Bandpass Bandpass Modulation Modulation

& & DemodulatioDemodulation Detectionn Detection

CHAPTER CHAPTER 44

School of Computer and Communication School of Computer and Communication Engineering, Amir Razif Arief b. Jamil Engineering, Amir Razif Arief b. Jamil

AbdullahAbdullahEKT 431: Digital EKT 431: Digital Communications Communications

Last time we talked Last time we talked about:about:

Another source of error due to filtering effect Another source of error due to filtering effect of the system: of the system:

Inter-symbol interference (ISI)Inter-symbol interference (ISI)The techniques to reduce ISIThe techniques to reduce ISI

Pulse shapingPulse shaping to achieve zero ISI at the to achieve zero ISI at the sampling timesampling timeEqualizationEqualization to combat the filtering effect to combat the filtering effect of the channelof the channel

Test 1

0

20

40

60

80

100

0 10 20 30 40 50 60 70Student ID

Scor

e

Series1

Average   65.9

Max   97.0

Min   35.0

Stdev   13.9

ModulationModulationDigital Bandpass Modulation Digital Bandpass Modulation TechniquesTechniquesDetection of Signals in Gaussian Detection of Signals in Gaussian NoiseNoiseCoherent DetectionCoherent DetectionNoncoherent DetectionNoncoherent DetectionM-ary Signaling and PerformanceM-ary Signaling and Performance

Baseband Modulation and Baseband Modulation and Demodulation DetectionDemodulation Detection

Today, we are going to Today, we are going to talk about:talk about:

Some bandpass modulation schemes used in Some bandpass modulation schemes used in DCS for transmitting information over channelDCS for transmitting information over channel

M-PAM, M-PSK, M-FSK, M-QAMM-PAM, M-PSK, M-FSK, M-QAMHow to detect the transmitted information at How to detect the transmitted information at the receiverthe receiver

Coherent detectionCoherent detectionNon-coherent detectionNon-coherent detection

ModulationModulationModulation~Modulation~

is the process of digital symbols are is the process of digital symbols are transform into waveforms that are transform into waveforms that are compatible with the characteristics of the compatible with the characteristics of the channel.channel.

Bandpass Modulation~Bandpass Modulation~the shape modulate the carrier wave. For the shape modulate the carrier wave. For radio transmission the carrier is converted to radio transmission the carrier is converted to an electromagnetic (EM) field for an electromagnetic (EM) field for propagation to the desired destination.propagation to the desired destination.

Through carrier wave modulation the size of Through carrier wave modulation the size of antenna can be antenna can be reduced reduced for high frequency for high frequency transformation.transformation.FDMA Uses to FDMA Uses to minimizeminimize the effect of the effect of interference, to separate different signal interference, to separate different signal transmitting using single channel. transmitting using single channel.

Block Diagram of a DCSBlock Diagram of a DCSDigital ModulationDigital Modulation

~ ~ digital symbols transform into waveforms that are digital symbols transform into waveforms that are compatible with channel characteristics.compatible with channel characteristics.

Baseband modulationBaseband modulation~ shaped pulses modulate a sinusoid carrier wave ~ shaped pulses modulate a sinusoid carrier wave (carrier) for radio transmission the carrier is converted (carrier) for radio transmission the carrier is converted to EM.to EM.

FormatSourceencode

FormatSourcedecode

Channelencode

Pulsemodulate

Bandpassmodulate

Channeldecode

Demod. SampleDetect

Channel

Digital modulation

Digital demodulation

Digital Bandpass Digital Bandpass Modulation TechniquesModulation Techniques

Bandpass modulationBandpass modulation~ ~ The process of converting a data signal to a The process of converting a data signal to a sinusoidal waveform where its sinusoidal waveform where its amplitudeamplitude, , phasephase or or frequencyfrequency, or a combination of them, are varied in , or a combination of them, are varied in accordance with the transmitting data. accordance with the transmitting data.

Carrier wave;Carrier wave;wherewhere

oo~ radian frequency~ radian frequency(t)~ phase(t)~ phasef & f & ~ frequency ~ frequency denotes average symbol energy given by denotes average symbol energy given by

Coherent detection~Coherent detection~The receiver exploits the knowledge of the carrier’s The receiver exploits the knowledge of the carrier’s phase to detect the signals.phase to detect the signals.

noncoherent detection~noncoherent detection~The receiver does The receiver does not utilizenot utilize the the phasephase reference reference information.information.

)](cos[)()( 0 tttAts

Noncoherent demodulation~Noncoherent demodulation~Refers to systems employing demodulator Refers to systems employing demodulator that are designed to operate without that are designed to operate without knowledge of the absolute value of the knowledge of the absolute value of the incomming signal’s phaseincomming signal’s phaseIt It reduce complexityreduce complexity compare to coherent compare to coherent demodulation and increase probability error demodulation and increase probability error (P(PEE))

Phasor representation of sinusoidPhasor representation of sinusoid

eejwotjwot consists of consists of (1) inphase (real) component and (1) inphase (real) component and (2) quadrature (imaginary) component (2) quadrature (imaginary) component that are orthogonal to each other. that are orthogonal to each other.

tjte ootj o sincos

Bandpass ModulationBandpass ModulationBandpass signal:Bandpass signal:

where is the baseband pulse shape where is the baseband pulse shape with energy .with energy .

