Lecture 8 Modulation, Demodulation (Detection): … 8 Modulation, Demodulation (Detection): Part 2....

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EE4900/EE6720 Digital Communications Suketu Naik

EE4900/EE6720: Digital Communications

Lecture 8

Modulation,

Demodulation

(Detection): Part 2

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Block Diagrams of Communication System

Digital Communication System

Informatio

n (sound,

video, text,

data, …)

Transducer &

A/D ConverterModulator

Source

Encoder

Channel

Encoder

Tx RF

System

Output

Signal

D/A Converter

and/or output

transducer

DemodulatorSource

Decoder

Channel

Decoder

Rx RF

System

Channel

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M-ary Pulse Amplitude

Modulation (PAM)

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Pulse Amplitude Modulation (PAM)

PAM is used in Digital TV, 10GBase-T Ethernet, LED

driver, Controls

PAM: Width is fixed, Amplitude varies

Original Signal

PAM Signal

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Modulator based on Synthesis Equation

Data/Audio/Video

[101 100 001 000 010 011 110 111]

Serial to Parallel

Group of

3 bits

One look-up table

per symbol

Constructing one

symbol so(t)

signal s(t) is created

from K-symbols

Example

Same group of bits

go to each path

1) Group of bits (e.g. 101)= the

decimal index (e.g. 5)

2) Now the coefficient with that

index is selected

Pulse-shaping filter

can be used here

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M-ary PAM Constellations

M-ary PAM is a 1-dimensional signal

Basis function=unit energy pulse (App.A: Pulse Shapes)

Binary PAM

or 2PAM

4PAM M=4, 2-bits

Eavg=5A2

M=2, 1-bit

Eavg=A2

8PAMM=8, 3-bits

Eavg=21A2

M-ary PAM log2(M) bits

Eavg=(M2-1)A2/3

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Discrete-time Binary PAM

Binary PAM

Constellation

Basis

Function=Pulse

Shape (NRZ, MAN,

HS or SRRC)

𝒙𝒌 = න𝑻𝟏

𝑻𝟐

𝒓 𝒕 ∅𝒌 𝒕 𝒅𝒕Analysis

Equation

𝒔(𝒕) =

𝒌=𝟎

𝑲−𝟏

𝒂𝒌∅𝒌(𝒕)Synthesis

Equation

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Signal Space Projections or Phase Diagram or Constellation

𝒔(𝒕) =

𝒌=𝟎

𝑲−𝟏

𝒂𝒌∅𝒌(𝒕)𝒙𝒌 = න

𝑻𝟏

𝑻𝟐

𝒓 𝒕 ∅𝒌 𝒕 𝒅𝒕

Goal: find the approximate vector xk

Analysis

Equation

Synthesis

Equation

Received Signal

Approximate

Received Signal

Basis Function 2

Basis Function 1

Approximate

Vector, xk

An example with K=2

Things to remember:

1) Phase diagram shows

Points

2) Points are denoted by

Vectors from origin

3) Points and Vectors

represent an actual analog

baseband signal

4) The amplitude of the

baseband signal = point in

the phase diagram

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Discrete-time Binary PAM with Up-sampling

3 clocks:

1) Bit Rate (before S/P)=BR

2) Symbol Rate (after S/P)

=BR/log2M

3) Pulse Rate (after Pulse

Shaping Filter)=N(BR/log2M)

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Up-sampling

D/A Conversion is preceded by up-sampling to increase the

number of samples so that sampling rates are matched

Up-sampling by N narrows the spectrum by factor of N

Up-sampling by N

Spectrum shrinks by N

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Up-sampling and Filtering: Interpolation

Up-sampling stuffs zeros in between two samples

Filtering can “interpolate” the samples and remove the zeros

Interpolated Samples Spectral copies are spaced apart

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Eye Diagram

Eye Diagram is an important diagnostic tool

Smaller Eye Opening=More Noise

Bigger Eye Opening=Less Noise

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Binary PAM Eye Diagram

Non-Return-to-Zero (NRZ)

Half-Sine (HS)

Manchester (MAN)

Square-Root-Raised-Cosine (SRRC)

Always look at

multiple symbols

and overlay them

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Assignment 3 [20]

Simulate binary-PAM Comm. System and decode the

secret message [10]

Modulator (for testing demodulator)

Demodulator

Simulate 8-PAM Comm. System in Simulink and decode

the secret message [10]

Build the following:

Modulator (for testing demodulator)

Demodulator

Submit the following:

1) Simulink models

2) Time-domain plots

3) Eye-diagrams and Constellations

4) Decoded Message

Lecture 8 Modulation, Demodulation (Detection): … 8 Modulation, Demodulation (Detection): Part 2....

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