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Digital CommunicationSystems

Dr. Shurjeel Wyne

Lecture 9

CH 4 -Bandpass Modulation& Demodulation

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Today, we are going to talkabout:

Some bandpass modulation schemes used

in DCS for transmitting information over

channel

Passband M-ASK, M-PSK, M-QAM, M-FSK

How to detect the transmitted information at the

receiver

Coherent detection

Non-coherent detection

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Block diagram of a DCS

FormatSource

encode

FormatSource

decode

Channel

encode

Pulse

modulate

Bandpass

modulate

Channel

decode

Demod.

SampleDetect

Channel

Digital modulation

Digital demodulation

4

Bandpass modulation

Bandpass modulation: The process of converting datasignal to a sinusoidal waveform whose amplitude, phase,

frequency, ora combination of them, is varied in accordance

with the transmitted data.

General Bandpass signal:

where is the baseband pulse shape with energy .

We assume here (unless stated otherwise):

is a rectangular pulse shape with unit energy.

Gray coding is used for mapping bits to symbols.

denotes average symbol energy given by

)(tgT

)(tgT gE

sE M

i isE

ME

1

1

TtttfifT

Etgts ic

iTi 0,)()1(2cos

2)()(

1gE

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Demodulation and detection Demodulation: The receiver signal is converted to

baseband, filtered and sampled.

Detection: Sampled values are used for detection using a

decision rule such as ML detection rule.

Nz

z

1

z

T

0

)(1 t

T

0

)(tN

)(tr

1z

Nz

zDecision

circuits

(ML detector)m

6

Coherent and Non-coherentdetection

Coherent detection

requires carrier phase recovery at the receiver

and hence, circuits to estimate carrier phase

Possible sources of carrier-phase mismatch at

the receiver:

Propagation delay causes carrier-phase offset in

the received signal. The oscillators at the receiver which generate the

carrier signal, are not usually phased locked to the

transmitted carrier.

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Coherent and non-coherent

detection Circuits such as Phase-Locked-Loop (PLL) are

implemented at the receiver for carrier phaseoffset estimation ( ).

Non-coherent detection

does not require carrier phase recovery (useseither differentially encoded modulation or

energy detectors. It has lesser complexity thancoherent detection, but at the price of a highererror rate.

PLL

Oscillator 90 deg.

)()(cos2

)()( tnttT

Etgtr ii

iT cos

2t

Tc

sin2

tT

c

Used by

correlators

I branch

Q branch

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Bandpass Modulation Schemes

One dimensional waveforms

Amplitude Shift Keying (ASK)

On-Off Keying

M-ary Amplitude Shift Keying (M-ASK)

Two dimensional waveforms

M-ary Phase Shift Keying (M-PSK)

M-ary Quadrature Amplitude Modulation (M-QAM) Multidimensional waveforms

M-ary Frequency Shift Keying (M-FSK)

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One dimensional modulation

Amplitude Shift Keying (ASK) modulation:

tT

Ets cii cos2

)(

cos2)(

2,,1)()(

1

1

ii

c

ii

Ea

tT

t

Mitats

)(1 t1s2s

01E

0 1

Example:

On-off keying (M=2):

10

One dimensional modulation

M-ary Amplitude shift Keying (M-ASK)

tT

ats cii cos2

)(

gs

gii

gi

c

ii

EM

E

MiEE

EMia

t

T

t

Mitats

3

)1(

12

)12(

cos2

)(

,,1)()(

2

22

1

1

s

Example:

4-ASK

)(1 t2s1s

0gE3

00 01

4s3s11 10

gE gE gE3

...

M

i isE

ME

1

1

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Example of bandpass modulation:

Binary ASK (M=2)

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Coherent detection of M-ASK

T

0

)(1 t

ML detector(Compare with M-1 thresholds)

)(tr1z

m

One dimensional modulationdemodulation and detection

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Two dimensional modulation

M-ary Phase Shift Keying (M-PSK)

M

it

T

Ets c

si

2cos

2)(

2

21

21

2211

2sin

2cos

sin2

)(cos2

)(

,,1)()()(

iis

sisi

cc

iii

EE

M

iEa

M

iEa

tT

ttT

t

Mitatats

s

...