We assume here (otherwise will be stated):We assume here (otherwise will be stated): is a rectangular pulse shape with is a rectangular pulse shape with unit energy.unit energy.Gray coding is used for mapping bits to Gray coding is used for mapping bits to symbols.symbols. denotes average symbol energy given denotes average symbol energy given by by

)(tgT

)(tgT

gE

sE

M

i is EM

E1

1

Contd… Bandpass ModulationContd… Bandpass Modulation

Bandpass ModulationBandpass ModulationBandpass signal:Bandpass signal:

where is the baseband pulse shape where is the baseband pulse shape with energy.with energy.

We assume here (otherwise will be stated):We assume here (otherwise will be stated): is a rectangular pulse shape with is a rectangular pulse shape with unit energy.unit energy.Gray coding is used for mapping bits to Gray coding is used for mapping bits to symbols.symbols. denotes average symbol energy given denotes average symbol energy given by by

)(tgT

)(tgT

TtttitTEtgts ici

Ti 0 )()1(cos2)()(

gE

sE

M

i is EM

E1

1

Frequency Shift Keying Frequency Shift Keying (FSK)(FSK) General analytic expression for General analytic expression for FSKFSK;;

where where wwii have M discrete values, s have M discrete values, s(t)(t) is an is an arbitrary constantarbitrary constant

symbol transition depicts a symbol transition depicts a gentle shiftgentle shift from from one frequency tone to another. True for one frequency tone to another. True for CPFSK only.CPFSK only.

In MFSK the change to a different tone is In MFSK the change to a different tone is quite abrupt.quite abrupt.

OrthogonalOrthogonal signal, signal with mutually signal, signal with mutually perpendicular vector.perpendicular vector.

MiTt

tTEts ii ,...,1

0]cos[2)(

Contd.. Frequency Shift Keying (FSK)Contd.. Frequency Shift Keying (FSK)FSK Bandwidth;FSK Bandwidth;f ~ (fm-fs)/2f ~ (fm-fs)/2f ~ frequency space and mark between f ~ frequency space and mark between different absolute (Hz) deviation frequency.different absolute (Hz) deviation frequency.fm-fs ~ absolute different between mark and fm-fs ~ absolute different between mark and space frequency.space frequency.

B= |(fs-fb) - (fm-fb)|B= |(fs-fb) - (fm-fb)| = |fs-fm| + 2fb= |fs-fm| + 2fb = 2= 2f + fbf + fb

Contd.. Frequency Shift Keying (FSK)Contd.. Frequency Shift Keying (FSK)FSKFSK

Amplitude Shift Keying Amplitude Shift Keying (ASK)(ASK) General analytic expression for General analytic expression for ASKASK;;

where swhere sii(t) will have M discrete values(t) will have M discrete values where where wwii have M discrete values, s have M discrete values, s(t)(t) is an is an

arbitrary constantarbitrary constant

MiTt

tTEtsi ,...,1

0]cos[2)( 0

Phase Shift Keying Phase Shift Keying (PSK)(PSK)

General analytic expression for General analytic expression for PSKPSK;;

where swhere sii(t) will have M discrete values(t) will have M discrete valuesE ~ energyE ~ energyT~ durationT~ durationFor BPSK, M=2For BPSK, M=2Shift sShift sii(t) phase state zero and(t) phase state zero and

(() 180) 18000..

MiMit

MiTt

ttTEts

i

ii

,...,12)(

,...,10

)](cos[2)( 0

Contd… Phase Shift Keying (PSK)Contd… Phase Shift Keying (PSK)BPSK transmitterBPSK transmitter

BPSK ReceiverBPSK Receiver Bit value 0 –sine wave Bit value 1 –inverted sine wave Very simple PSK Low spectral efficiency Robust , used in satellite system

Two Dimensional Two Dimensional Modulation, demodulation Modulation, demodulation

and detection (M-PSK)and detection (M-PSK)M-ary Phase Shift Keying (M-PSK)M-ary Phase Shift Keying (M-PSK)

2

21

21

2211

2sin 2cos

sin2)( cos2)(

,,1 )( )()(

iis

sisi

cc

iii

EE

MiEa

MiEa

tT

ttT

t

Mitatats

s

Mit

TEts cs

i 2cos2)(

Two Dimensional Mod.,… Two Dimensional Mod.,… (MPSK)(MPSK)

)(1 t

2s1sbE

“0” “1”

bE

)(2 t

3s

7s

“110”)(1 t

4s 2ssE

“000”

)(2 t

6s 8s

1s5s

“001”“011”

“010”

“101”

“111” “100”

)(1 t

2s 1s

sE

“00”

“11”

)(2 t

3s 4s“10”

“01”

QPSK (M=4)

BPSK (M=2)

8PSK (M=8)

