chapter 3

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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)


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Outline

Fundamental of Data Transmission Digital Modulation Techniques Probability of Bit Error Multicarrier Modulation Multicarrier Equlization Intersymbol Interference Pulse Shaping


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Data Transmission

Anatomy of a wireless Digital Comm Sys


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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).


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Data Transmission

Source of Transmission Error

The linear filter channel with additive noise


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Data Transmission

Additive White Gaussian Noise (AWGN) White noise assumption in most situations Gaussian pdf


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Data Transmission

Additive White Gaussian Noise (AWGN)

Histogram of AWGN superimposed on the probability density function for a Gaussian random variable of N(0,0.25)

Power spectral density of AWGN with N(0,0.25)


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Data Transmission

Nearest neighbor detection

AWGN N(0,0.01) AWGN N(0,0.25)


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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


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Representation of Signals


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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


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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

)()()()(


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Power Efficiency

Measures the largest minimum signal distance achieved given lowest transmit power Energy per symbol

Energy per bit

dttsPEM

ii

i

s

1

0

2 )(

M

EE sb

2log


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Power Efficiency

Power efficiency

bP E

d 2min


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M-ary Phase Shift Keying

1,,1,0),2

cos()(

Mmm

ttAts ci


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M-ary Quadrature Amplitude Modulation


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M-ary Quadrature Amplitude Modulation


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M-ary Quadrature Amplitude Modulation Receiver

Simple receiver structure makes M-QAM popular in digital communication systems.


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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


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Derivation of BER

Assuming was transmitted, then an error event occurs if

where

)(1 ts

dttstrdttstrTT

)()()()( 2010

)()()( 1 tntstr


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Derivation of BER

P(error)=

is the noise density is the correlation between and

Q-function defines the area under the tail of a Gaussian pdf

x

y dyexQ 2/2

2

1)(

0

12

N

EQ

0N

12 )(1 ts )(2 ts


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Derivation of BER

When ,

and therefore

0

1221

2

2

N

EEQ

21 ss EE

2min1221 2 dEE

0

2min

2N

dQPe


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Upper Bound on BER

At least one error occurs

Therefore

j

m

j

m

12

1141312

m

j

ij

e N

dQP

2 0

2

2


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Lower Bound on BER

The smaller , the more likely an error happens.

Therefore

0

2min

2N

dQPe

2ijd


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Multicarrier modulation

Advantages:•Transmission agility•High datarate•Immunity to non-flat fading response.•“divide-and-conquer” channel distortion•Adaptive bit loading


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Multicarrier modulation

Disadvantages:•Sensitive to narrowband noise•Sensitive to amplitude clipping•Sensitive to timing jitter, delay


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Multicarrier Modulation

Transmitter

Receiver


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Comparison between single carrier and multicarrier tt


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OFDM

Orthogonal Frequency Division Multiplexing


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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


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OFDM

Transmitter

Receiver


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Multicarrier Equalization

Interference in multicarrier systems


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Distortion Reduction

Channel coding•Add redundancy to improve recovering


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Channel equalization

Before equalization

After equalization


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Channel equalization•Pre-equalization requires a feedback path from the receiver


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Intersymbol Interference

Signal being distorted by the temporal spreading and resulting overlap of individual symbol pulses

Simplified block diagram for a wireless channel


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RC-LPF filter response of combined modulation pulses when T=1, A=1


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Peak Interference/Distortion•When all symbols before and after have destruct effect on the symbol on cursor


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Pulse Shaping

Nyquist Pulse Shaping Theory•Time domain condition for zero ISI

No ISI if sampling at t=kT


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Nyquist Pulse Shaping Theory

Nyquist-I Pulse (W=1/(2T))


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Nyquist-II Pulse (W>1/(2T))


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Frequency domain No ISI criterion

Tf

T

kfHfH

TfCfH

N

Nkeq

eq

2

1),()(

2

1,)(


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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

chapter 3

Documents

hou elsevier

total noise

gaussian noise interference

data transmissionanatomy

signal power

noise ratio cnr

noise ratio snr

communication signal