PETER PAZMANY CATHOLIC UNIVERSITY · • Signal propagation overview • Path loss models • Log...

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Development of Complex Curricula for Molecular Bionics and Infobionics Programs within a consortial* framework**

Consortium leader

PETER PAZMANY CATHOLIC UNIVERSITYConsortium members

SEMMELWEIS UNIVERSITY, DIALOG CAMPUS PUBLISHER

The Project has been realised with the support of the European Union and has been co-financed by the European Social Fund ***

**Molekuláris bionika és Infobionika Szakok tananyagának komplex fejlesztése konzorciumi keretben

***A projekt az Európai Unió támogatásával, az Európai Szociális Alap társfinanszírozásával valósul meg.

PETER PAZMANY

CATHOLIC UNIVERSITY

SEMMELWEIS

UNIVERSITY

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Peter Pazmany Catholic University

Faculty of Information Technology

Ad hoc Sensor Networks

Digital modulation

www.itk.ppke.hu

Érzékelő mobilhálózatok

Digitális moduláció

Dr. Oláh András

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Lecture 3 review• Signal propagation overview• Path loss models• Log Normal Shadowing• Narrowband Fading Model• Wideband Multipath Channels

Ad hoc Sensor Networks: Digital modulation

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Outline• Advantage of digital modulation• Bandwidth of signals• ISI-free system requirements• IQ modulator• Constellation and “eye” diagrams• Tradeoff between spectral efficiency and power efficiency• Linear and constant envelope modulation scheme• Spread Spectrum Modulation

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Structure of a wireless communications link

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Modulation• It is defined as a technique of mapping the information signal

to a transmission signal (modulated signal) which is bettersuited for the operating medium (i.e. the wireless channel).

• The transmitted radio signal can be described as

• By letting the transmitted information change the amplitude,the frequency, or the phase to carry the information we get thethree basic types of digital modulation techniques:– ASK (Amplitude Shift Keying)– FSK (Frequency Shift Keying)– PSK (Phase Shift Keying)

( ) ( ) ( )( )cos 2s t A t ft tπ= +Θ

Amplitude Frequency Phase

Constant amplitude

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Modulation (cont’)

( ) ( ) ( )( )cos 2s t A t ft tπ= +Θ

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Advantage of digital communications• It allows information to be “packetized”

– It can compress information in time and efficiently send as packets through network.

– In contrast, analog modulation requires “circuit-switched” connections that are continuously available.

• Inefficient use of radio channel if there is “dead time” in information flow.

• It allows error correction to be achieved– Less sensitivity to radio channel imperfections.

• It enables compression of information.– More efficient use of channel.

• It supports a wide variety of information content.– Voice, text and email messages, video can all be represented as digital

bit streams.

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Digital modulation• Better performance and more cost effective than analog modulation methods

(AM, FM, etc.)• Performance advantages:

– the digital transceivers are much cheaper, faster and more power-efficient thananalog transceivers;

– higher data rates are achieved compared to analog with the same signal bandwidth;– powerful error correction techniques make the signal much less susceptible to noise

and fading, and equalization can be used to mitigate ISI [→see later];– more efficient multiple acces strategies (spread spectrum techniques applied to

digital modulation can remove or combine multipath, resist interference, and detectmultiple users simultaneously);

– better security and privacy for digital systems;– combination of multiple information types (voice, data, & video) in a single

transmission channel;– implementation of modulation/demodulation functions using DSP software (instead

of hardware circuits).

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Digital modulation (cont’)• Choice of digital modulation scheme• Many types of digital modulation methods → small differences• Performance factors to consider (corresponding metrics)

– low Bit Error Rate (BER) at low S/N (BER performance)– resistance to interference and multipath fading– high data rate– high spectral efficiency (SE [bps/Hz])– easy and cheap implementation of mobile units (Receiver complexity)– transmission power amplifier linearity requirements (linearity)– efficient use of battery power in mobile unit (Power efficiency, PE)

• No existing modulation scheme can simultaneously satisfy all of these requirements.

• Each one is better in some areas with trade-offs of being worse in others.

