ELEC 7073 Digital Communications III, Dept. of E.E.E., HKUp. 1

Part 3.1 Basic Modulation

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Modulation Process

Modulation implies varying one or more characteristics (modulation parameters a1, a2, … an) of a carrier f in accordance with the information-bearing (modulating) baseband signal.

Sinusoidal waves, pulse train, square wave, etc. can be used as carriers

( )1 2 3

1 2 3

, , ,... , ( carrier), , ,... ( modulation parameters)

( time)

n

n

f f a a a a ta a a at

= →

→→

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Continuous Carrier

Carrier: A cos[ωt +ϕ]– A = const– ω = const – ϕ = const

Amplitude modulation (AM)– A = A(t) – carries information

– ω = const – ϕ = const

Frequency modulation (FM)– A = const– ω = ω(t)– carries information

– ϕ = const

Phase modulation (PM)– A = const– ω = const – ϕ = ϕ(t) – carries information

Modulation methods: using amplitude, phase or frequency of the carrier.

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Basic Modulation

Modulation involves operations on one or more of the three characteristics of a carrier signal: amplitude, frequency and phase.

The three basic modulation methods are:– Amplitude Shift Keying (ASK)

– Phase Shift Keying (PSK)

–Frequency Shift Keying (FSK)

These could be applied to binary or M-ary signals.

There are other variants as well.

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Amplitude Shift Keying (ASK) (1)

The modulation signal set is

− Ts is the symbol period − fc is the carrier frequency, is the carrier initial phase− g(t) is a real-value signal pulse whose shape influences the spectrum

of the transmitted signal; Pulse shaping− Used to simultaneously reduce the intersymbol effects and the spectral

width of a modulated digital signal− Example: rectangular pulse, Nyquist pulse shaping, raised cosine pulse

shaping, Gaussian pulse shaping, etc.

− Ai=(2i-1-M)d, each symbol represents log2M bits

[ ]1,2, ,

( ) ( )cos 2 ,0i i c c

s

i Ms t A g t f t

t Tπ θ

== +

≤ ≤L

cθ

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Amplitude Shift Keying (ASK) (2)

The single basis signal is

The modulated signal:

[ ]12( ) ( )cos 2 c c

g

t g t f tφ π θε

= +

1( ) ( ), 2i i i i gs t s t s Aφ ε= =

• ASK demonstrates poor performance, as it is heavily affected by noise, fading, and interference. It is rarely used on its own.

Rectangular pulse

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Phase Shift Keying (PSK)

The modulation signal set is

− Ac is the carrier amplitude,

− carries information, each symbol represents log2M bits

[ ]( ) ( )cos 2 , 1,2, ,2 0( 1)

i c c c i

si

s t A g t f t i Mt Ti

M

π θ ϕπϕ

= + + =≤ ≤= −

L

iϕ

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Binary Phase Shift Keying (BPSK) (1)

M=2: minimum phase separation: 180 o

− s1(t) and s2(t) represent bit 0 and bit 1,respectively

− The single basis:

− The set :

[ ]( ) ( )cos 2 ( 1) , 1,2, 0i c c c bs t A g t f t i i t Tπ θ π= + + − = ≤ ≤

[ ]12( ) ( )cos 2 c cg

t g t f tφ π θε

= +

1 1( ), ( )2 2g g

c cS A t A tε εφ φ

⎧ ⎫⎪ ⎪= −⎨ ⎬⎪ ⎪⎩ ⎭

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Binary Phase Shift Keying (BPSK) (2)

2

0.5

b

bB

B RRB

η

≈

= =

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Quadrature Phase Shift Keying (QPSK) (1)

M=4: symbol period Ts=2Tb, minimum phase separation: 90 o

− The basis signals:

− Constellation diagram:

( ) ( )cos 2 ( 1) , 1,2,3,4, 02i c c c ss t A g t f t i i t Tππ θ⎡ ⎤= + + − = ≤ ≤⎢ ⎥⎣ ⎦

[ ] [ ]1 22 2( ) ( )cos 2 , ( ) ( )sin 2c c c cg g

t g t f t t g t f tφ π θ φ π θε ε

= + = − +

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Quadrature Phase Shift Keying (QPSK) (2)

1

b

bB

B RRB

η

≈

= =

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PSK: Bandwidth vs. Power Efficiency

The system using ideal Nyquist pulse shaping is operated in AWGN channel.

