lecture 9 modulation, demodulation (detection): part 3 · quadratureamplitude modulation (qam)...

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EE4900/EE6720 Digital Communications Suketu Naik

EE4900/EE6720: Digital Communications

Lecture 9

Modulation,

Demodulation

(Detection): Part 3

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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 Quadrature

Amplitude Modulation

(QAM)

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Quadrature Amplitude Modulation (QAM)

Applications

QAM (rhymes with Guam and VietNAM) is commonly

used in communications

Example1:

DOCSIS Cable modems use 64-QAM, 256-QAM for

downstream channel (to home) and QPSK, 16-QAM for

the upstream channel (from home)

Example 2:

Satellite TV and Military SatCOM use QAM

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Quadrature Amplitude Modulation (QAM)

QAM: Amplitude and Phase of the baseband signal

changes BPSK: Binary Phase Shift Keying

(2 transitions, 1 bit/symbol)

QPSK: Quadrature Phase Shift Keying

(4 transitions, 2-bits/symbol)

8PSK:Eight Phase Shift Keying

(8 transitions, 3-bits/symbol)

16-QAM (16 transitions, 4-bits/symbol)



Example: 8PSK Time Domain

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QAM: BPSK and QPSK

BPSK: Phase of the baseband signal changes from 0 deg

to 180 deg (2 transitions)=1 bit per symbolQ (out of phase)

I (in phase)Phase Diagram 01

QPSK: Phase of the baseband signal changes from 45

deg, 135 deg, 225 deg, 315 deg (4 transitions)=2 bits per

symbol Q (out of phase)

I (in phase)Phase Diagram

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10

01

00

Radius= 𝑬𝒂𝒗𝒈


M=2, 1-bit

Eavg=A2

M=4, 2-bits

Eavg=A2

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QAM: 8-PSK and 4-QAM

8PSK = 8 phase transitions= 3 bits per symbol

4-QAM = 4 transitions = 2-bits/symbol

8-PSK Phase

Diagram

4-QAM

Phase Diagram

Q (out of phase)

I (in phase)

I (in phase)

Q (out of phase)


M=8, 3-bits

Eavg=A2

M=4, 2-bits

Eavg=2A2

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QAM: 16-PSK and 32-QAM 16-QAM = 16 transitions = 4-bits/symbol

64-QAM = 64 transitions = 6-bits/symbol

64-QAM

Phase Diagram

Q (out of phase)

I (in phase)

I (in phase)

Q (out of phase)

16-QAM

Phase Diagram

M=16, 4-bits

Eavg=10A2

M=64, 6-bits

Eavg=42A2

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8-QAM, 32-QAM, 128-QAM: Odd # of bits

Q (out of phase)

I (in phase)

8-QAM

M=8, 3-bits

Eavg=6A2

Q (out of phase)

I (in phase)

32-QAM 128-QAM

Q (out of phase)

I (in phase)

M=32, 5-bits

Eavg=20A2

M=128, 7-bits

Eavg=82A2

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Continuous-time QAM

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Continuous-time M-ary QAM Basics

M-ary QAM is a 2-dimensional signal

Basis function=unit energy pulse x sinusoid

Sinusoids (cosine and sine) are 90°out of phase with

each other (hence the name Quadrature)

QAM signal s(t) with k symbols*

𝝓𝟎(𝒕) = 𝟐𝒑 𝒕 𝐜𝐨𝐬 𝝎𝟎𝒕

𝝓𝟏(𝒕) = − 𝟐𝒑 𝒕 𝐬𝐢𝐧 𝝎𝟎𝒕

𝒔 𝒕 = 𝑰 𝒕 𝟐𝐜𝐨𝐬 𝝎𝟎𝒕 − 𝑸 𝒕 𝟐 𝐬𝐢𝐧 𝝎𝟎𝒕where,

𝑰 𝒕 =

𝒌

𝒂𝟎 𝒌 𝒑(𝒕 − 𝒌𝑻𝒔)

𝑸 𝒕 =

𝒌

𝒂𝟏 𝒌 𝒑(𝒕 − 𝒌𝑻𝒔)

In phase (‘Eye’)

Out-of-phase (‘Cue’)