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Bandwidth of a signal: the conceptMany definitions depending on application. Recall from

DSP course

FCC definition (99%)

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Frequency ranges of a some natural signals

Biological Signals

Type of Signal Frequency Range [Hz]Electroretinogram 0 - 20

Pneumogram 0 - 40

Electrocardiogram (ECG) 0 -100

Electroenchephalogram (EEG) 0 - 100

Electromyogram 10 - 200

Sphygmomanogram 0 - 200

Speech 100 - 4000

Seicmic signalsSeismic exploration signals 10 - 100

Eartquake and nuclear explosion signals 0.01-10

Electromagnetic signals

Radio bradcast 3x104 - 3x106

Common-carrier comm. 3x108 - 3x1010

Infrared 3x1011 - 3x1014

Visible light 3.7x1014 - 7.7x1014

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A simplified communication modellRecall from ICT course

PROBLEM:Bandlimited channel !

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Digital signal transmission over analog channelRecall from ICT course

PROBLEM:1. Nyquist pulse are noncausal and of infinite duration.2. We cannot implement the ideal lowpass filter in practice.3. It decays very slowly (~1/t).

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ISI-free system requirementsRecall from ICT course

0

1 00 otherwisel l

lg δ

=⎧= = ⎨

⎩

( ) ( )FTg t G f⎯⎯→

( ) ( )FTS

1 1n

ng nT G f G fT T

⎛ ⎞⎯⎯→ = + =⎜ ⎟⎝ ⎠

∑ 12

fT

≤

Nyquist criterion for ISI-free communication: (Not to mention the ISI caused by the coherence

bandwidth of the wireless channel.)

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ISI-free system requirements (cont’)• Nyquist criterion:

• Observations:– To satisfy the Nyquist criterion, the channel bandwidth B must be at

least 1/(2T)– For the minimum bandwidth the impulse response is Nyquist pulse.– The pulse shape g(t) fulfills the Nyquist criterion if it is center-

symmetric for 1/2T: (basis pulse shapping)

Recall from ICT course

( ) ( )FTS

1 1n

ng nT G f G fT T

⎛ ⎞⎯⎯→ = + =⎜ ⎟⎝ ⎠

∑

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ISI-free system requirements (cont’)Nyquist Pulse

( ) ( )N

sin f Tg t

f Tπ

π=

B=1/T B ~ 1/T

Raised-Cosine Pulse

( ) ( ) ( )( )RC 2

sin cos1 2

t T t Tg t

t T t Tπ απ

π α=

−α=0

B=(1+α)1/T

Recall from ICT course

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Nyquist criterion with matched filteringRecall from ICT course

T R1 1

n

n nG f G fT T T

⎛ ⎞ ⎛ ⎞+ + =⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

∑

( )( )

R

2Rmin

B

G fB

G f df−∫

GR(f) = GT(f)* matched filter

( ) ( ) ( ) 2T RG f G f G f=

Uncorrelated ηk :

( ) { } 0

0k l k

N k lR k E

k lη η−

=⎧= = ⎨ ≠⎩

( ) ( ) ( )20 R 0S f N G f N G fη = =

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Error probability Recall from ICT course

( )BPSKBER SNR= Φ −

{ } { } ( ) { } ( )( ){ } ( ) ( ){ } ( )

{ } { }0 0 0

ˆ ˆ ˆPr Pr 1 1 1 Pr 1 1 1

Pr sgn 1 1 1 Pr sgn 1 1 1

1 1 1 1Pr 1 0.5 Pr 1 0.5 12

BER y y y y p y y y p y

y y p y y y p y

N N N

η η

η η

= ≠ = = = − = − + = − = = =

= + = = − = − + + = − = = =

⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞= ≥ + < − = −Φ +Φ − = Φ −⎢ ⎥⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎣ ⎦

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• It describes the ability of a modulationtechnique to preserve the quality ofdigital messages at low power levels(low SNR):

required PE = Eb / N0

for a certain BER (e.g. 10-3)where Eb : energy/bit and N0 : noisepower/bit

• Tradeoff between signal power andfidelity:– as Eb / N0 ↓, than BER ↑

• It depends on the particular type ofmodulation employed.

Receiver sensitivity or power efficiency (PE)

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Bandwidth efficiency or spectral efficiency (SE)• Ability of a modulation technique to accommodate data in a

limited BWSE = R / B,

where R is the data rate, B is the system bandwidth.• Trade of between R data rate and B bandwidth:

– as R ↑, than B ↑

• For a digital signal

ss

1 so as , and R B R T BT

∝ ∝ → ↑ ↑

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M-ary Keying• each pulse or “symbol” having m finite states represents

n = log2 M bits/symbol– e.g. M = 0 or 1 (2 states) → n = 1 bit/symbol (binary)– e.g. M = 0, 1, 2, 3, or 4 (4 states) → n = 2 bits/symbol

• E.g.: when a system is changed from binary to 4-ary:– In the case of binary: "0" = - 1V and "1" = 1 V– In the case of 4-ary: "0" = - 1V, "1" = - 0.33V, "2" = 0.33 V, "3" = 1 V

• What would be the new data rate compared to the old data rate ifthe symbol periods were kept constant?

