
Channel equalization•Pre-equalization requires a feedback path from the receiver
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
36
Intersymbol Interference
Signal being distorted by the temporal spreading and resulting overlap of individual symbol pulses
Simplified block diagram for a wireless channel
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
37
Intersymbol Interference
RC-LPF filter response of combined modulation pulseswhen T=1, A=1
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
38
Intersymbol Interference
Peak Interference/Distortion•When all symbols before and after have destruct effect on the symbol on cursor
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
39
Pulse Shaping
Nyquist Pulse Shaping Theory•Time domain condition for zero ISI
No ISI if sampling at t=kT
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
40
Nyquist Pulse Shaping Theory
Nyquist-I Pulse (W=1/(2T))
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
41
Nyquist Pulse Shaping Theory
Nyquist-II Pulse (W>1/(2T))
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
42
Nyquist Pulse Shaping Theory
Frequency domain No ISI criterion
Tf
TkfHfH
TfCfH
N
Nkeq
eq
21),()(
21,)(
“Cognitive Radio Communications and Networks: Principles and Practice”By A. M. Wyglinski, M. Nekovee, Y. T. Hou (Elsevier, December 2009)
43
Chapter 3 Summary Digital communication theory at the
core of cognitive radio operations Mathematical tools necessary for
enabling advanced features Various modulation schemes can be
used for transmission under different constraints and expectations
Bit Error Rate is primarily used to define performance