QPSK can be interpreted as two independent BPSK systems (one on the I-channel and the other on Q-channel), and thus the same performance but twice the bandwidth efficiency.

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Quadrature Amplitude Modulation (QAM) (1)

Combined amplitude/phase shift keying

− As both amplitude and phase are used to carry symbol information, it is very bandwidth efficient

− Signal set size M=M1M2: 21 × 21 = 4, 22 × 22 = 16, 23

× 23 = 64, etc → 4QAM, 16QAM, 64QAM

− The larger M is, the better bandwidth efficiency but lower robustness against noise and fading

1 2

( ) ( )cos 2 ,

1,2, , , 1,2, , ,0i i c c j

s

s t A g t f t

i M j M t T

π θ ϕ⎡ ⎤= + +⎣ ⎦= = ≤ ≤L L

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Quadrature Amplitude Modulation (QAM) (2)

Examples of constellation:

Rectangular constellation

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QAM: Bandwidth vs. Power Efficiency

The system using optimum raised cosine pulse shaping is operated in AWGN channel.

In terms of power efficiency, QAM is superior to M-ary PSK.

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Frequency Shift Keying (FSK)

The modulation signal set is

BFSK: M=2

− Bit 0:

− Bit 1:

[ ]( ) cos 2 , 1,2, , ,0i c i c ss t A f t i M t Tπ θ= + = ≤ ≤L

1 12, ( ) cos(2 ( ) )b

c c cb

f f f s t f f tTε π θ= − Δ = − Δ +

2 22, ( ) cos(2 ( ) )b

c c cb

f f f s t f f tTε π θ= + Δ = + Δ +

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FSK: Bandwidth vs. Power Efficiency

•Nonlinear modulation: bandwidth inefficient but power efficient, no need for expensive linear amplifiers

•The orthogonality characteristic of MFSK OFDM as a means of providing power efficient signaling

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Other Modulations

Differential phase shift keying (DPSK)− The input binary sequence is differentially encoded before

BPSK modulation− Avoids the need for a coherent reference signal at the receiver

Offset QPSK− The phase transitions are limited to 900, the transitions on the

I and Q channels are staggered.π/4 QPSK− The phase transitions are limited to 1350

Continuous-phase FSK (CPFSK)− Avoids sudden change in the signal frequency, i.e., large

spectral side lobes outside of the main spectral band− Minimum shift keying (MSK), Gaussian MSK(GMSK)

( )1k k kd m d −= ⊕

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Performance in AWGN Channel (1)

The channel is assumed to corrupt the signal by the additive white Gaussian noise.

Distortion

Channels(t)

n(t)

r(t)=s(t)+n(t)

Perfect channel White noise

2 0noise power: 2n

Nσ =

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Performance in AWGN Channel (2)

212ε

The optimum ML AWGN receiver: max P(r(t)|si(t))

( )( ) ( )

( )

MAP: max ( ) | ( )

( ) | ( ) ( )max

( )

i

i i

P s t r t

P r t s t P s tP r t

=

MAP = ML when the M signals si(t) are equally probable. P(si(t))=1/M

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Performance in AWGN Channel (3)

ASK: symbol error probability

( )( )

2 ,2

0

,

6 log2( 1)1

is the average bit energy

b avM

b av

MMP QM M N

ε

ε

⎛ ⎞− ⎜ ⎟=⎜ ⎟−⎝ ⎠

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Performance in AWGN Channel (4)

PSK: symbol error probability

( )0

2

b

0

22 sin , 4

log is the symbol energy

BP 2 SK & QPSK:

sM

s b

M

P Q MN M

M

P QN

ε π

ε ε

ε

⎛ ⎞⎛ ⎞≈ >⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

=

⎛ ⎞= ⎜ ⎟

⎝ ⎠

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Performance in AWGN Channel (5)

QAM: symbol error probability

For rectangular QAM constellations:

( )

( )

,

0

, 2 ,

34 ,

1

The average symbol energy:log

s avM

s av b av

P QM N

M

ε

ε ε

⎛ ⎞≤ ⎜ ⎟⎜ ⎟−⎝ ⎠

=

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Performance in AWGN Channel (6)

FSK: symbol error probability

( )0

2

( 1) ,

log

sM

s b

P M QN

M

ε

ε ε

⎛ ⎞≤ − ⎜ ⎟

⎝ ⎠=