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• Most famous result in communication theory.

– B : bandwidth– C : channel capacity (bps) of real data (not

retransmissions or errors)– To produce error-free transmission, some of the

bit rate will be taken up using retransmissions orextra bits for error control purposes.

– Lower bit error rates from higher power resultsmore real data

– As noise power PN increases, the bit rate wouldstill be the same, but SEmax decreases.

• SEmax is fundamental limit that cannot beachieved in practice.

Maximum SE: Shannon’s theorem (1948)Recall from ICT course

Claude Elwood Shannon (1916-2001)

S bmax 2 2

N 0

log 1 log 1P EC RSEB P N B

⎛ ⎞ ⎛ ⎞= = + = +⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

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Fundamental trade-off between SE and PE• If SE improves then PE deteriorates (or vice versa)

– One may need to waste more power to get a better data rate.– One may need to use less power (to save on battery life) at the expense of

a lower data rate.• SE vs. PE is not the only consideration, we use other factors to

evaluate, e.g.:– resistance to interference and multipath fading;– easy and cheap implementation in mobile unit;– etc.

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Ad hoc Sensor Networks: Wireless channel characterization and models

• The canonical form of a band passtransmitted radio signal is

where ej2πft is the carrier factor.• The signal s(t) can be written as

• We will define the following quantities

• The complex envelope of s(t) is nowwritten as

and

Convex envelope theory

( ) ( ) ( )( ) ( ) ( ){ }jj2πfcos Re e e tts t A t t t A tω Θ= +Θ =

( ) ( ) ( )( ) ( ) ( ) ( )( ) ( )cos cos sin sins t A t t t A t t tω ω= Θ − Θ

( ) ( ) ( )( )( ) ( ) ( )( )

Q

I

cos

sin

s t A t t

s t A t t

= Θ

= Θ

( ) I Qjs t s s= +

( ) ( ){ }j2πRe e fts t s t=

Recall from Chapter 3

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Constellation diagrams

• Plot I/Q samples on x-y axis• The constellation diagram provides a sense of

how easy it is to distinguish between differentsymbols

• Assign each I/Q symbol to a set of digital bits(eg. Gray code)

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Constellation diagrams

• Noise corrupts sampled I/Q values• The points in the constellation diagram no

longer consist of single dots for each symbol• What is the best way to match received I/Q

samples with their corresponding symbols?(Detection)

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Constellation diagrams properties• Distance between signals is related to differences in modulation

waveforms– Large distance → easy to discriminate → good BER at low SNR– Power Efficient related to density

• Occupied BW ↓ as number of signal states ↑– If we can represent more bits per symbol, then we need less BW for a

given data rate.– Small separation → “dense” → more signal states/symbol → more

information/Hz !!– Bandwidth Efficient

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• Key idea: wrap signal back onto itself inperiodic time intervals and retain alltraces– Similar to the action of an oscilloscope

• Increasing the number of symbolseventually reveals all possible symboltransition trajectories– It shows the ISI present as well as timig

jitter present.• Eye diagram allows visual inspection of

the impact of sample time and decisionboundary choices– Large eye opening implies less

vulnerability to symbol errors

Eye diagrams

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Modulation schemes

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Binary Phase Shift Keying (BPSK)

• Phase transitions force carrier amplitudeto change from “+” to “−”.– Amplitude varies in time.

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Quaternary Phase Shift Keying (QPSK)

• Four different phase states in one symbol period• Two bits of information in each symbol• double the SE of BPSK → or twice the data rate in

same signal BW• same PE (same BER at specified Eb/N0)

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Transmit power amplifier

When a modulation signalencounters a nonlinearity the signalbecomes distorted and its occupiedfrequency bandwidth increases(spectrum re-growth). The mostsignificant source of nonlinearitycomes from the transmission PA.

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Offset QPSK

QPSK OQPSK

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Quaternary Phase Shift Keying (QPSK)

• OQPSK ensures there are fewer baseband signaltransitions applied to the RF amplifier, helpseliminate spectrum regrowth after amplification.