*= the book often switches between notation k and M. Here we will assume that k=M. For example, 16-QAM has M=16

and k=16 symbols

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M-ary QAM Signal

kth QAM symbol in Rectangular and Polar Forms

Rect. Form: 𝒂𝟎 𝒌 𝒑(𝒕 − 𝒌𝑻𝒔) 𝟐𝐜𝐨𝐬 𝝎𝟎𝒕 − 𝒂𝟏 𝒌 𝒑(𝒕 − 𝒌𝑻𝒔) 𝟐 𝐬𝐢𝐧 𝝎𝟎𝒕

Polar Form: 𝒂𝟎𝟐 𝒌 + 𝒂𝟏

𝟐 𝒌 𝒑(𝒕 − 𝒌𝑻𝒔) 𝟐 𝐜𝐨𝐬 𝝎𝟎𝒕 + 𝒕𝒂𝒏−𝟏𝒂𝟏 𝒌

𝒂𝟎 𝒌

Amplitude changes Phase changes

In Phase (I) Out-of-phase (Q)

8PSK signalkth QAM symbol

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Continuous-time QAM Modulator

Basis

Function

ϕ0(t)

Basis

Function ϕ1(t)

Example: 16-QAM

Constellation

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Continuous-time QAM Demodulator

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Continuous-time QPSK Modulator

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Continuous-time QPSK Demodulator

I & Q signals

corrupted by noise

Eye Diagram

Eye Diagram

Eye Diagram

Eye Diagram

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Continuous-time QPSK: Eye DiagramQPSK 16-QAM

QPSK 16-QAM

α=1

(100%

excess BW)

α=0.5

(100%

excess BW)

SRRC Pulse

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Problems: Phase Offset and Symbol Timing Error

1) Uncompensated carrier phase

offset can distort the constellation

and ‘corrupt’ the received bits

- Counterclockwise

(CCW) rotation of °How to compensate?

Carrier Phase Synchronization

(Ch7)

2) Matched filter output: where is

the starting sample?

How to start?

Symbol Timing Synchronization

(Ch8)

Rotation of constellation due

to carrier phase offset

Scattered constellation points due to

symbol timing error

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Discrete-time QAM

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Discrete-time QAM Modulator

Basis Function

ϕ0(t)

Example: 16-QAM

Constellation

Basis

Function ϕ1(t)

Direct Digital Synthesizer

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Discrete-time QAM Modulator

We replace t with nT where n=sample index, T=sampling time

We will also up-sample and down-sample the symbol amplitudes

by factor N (insert N-1 zeros between each sample)

Discrete-time I and Q signals: Eq. 5.83, Eq. 5.84, Eq. 5.85

Next, the I & Q signals are passed through discrete-time pulse-

shaping filter which interpolates the samples (inserted zeros now

change into samples): pulse=samples of impulse response h(t)

Next, the interpolated I & Q signals are multiplied with discrete-

time sinusoids (cosine and sine): frequency of the sinusoids, Eq. 5.86

Finally, we add the I & Q signals and create a QAM signal, which

is passed through DAC and transmitted using a carrier signal

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Demodulator and the Signal Space Projections (Constellation Points)

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 QAM Demodulator

Time-reversal of the pulse shaping filter

Note: When building a model, we simply pass it

through the pulse-shaping filter again

x(kTs) and y(kTs) contain the

original constellation point +

noise: Eq. 5.91Eye Diagram

Eye Diagram

Eye Diagram

Eye

Diagram

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Problems: Phase Offset, ADC Sampling Rate, Symbol Timing Error

1) Uncompensated carrier phase

offset can distort the constellation

and ‘corrupt’ the received bits

- Counterclockwise (CCW)

rotation of °How to compensate?

Carrier Phase Synchronization (Ch7)

2) ADC sample rate is not an integer

multiple of symbol rate.

How to match sampling rates?

Resampling Filters (Ch9)

3) Matched filter output: where is

the starting sample?

How to start?

Symbol Timing Synchronization

(Ch8)

Rotation of constellation due

to carrier phase offset

Dispersed constellation points due to

symbol timing error

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Assignment 4 [10]

Simulate BPSK Communication 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-diagram and Constellation

4) Decoded Message

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Assignment 5 [20]

UG (EE4900): Simulate QPSK and 16-QAM

Communication System using Simulink and decode the

secret message [20]

G (EE6420): Simulate QPSK, 8PSK, and 16-QAM

Communication System in Simulink and decode the secret

message [30]

Build the following:

1) Modulators (for testing demodulators)

2) Demodulators

Submit the following:

1) Simulink models

2) Time-domain plots

3) Eye-diagrams and Constellations

4) Decoded Message

lecture 9 modulation, demodulation (detection): part 3 · quadratureamplitude modulation (qam)...

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