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Two dimensional mod, (MPSK)

)(1 t

2s1s

bE

0 1

bE

)(2 t

3s

7s

110

)(1 t

4s 2ssE

000

)(2 t

6s 8s

1s

5s

001011

010

101

111 100

)(1 t

2

s1

s

sE

00

11

)(2 t

3s 4s10

01

QPSK (M=4)

BPSK (M=2)

8PSK (M=8)

Exceptional case: can be represented by single dimension

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Two dimensional mod,(MPSK)

demodulation and detection

Coherent detection of MPSK

Compute Choose

smallest2

1arctanz

z

|| i

T

0

)(1 t

T

0

)(2 t

)(tr

1z

2z

m21

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Two dimensional modulation M-ary Quadrature Amplitude Mod. (M-QAM)

ici

i tT

Ets cos

2)(

3

)1(2andsymbolsPAMareandwhere

sin2

)(cos2

)(

,,1)()()(

21

21

2211

MEaa

tT

ttT

t

Mitatats

sii

cc

iii

...

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Two dimensional mod, (M-QAM)

)(1 t

)(2 t

2s1s 3s 4s0000 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

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Two dimensional mod, (M-QAM)demodulation and detection

Coherent detection of M-QAM

T

0

)(1 t

ML detector1z

T

0

)(2 t

ML detector

)(tr

2z

mParallel-to-serialconverter

s)threshold1with(Compare M

s)threshold1with(Compare M

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Example of two dim. modulation

)(1 t

2s 1s

sE

00

11

)(2 t

3s 4s10

01QPSK

3

s

7s

110

)(1 t

4s 2ssE

000

)(2 t

6s 8s

1s

5s

001011

010

101

111 100

8PSK

)(1 t

)(2 t

2s1s 3s 4s0000 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

16QAM

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Multi-dimensional modulation M-ary Frequency Shift keying (M-FSK)

detectioncoherent-non,1

detectioncoherent,2

1

)1(2cos2

cos2

)(

HzT

f

HzT

f

tfifT

Et

T

Ets c

si

si

2

1

0cos

2)(

,,1)()(

iis

sijii

M

jjiji

EE

ji

jiEat

Tt

Mitats

s

)(1 t

2s

1s

3s

)(3 t

)(2 t

sE

sE

sE,...,

frequency spacing required

to guarantee orthogonal

FSK waveforms

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Multi-dimensional mod,(M-FSK)

demodulation & detection

Coherent detection of M-FSK

Mz

z

1

z

T

0

)(1 t

T

0

)(tM

)(tr

1z

Mz

z

ML detector:Choose waveform

corresponding to

the largest element

in the observed vector

m

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Non-coherent detection Non-coherent detection:

No need for a reference in-phase with the

received carrier

Less complexity as compared to coherent

detection at the price of higher error rate.

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Types of non-coherent detection

1. Differentially coherentdetection Example: Differential PSK (DPSK)

The term differentially coherentdetection ofdifferentially encoded PSK (which is the usualmeaning of DPSK) refers to a detection schemeoften classified as non-coherent because it does notrequire a reference in-phase with the receivedcarrier.

At the transmitter, the current information bits and

previous symbol, determine the phase of the currentsymbol (called differential encoding).

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Non-coherent detection (DPSK)

Differential encoding of the DPSK message The symbol phase, , changes if data bits in

current symbol interval differ from data bits in

previous symbol interval.

,...,MiTtttT

Ets i

si 1,0,)(cos

2)( 0

)(1 t1s2s 0

0 1 2 3 4 5 6 7

1 1 0 1 0 1 1

1 1 1 0 0 1 1 1

0 0

Symbol index:

Data bits:

Diff. encoded bits:

Symbol phase: k

kmk

ki

Binary (M=2) DPSK encoding example

Note: The first bit of the encoded bit sequence, c(k), is chosen arbitrarily, here taken to be binary 1.

kc

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Consider the received signal with phase shift

sequence entering the correlator, in the

absence of noise:

0 0 k

Non-coherent detection (DPSK)

k 0 1 2 3 4 5 6 7

Detection for the Binary (M=2) DPSK encoding example

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2. Energy detection

Example: energy detection for orthogonal

signals such as M-FSK.

The received energy corresponding to each

candidate signal is used for detection.

Types of non-coherent detection

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