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Frequency Shift Keying (FSK)

• Constant Envelope as compared to AM– Linear: Amplitude of the signal varies according to

the message signal.– Constant Envelope: The amplitude of the carrier is

constant, regardless of the variation in the messagesignal. It is the phase that changes.

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M-ary Phase Shift Keying (MPSK)

• The SE ↑ with M↑• The PE ↓ with M↑

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M-ary QAM

• Basic trade-off: Better bandwidth efficiency atthe expense of power efficiency– More bits per symbol time → better use of

constrained bandwidth– Need much more power to keep constellation

points far enough apart for acceptable bit errorrates.

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M-ary FSK• Frequencies are chosen in a special way so

that they are easily separated at thedemodulator (orthogonality principle).

• M-ary FSK transmitted signals:

– fc = nc / 2T for some integer nc– The M transmitted signals are of equal energy

and equal duration• The SE of an M-ary FSK signal ↓ with M↑• The PE ↑ with M↑

– Since M signals are orthogonal, there is nocrowding in the signal space

s2( ) cos ( )

0 0,1,...,

i cEs t n i tT T

t T i M

π⎡ ⎤= +⎢ ⎥⎣ ⎦≤ ≤ =

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Modulation scheme comparisons

Given a modulation scheme and a targeted BER then the communication system designercan determine the SE (spectral efficiency) and the PE (Eb/N0 required to maintain theaverage BER target).

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• The transmitter expands (spreads) signal Bs bandwidth many times with a p(t) spreading code and the signal is then collapsed (despread) in receiver side with the same code.

• Other signals created with other codes just appear at the receiver as random noise.• Processing Gain (PG)= Bs /BT

Spread Spectrum Modulation (SSM)

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Spread Spectrum Modulation (SSM) advantage• Resistant to narrowband interference.• It allows multiple users with different codes to share same the

wireless channel– no frequency reuse needed– rejects interference from other users

• It combats multipath fading → if a multipath signal is received with enough delay (more than one chip duration), it also appears like noise.

• As number of simultaneous users ↑ the SE↑

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Spreading codes• Signal spreading is done by multiplying the data signal by a

pseudo-noise (PN) code or sequence– the pseudo-noise signal looks like noise to all observers except those who

know how to recreate the sequence.

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Spreading codes: PN codes• Binary sequence with random properties → noise-like (called

"pseudo-noise" because they are not noise technically)• ≈ equal #’s of 1’s and 0’s• Very low correlation between time-shifted versions of same

sequence• Very low cross-correlation between different codes

– each user assigned unique code that is approximately orthogonal to all other codes

– the other users’ signals appear like random noise!

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Type of spread spectrum modulation • Direct Sequence (DS)

– Multiply baseband data by PN code (same as above)– Spread the baseband spectrum over a wide range.– The Rx spread spectrum signal

– where m(t) : the data sequence and p(t) the PN sequence• Frequency Hopping (FH)

– Randomly change fc with time– In effect, this signal stays narrowband but moves around a lot to use a wide band of

frequencies over time.– Hopset: the set of possible carrier frequencies– Hop duration: the time during between hops– Classified as fast FH or slow FH

• fast FH: more than one frequency hop during each Tx symbol• slow FH : one or more symbol are Tx in the time interval between frequency hops.

( )2( ) ( ) ( )cos 2 si c

s

Es t m t p t f tT

π θ= +

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Spread spectrum modulation and the multiple access• With Spread Spectrum Modulation, users are able to share a common

band of frequencies yielding a multiple access technique– TDMA: Users share a band of frequencies, but use a different time slot– FDMA: Users share a band of frequencies, but use a different slice of

frequency– SSM enables CDMA (Code Division Multiple Access): Users share a band of

frequencies and a number of time-slots, but each use a different spreading code.

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Summary• Nyquist criterion for ISI-free communication.• No existing modulation scheme simultaneously satisfies all of

these requirements well.• Given a modulation scheme and a targeted BER then the

communication system designer can determine the SE(spectral efficiency) and the PE (Eb/N0 required to maintain theaverage BER target).

• With Spread Spectrum Modulation, users are able to share acommon band of frequencies a multiple access technique(CDMA)

• Next lecture: Detection and channel equalization


PETER PAZMANY CATHOLIC UNIVERSITY · • Signal propagation overview • Path loss models • Log...

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