Two Dimensional Mod.,…Two Dimensional Mod.,…(MPSK)(MPSK)

Coherent detection of MPSKCoherent detection of MPSK

Compute Choose smallest2

1arctanzz ̂

|ˆ| i

T

0

)(1 t

T

0

)(2 t)(tr

1z

2z

m̂

Two Dimensional Mod., (M-Two Dimensional Mod., (M-QAM)QAM)

M-ary Quadrature Amplitude Mod. (M-QAM)M-ary Quadrature Amplitude Mod. (M-QAM)

ici

i tTEts cos2)(

3)1(2 and symbols PAM are and where

sin2)( cos2)(

,,1 )( )()(

21

21

2211

MEaa

tT

ttT

t

Mitatats

sii

cc

iii

)1,1()1,3()1,1(

)3,1()3,3()3,1()1,1()1,3()1,1(

, 21

MMMMMM

MMMMMMMMMMMM

aa ii

Two dimensional mod (M-Two dimensional mod (M-QAM)QAM)

)(1 t

)(2 t

2s1s 3s 4s“0000” “0001” “0011” “0010”

6s5s 7s 8s

10s9s 11s 12s

14s13s 15s 16s

1 3-1-3

“1000” “1001” “1011” “1010”

“1100” “1101” “1111” “1110”

“0100” “0101” “0111” “0110”

1

3

-1

-3

16-QAM

Two dimensional mod., (M-Two dimensional mod., (M-QAM)QAM)Coherent detection of M-QAMCoherent detection of M-QAM

T

0

)(1 t

ML detector1z

T

0

)(2 t

ML detector

)(tr

2z

m̂Parallel-to-serialconverter

s) threshold1 with (Compare M

s) threshold1 with (Compare M

Multi-Dimensional Multi-Dimensional Modulation, Demodulation & Modulation, Demodulation &

DetectionDetectionM-ary Frequency Shift keying (M-FSK)M-ary Frequency Shift keying (M-FSK)

Tf

titTEt

TEts c

si

si

21

2

)1(cos2cos2)(

2

1

0

cos2)(

,,1 )()(

iis

sijii

M

jjiji

EE

jijiEat

Tt

Mitats

s

)(1 t

2s

1s

3s

)(3 t

)(2 tsE

sE

sE

Multi-dimensional mod.,…Multi-dimensional mod.,…(M-FSK)(M-FSK)

Mz

z1

zT

0

)(1 t

T

0

)(tM)(tr

1z

Mz

zML detector:

Choose the largest element

in the observed vector

m̂

Non-Coherent DetectionNon-Coherent Detection Non-coherent detection:Non-coherent detection:

No need for a reference in phase with the No need for a reference in phase with the received carrierreceived carrier

Less complexity compared to coherent Less complexity compared to coherent detection at the price of higher error rate.detection at the price of higher error rate.

Lecture 7Lecture 7 29292006-02-132006-02-13

Non-Coherent Detection …Non-Coherent Detection … Differential coherent detectionDifferential coherent detection

Differential encoding of the messageDifferential encoding of the messageThe symbol phase changes if the The symbol phase changes if the

current bit is different from the current bit is different from the previous bit. previous bit.

,...,MiTtttTEts ii 1 ,0 ,)(cos2)( 0

)())1(()( nTTnnT ikk

)(1 t

i

1s2s 0

0 1 2 3 4 5 6 7 1 1 0 1 0 1 11 1 1 0 0 1 1 1

0 0

Symbol index: Data bits:Diff. encoded bitsSymbol phase:

k

kmk

Non-Coherent Detection …Non-Coherent Detection … Coherent detection for diff encoded Coherent detection for diff encoded

mod.mod.assumes slow variation in carrier-phase assumes slow variation in carrier-phase

mismatch during two symbol intervals.mismatch during two symbol intervals.correlates the received signal with basis correlates the received signal with basis

functionsfunctionsuses the phase difference between the uses the phase difference between the

current received vector and previously current received vector and previously estimated symbolestimated symbol

TttnttTEtr i 0 ),()(cos2)( 0

)(1 t

)(2 t

),( 11 ba),( 22 ba

i

)())1(()())1(()( nTTnnTTnnT ijiji

Non-Coherent Detect…Non-Coherent Detect…

Optimum differentially coherent detectorOptimum differentially coherent detector

Sub-optimum differentially coherent detectorSub-optimum differentially coherent detector

Performance degradation about 3 dB by Performance degradation about 3 dB by using sub-optimal detectorusing sub-optimal detector

T

0

)(1 t

)(tr m̂DecisionDelay

T

T

0)(tr m̂Decision

DelayT

Non-coherent detection Non-coherent detection ……

Non-coherent detection of BFSKNon-coherent detection of BFSK

T

0

)cos(/2 1tT

T

0)(tr

11z

12z

T

0

T

0

21z

22z

Decision stage:)cos(/2 2tT

)sin(/2 2tT

)sin(/2 1tT

2

2

2

2 +-

)(Tz

0ˆ ,0)( if1ˆ ,0)( if

mTzmTz

m̂

212

211 zz

222

221 zz