Principles of CommunicationsLecture 7: Analog Modulation Techniques (5)

Chih-Wei Liu 劉志尉National Chiao Tung Universitycwliu@twins.ee.nctu.edu.tw

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Outlines

Linear Modulation

Angle Modulation

Interference

Feedback Demodulators

Analog Pulse Modulation

Delta Modulation and PCM

Multiplexing

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Analog Pulse Modulation

Message waveform is represented by regularly spaced sample values (sample signals) – discrete in time.

Historically, these methods are the early attempts to achieve modern communications. They are in the twilight zone between analog and digital modulations.

Today, their basic forms can still be found in some electronic components such as ADC.

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Analog/Digital Pulse-coded

Analog pulse modulation: A pulse train is used as the carrier wave. Some characteristic feature of each pulse (e.g., amplitude, duration, or position) is used to represent message samples.PAM – pulse amplitudePDM – pulse durationPPM – pulse position

Digital Pulse Modulation: Messages are discrete-amplitude (finite levels) samples.DM – delta modulationPCM – pulse-code modulation

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Pulse-Amplitude Modulation (PAM)

The amplitude of each pulse corresponds to the value of the message signal m(t) (at the leading edge of the pulse).

The pulse generator can be considered as a “filter”.

( 0.5 )( ) ( )

1, 2where 0, otherwise

Sc S

n

t nTm t m nT

WttW

ττ

∞

=−∞

− +⎡ ⎤= ⋅Π ⎢ ⎥⎣ ⎦⎧

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PAM Signals

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Demodulation

Recover Mδ(f) ↔ mδ(t) samples

Recover M(f) ↔ m(t) message

Equalizer: Recover distorted signals particularly when the distortion method is known or estimated.

1/H(f) LPF

equalizer

mc(t) mδ(t) m(t)

)()()(

fHfMfM c=δ

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Pulse-Width Modulation (PWM)

Pulse width ∝ the values of messageSpectrum: complicated (Fourier-Bessel spectra)

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PWM/PPM Generation

Mod:

Demod: area of “pulse”.

Low-pass filtering (integration)

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Pulse-Position Modulation (PPM)

Pulse position ∝ the values of message

Spectrum: complicated

Demodulation: (1) LPF & integration

(2) convert PPM to PWM → LPFConversion of PPM or PWM to PAM: a ramp generator (re)starts at kTs and stops at tk. (next page)

( ) ( )nn

x t g t t∞

=−∞

= −∑

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Conversion Between PWM & PPM

(integration)

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Delta Modulation

m(t) → samples (analog amplitude) → difference → binary

or m(t) → difference → binary → samplesOperations:

(1)

(2)

(3)

(4)

)()()( tmtmtd s−=

0

0

, 0( ) ( ( )) =

, ( ) 0d(t)

t threshold d td t

δδ

≥⎧Δ = ⎨−

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DM Signal Generation

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Slope Overload

The message signal m(t) has a slope greater than can be followed by the stair-step approximation ms(t).

Assume step-size = δ0 → slope (max) = δ0/Ts

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Solution to Overload

Adaptive delta modulation -- adjust the step-size δ0based on xc(t).

Idea: If m(t) ≈ constant, xc(t) alternates in sign

⇒ make δ0 ↓.

If m(t) ↑ ( or ↓ ) rapidly, xc(t) has the same polarity

⇒ make δ0↑.Method: Detect the “trend” of signal

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Adaptive DM

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ADM Receiver

Transmit step-size or regenerate the step-size at the receiver according to pre-decided “rules”.

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Pulse-Code Modulation (PCM)

m(t) → samples (analog amplitude) → quantized samples → binary representation → binary modulated waveform (ASK (AM), PSK (PM), FSK (FM) to be discussed in Commun.II )

Main advantages of digital communication

– more reliable communication

Main disadvantages of digital communication

– wide BW ( reduced by “compression”)

– complicated circuits ( cost reduced by VLSI)

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PCM Signal Generation

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BW of PCM

Assume the number of quantization levels=q=2n

Message BW = W

Sampling rate = 2W

⇒ 2nW binary pulses/secondAssume maximum width of pulse,

⇒ transmission BW ≈ knW, k=constant

Hence, B ≈ k2Wlog2qRecovered message error is due to mainly quantization error. Thus, q↑ error↓ B↑

12nW

τΔ =

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Multiplexing

A number of data sources share the same communication channel.

Frequency-Division Multiplexing (FDM)

Quadrature Multiplexing (QM)

Time-Division Multiplexing (TDM)

Nov 2009hmhang, EE/NCTU 23

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FDMSeveral message signals are translated, using modulation, to different spectral locations and added to form a baseband signal.

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Example: Stereophonic FM

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Quadrature Multiplexing (QM)

Quadrature-carrier multiplexing: transmit two signals on the same carrier frequency. (not exactly FDM)

Note that cos and sin are orthogonal.QM Quadrature Amplitude Modulation (QAM)

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1 2

1 2

1

( ) [ ( )cos ( )sin ].

If the receiver has a carrier phase error, i.e.,

( ) 2cos( ).( ) 2cos( )

[ ( )cos ( )sin ] + [ ( )cos(2 )

c C c c

c

r c

C

C c

x t A m t t m t t

LO t tx t t

A m t m tA m t t

ω ω

ω θω θθ θ

ω θ

= +

= +⋅ +

= −+ 2

1 2

( )sin(2 )].( ) [ ( )cos ( )sin ]. (ideal : 0 )

c

DD C

m t ty t A m t m t

ω θθ θ θ+ +

⇒ = − →

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Time-Division Multiplexing (TDM)

Each message signal occupies a small time slot in every Ts second.

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BW of TDM

A “rough” estimate of BW

1

1

Baseband message BW = . There are channels.Samples per second = 2 .

Total samples per second: 2 . Or,

Total samples per second = 2 .

Total baseband BW to accommodate all sources

i

iN

s ii

N

ii

W NT WT

T n WT

W

=

=

= ∑

∑

1

= .N

ii

B W=∑

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Example: Digital telephony system

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Comparison of MUX

FDM: simple to implement,inter-modulation distortion (crosstalk) due to nonlinear channels

TDM: less crosstalk (in memoryless channels),difficult to keep synchronization (frame structure, header), “digital” (sampled) signals

QM: efficient use of channel, crosstalk between I & Q channels (needs coherent demodulation)