Core: Modulation and demodulation

Def) ModulationConverting (processing) source signal to another signal more suitable for transmission

Basics of communications

Why modulate?• TX antenna size

– For efficient radiation, the radiating element (transmit antenna) should be a significant fraction of the wavelength.

– C = f λ : if f = 3kHz, λ = 105 m• Diffraction

– With longer wavelength, it is more difficult to make a narrow beam

– Diffraction angle is proportional to l/D, where D is the diameter of the radiator.

• Multiplexing– FDM– E.g., Voice 4KHz t

Modulation

• Core of communication: Modulation & Demodulation

modulator channel demodulatorSourcesignal Dest.+

n(t)

AM

Xx(t)

( )ccos 2 : carrier frequencycf t fπ

ttX

x(t)

( )ccos 2 f tπ

FMx(t) FM ( )( )

0cos 2

tcA f t x dπ τ τ + ∫

( )1 ( )

frequency of cos ( )2

frequency of FM signal ( )c

dg tg t f

dt

f x t

π= =

= +

t

t

x(t)

( )( )0

cos 2t

cA f t x dπ τ τ + ∫

Basics of Digital Comm.

modulator channel demodulatorSourceSignal

Bit stream

Dest.

bit

+

n(t)

Converting bits to waveforms

e.g., Digital modulation

Network perspective

Phy

NW

DLC

Phy

NW

DLC

Physical Channel(waveform)

Modulation Demodulation

Reliable Packet Pipe

Unreliable Bit Pipe

Digital Modulation examples

1 1 1 10 0 0

t

ON-OFF keyinge.g. optical fiber

01 01 11 00 1100 m001 m110 m211 m3

Bits Symbol

Amplitude Shift Keying (ASK)

Ts

m0

m1

m2

m3

Bit duration vs Symbol duration

Frequency Shift Keying (FSK)

Ts

m0

m1

( )[ ]0cos 2 cA f t f tπ + ∆

( )[ ]1cos 2 cA f t f tπ + ∆

mi( )[ ]cos 2 c iA f t f tπ + ∆

Phase Shift Keying (PSK)

{ }

( )

0 1 1, , ,

cos 2

i M

i c i

m m m m

m A f tπ θ

−∈

= +

tTs

different Phase

Quadrature PSK

( )[ ] ( ) ( )[ ] ( )

( )( )( )( )

0 0

1 1

2 2

3 3

: cos(2 ) cos cos 2 sin sin 2

1 1(0, 0) : , ,

4 2 23 1 1

(0,1) : , ,4 2 25 1 1

(1,1) : , ,4 2 27 1 1

(1, 0) : , ,4 2 2

i c i i c i cm f t f t f t

m

m

m

m

π θ θ π θ π

πθ

πθ

πθ

πθ

+ = −

=

−=

− −=

−=

QPSK modulator

X

X

+ channel

I1

S2

=

Q1

S2

−=

( )cos 2 cf tπ

( )sin 2 cf tπ

m3 :

( )

( )

1cos 2

21

sin 22

c

c

f t

f t

π

π−

+

r(t)

QPSK Demodulator

( )

0

sT

dt∫ i

( )

0

sT

dt∫ i

X

X

( )cos 2 cf tπ

( )sin 2 cf tπ−

( ) ( )

( )

( )

I

Q

S cos 2

+S sin 2

c

c

r t f t

f t

n t

π

π

=

+

IS2s

IT

n+

QS2s

QT

n+

( ) ( )

( ) ( )( ) ( ) ( ) ( )2I Q

cos 2

S cos 2 +S sin 2 cos 2 cos 2

c

c c c c

r t f t

f t f t f t n t f t

π

π π π π= − +

1integer multiple of sc

T f=

note

( ) ( ) ( )

( )( )

( )( )

( )

2

2

2

0

1sin 2 cos 2 sin 2 2

2

1 cos 2 2cos 2

2

1 sin 2 2sin 2

2

cos 22

s

c c c

cc

cc

Ts

c

f t f t f t

f tf t

f tf t

Tf t dt

π π π

ππ

ππ

π

⋅ = ⋅

+ ⋅=

− ⋅=

=∫

8PSK

001 110 101 111

000 m0001 m1

111 m7

I-Q representation of QPSK

( ) ( ) ( ) ( ) ( )( ): cos cos 2 sin sin 2i X i c i cm S t f t f tθ π θ π= + −

( )( )( )( )

0

1

2

3

1 1: ,

2 21 1

: ,2 21 1

: ,2 21 1

: ,2 2

m

m

m

m

−

− −

−

m0m1

m3m2

12

12

( )cos 2 cf tπ

( )sin 2 cf tπ−

In-phasecomponent

Quadrature-phasecomponent

I-Q representation of 8PSK

m0

m1

m4

m3

12

( )cos 2 cf tπ

( )sin 2 cf tπ−

In-phasecomponent

Quadrature-phasecomponent

m2

m5

m6

m7

“Symbol constellation”“Signal constellation”

Amplitude-Phase Shift Keying (M-QAM)

Imperfect Channel:Distortion and Noise

• Distortion and Noise• Fading, Shadowing of wireless channel

Band-limited channel

• Example of Bertsekas and Gallager, “Data Networks” 1992. Fig. 2.3

– Low pass filter

channel

Distortion of band-limited channel.Introduces inter-symbol interference (ISI).

Note

A rectangular wave’s bandwidth is large.The band-limited channel clips the high-frequency component of the signal.

Wireline Channel

( ) ( ) ( )

Baseband( ) ( ) ( )b b b b

y t x h t w t

y t x h t w t

= ∗ +

= ∗ +

Pulse modulation( )

( )

( )

( )

[ ]

Baseband( )

( ) ( )

Receive fitler ( ) and sampling( ) ( )

( ) ( )

Nyquist zero-forcing criteria of () : [ ] [ ]

In general

b kk

b k b bk

b k b bk

b k b bk

b

x t s p t kT

y t s p g t kT w t

q tr t s p g q t kT w t

r nT s p g q nT kT w nT

p g q r n s n w n

= −

= ∗ − +

= ∗ ∗ − +

= ∗ ∗ − +

∗ ∗ = +

∑

∑

∑

∑

[ ] [ ] [ ] [ ] [ ], [ ] [ ]

Discrete-time convolution!!k k

r n h n k s k w n h k s n k w n= − + = − +∑ ∑

Pulse Modulation Implementation

X

X

+ channel

IS ( )n

QS ( )n

( )cos 2 cf tπ

( )sin 2 cf tπ

p(t-nT)

p(t-nT)

In the previous example, p(t) was a rectangular wave.