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Intro. to Comm. Systems & Networks - ENEL 471 Fapojuwo45

DemodulationDemodulation:

- process of recovering the original message from the modulated signal

(i.e., inverse of the modulation process)

- always performed at the receiver

Treatment is in 2 stages:

1) Modulated signal is not corrupted by channel noise (ideal case)

==> Detected message is the same as the original message at the transmitter

2) Modulated signal is corrupted by channel noise (realistic case)

==> Detected message is an estimate of the original message

Demodulator Detected MessageModulated signal

(= original messageif the demodulatoris perfect!)

(no channelnoise)

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Amplitude Demodulation

Approaches for Amplitude Demodulation:

1. Non-coherent Demodulation (Envelope Detector)

- does not require any carrier recovery at the receiver (since the carrier wastransmitted as a component of the modulated wave) ==> simplicity of receiver

- Application: Conventional AM scheme

2. Coherent Demodulation

- requires carrier recovery at the receiver ==> increased complexity of the receiver

- Application: DSB-SC, SSB and VSB schemes

Conclusion: The choice of a demodulation approach is dependent on the type of amplitudemodulation

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The Envelope Detector

Main Characteristics:

Combination of a diode and a resistor-capacitor (RC) low-pass filter

Conditions for proper operation:

1. 0 < < 1: to ensure the detected envelope is always positive

2. fm

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The Envelope Detector Circuit Diagram

Important Parameters:1. Capacitor charging time constant, Tchg = time for the capacitor C to charge to the peak voltage

Design Requirement:

2. Capacitor discharging time constant, Tdchg

= time for the capacitor C to discharge between twopeaks of the modulated wave

Design Requirement:

Vc(t) = g1 + g2m(t) --> m(t)

rf

AM

dccomponent

gain factor

Tchg rf Rs+ C=

rf Rs+ C1

fc---

Tdchg RlC=1

c

--- RlC1

W-----

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Input and Output of the Envelope Detector

AM wave

input

Envelope

detector

output

Vc(t)

sAM(t)

Clearly, the

output is a

good replica

of AM wavesenvelope

AM wavesenvelope

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Coherent Demodulation

Main Characteristics:

- Carrier recovery process at the receiver: estimate the carrier frequency & phase

- The locally generated carrier at the receiver must be exactly coherent orsynchronized in both frequency and phase with the carrier signal at the Tx

- Reality: achieving perfect synchronization is very difficult in practice due to therandom variations of the communication channel

LPFXModulated

signal

Detectedmessage

v0(t)

v(t)

mixer output

~

Local oscillator

c(t)

locally generatedcarrier

Coherent demodulator

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Coherent Demodulation TheoryAnalysis Assumptions:

A1. DSB-SC modulation is used at the transmitter

A2. Bandwidth of the message Wis much less than the carrier frequency fc

A3. Carrier recovery process is imperfect: i.e., imperfect synchronization

- a phase error of radians exists between the estimated phase at the receiver andthe actual phase of the carrier at the transmitter

- the carrier amplitude at the receiver ( ) also differs from the amplitude of the

carrier at the transmitter

Analysis Task:

- Derive the expression for v0(t), the demodulated signal (or detected messagesignal)

Ac

Ac

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Coherent Demodulation Theory (contd)

By Assumption A1, the DSB-SC modulated signal is given by:

sDSB(t) = m(t)Accos(2fct) (from Page 21)

By Assumption A3, the locally generated carrier is given by:

The mixer output is given by:

Take the Fourier transform ofv(t), to obtain its spectrum V(f):

c t Ac

2fct + cos=

' '( ) = cos(4 ) ( ) + cos( ) ( )

2 2cc c c cA A A Av t f t m t m t

' ''( ) = ( 2 ) + ( 2 ) + cos( ) ( )

4 4 2j jc c c c c c

c cA A A A A A

V f e M f f e M f f M f

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Spectrum of the Mixer Output, V(f)

Clearly, the sidebands can be filtered out by a LPF with cutoff frequency Bc, provided

W < Bc < (2fc - W)

The above inequality is satisfied, based on Assumption A2: W

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Coherent Demodulation Theory (contd)

Finally, at the LPF output, the demodulated signal v0(t) is therefore given by:

Conclusions:

1. The original message can be recovered by the coherent demodulator

- The demodulated signal v0(t) is proportional to m(t), the original message

2. Since , the demodulated signal is attenuated by a factor of

Question: Under what condition will not cause a distortion in the detected signal?

Hint: Recall the conditions for distortionless transmission (from Topic 2)

0

'

( ) = cos( ) ( )2c cA A

v t m t

cos 1 cos

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Amplitude Modulation-Demodulation System in the Presenceof Additive White Gaussian Noise (AWGN) Channel

What is an Additive White Gaussian Noise Channel?

- Additive: noise samples can be added to the modulated signal at the receiver input

- White: noise power spectral density (PSD) SN(f) in Watts/Hz is flat for all frequencies

- Gaussian: noise samples follow a Gaussian distribution with zero mean

Notes: 1. The white noise process has infinite average power, hence it is not physically realizable.

2. However, the noise process at the input of a system can be modeled as white provided thebandwidth of the noise process is larger than that of the system - this is true in practice

f f-f

N0

N0/2

SN(f)SN(f)

Double-sided PSD Single-sided PSD

N0 = average noise power per unit bandwidth

Flat PSD

0 0

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A Generic Receiver Model in the Presence of Noise

Band-pass filter:

- represents the combined filtering of the receiver front-end amplifiers

- assumed to be ideal, with a bandwidth equal to message transmission bandwidth, centered at fc

Noise:

- The noise process w(t) is modeled as AWGN with zero mean and power spectral density N0/2

- At the BPF output, w(t) becomes the filtered noise n(t) defined by:

where nI(t) is the in-phase noise component and nQ(t) is the quadrature noise component

Demodulator input signal: x(t) = s(t) + n(t)

Receiver

n t nI t 2fct cos nQ t 2fct sin=

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Receiver Performance Metric: Signal-to-Noise Ratio (SNR)

Receiver

SNRref SNRo

Average power of the modulated signalReference Signal-to-Noise Ratio, =Average power of noise in the message bandwidthref

SNR

Average power of the demodulated message signalOutput Signal-to-Noise Ratio, =

Average power of the noise at receiver outputoSNR

Figure of Merit, = o

ref

SNRFOM

SNR

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Performance of DSB-SC with Coherent Detection in thePresence of Noise

y(t) = 0.5CAcm(t) + 0.5nI(t)

Hence: FOMDSB = 1.0

LPFXModulatedsignal

Detectedmessage

y(t)

v(t)

~Local oscillator

cos(2fct)

Coherent detector

BPFx(t)

+

Noisew(t)

sDSB(t)

DSB

Coherent Receiver

2 2

,,0

= =2

co DSBref DSB

C A PSNR SNRWN

C= scaling factor

P = E[m2(t)]

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Performance of AM with Envelope Detection in the Presence of Noise

Hence:

EnvelopeModulatedsignal

Detectedmessage

y(t)

BPFx(t)

+

Noisew(t)

sAM(t)

Amplitude

Non-coherent Receiver

Detector

2

,0

= 2c

ref AM

A P

SNR WN

,

2o AM o

PSNRWN

2< 1

+AM c

PFOM

A P

y(t) = m(t) + nI(t) (Approximation!)

P = E[m2(t)]

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