©1997 BG Mobasseri 1 04/20/23

V.29, V.32, V.32 bis...

THE INS AND OUTS OF MODEMS

©1997 BG Mobasseri 2 04/20/23

BUT FIRST...

©1997 BG Mobasseri 3 04/20/23

NONCOHERENT DETECTION

Handling Phase Sync Problems through

Differential Encoding

©1997 BG Mobasseri 4 04/20/23

PHASE SYNCHRONISM

Coherent detection requires precise phase

sync between the received signal and local

oscillator.

Ak cos ωct+θk( )

Ac cos ωct+θc( )

AkAc cos θk−θc( )LPF

phase error

©1997 BG Mobasseri 5 04/20/23

DIFFICULTY ESTABLISHING ABSOLUTE PHASE REFERENCE

What is the phase of the RF pulse seen on the

scope?

©1997 BG Mobasseri 6 04/20/23

CONVENTIONAL ENCODING

Take a 4-phase modulation, known as

Quadrature Phase Shift Keying(QPSK)

90

180

270

000

01

10

11

Es cos 2πfct( )

Escos2πfct+π2

⎛ ⎝

⎞ ⎠

Escos2πfct+π( )

Escos2πfct+3π2

⎛ ⎝

⎞ ⎠

©1997 BG Mobasseri 7 04/20/23

DIFFERENTIAL ENCODING

Although the absolute phase of the incoming

signal varies, by as much as 50o, phase

transitions across symbols are very stable

Instead of mapping symbols into absolute

phases, they are encoded by phase

transitions

©1997 BG Mobasseri 8 04/20/23

MAPPING DATA TO PHASE CHANGES: BINARY EXAMPLE

Data is encoded such that a digit 1 causes a

180 phase shift relative to the previous phase

but 0 causes no phase shift

Receiver will in turn look for phase changes

rather than absolute phases

©1997 BG Mobasseri 9 04/20/23

DIFFERENTIAL ENCODING FOR BPSK

Encode 1 0 1 1 0 1 in BPSK and differential

PSK (DPSK)

π

1 0 1 1 0 1

π π πPSK

phase

phase(reference

π

1 0 1 1 0 1

DPSK

π π

©1997 BG Mobasseri 10 04/20/23

DECODING

1 0 1 1 0 1

πphase change

symbol

Data

π π π

1 0 1 1 0 1

DPSK

π πphase

©1997 BG Mobasseri 11 04/20/23

QPSK WITH GRAY CODING

0 0.5 1 1.5 2 2.5 3 3.5 4-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1absolute phase: 0,90,180,270 - 00 01 11 10

00->001->9011->18010->270

00 01 11 10

©1997 BG Mobasseri 12 04/20/23

DQPSK

-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1Differential QPSK : 11 01 11 10

bits change00 001 9011 18010 270

11 01 11 1090

arbitrary ref.

270 0 180 90

©1997 BG Mobasseri 13 04/20/23

HOW DO MODEMS WORK?

A look into modulation methods

©1997 BG Mobasseri 14 04/20/23

A BIT OF HISTORY

Early modems designed in the 1950’s used

Frequency Shift Keying(FSK) at 300 bps over

public switched phone lines

In the 1960’s equalized bandwidth increased

to 2400Hz thus allowing bit rates of 2400 bps.

©1997 BG Mobasseri 15 04/20/23

FIRST MILESTONE:V.26

The first 2400 bps modem was made available

in 1962 using 4-PSK (actually, differential

PSK, DPSK)

This was followed in 1967by 8-DPSK at 4800

bps

Note that to achieve higher rates, one has to

go to larger constellation sizes:

BM-ary=Bbinary/logM=4800/3=1600 Hz

©1997 BG Mobasseri 16 04/20/23

BAUD vs. BITS

Baud is the number of symbols/sec.

Bauds and bits are related by logM, where M

is the number of modulation levels– R=Rb/logM

Commercial modems are rated by bits/sec

even though the box says “baud”

©1997 BG Mobasseri 17 04/20/23

9600 bits/sec: V.29/V.32

The first 9600 bps modem was introduced in

1976 using 16-QAM constellation

Baudrate=bandwidth=2400 Hz

Requires adaptive channel equalization to

reduce intersymbol interference

©1997 BG Mobasseri 18 04/20/23

QAM MODEMS

All modern modulation techniques used in

modems are based on the Quadrature

Amplitude Modulation (QAM) method

16-QAM

©1997 BG Mobasseri 19 04/20/23

NON-DIFFERENTIAL GRAY CODING

01010001

0000 0100

1101 1001

1100 1000

1110

1111

1010

1011

0010 0110

0011 0111

©1997 BG Mobasseri 20 04/20/23

L-fold AMBIGUITY

An L-fold rotationally symmetric constellation

maps onto itself for a rotation of +/-K.(2pi/L)

The receiver is unable to resolve a number of

possible carrier lock positions

00

01

10

1100

01

10

11

©1997 BG Mobasseri 21 04/20/23

DIFFERENTIAL QAM

Divide the signal space into L equal pie-

shaped sectors

For 16-QAM, L=4, differentially Gray encode

sectors by 00, 01, 11, 10

Gray encode the remaining 2 bits within each

sector.

©1997 BG Mobasseri 22 04/20/23

DQAM CONSTELLATION

00010011

0010 0000

0111 0101

0110 0100

1111

1110

1101

1100

1011 1001

1010 1000

©1997 BG Mobasseri 23 04/20/23

V.29

0

90

180

270

45135

225 315

3 535

3

5

√2

3√2

9600 bps V.2916-QAM

©1997 BG Mobasseri 24 04/20/23

DATA MAPPING

1

11

1

1

11

1

ASSIGNMENT OF FIRST BIT{0,1}Q2Q3Q4

©1997 BG Mobasseri 25 04/20/23

ENCODING THE REMAINING 3 BITS

The remaining 3 bits are differentially Gray

coded:

Q2 Q3 Q4 Phase Change

0 0 1 0

0 0 0 45

0 1 0 90

0 1 1 135

1 1 1 180

1 1 0 225

1 0 0 270

1 0 1 315

©1997 BG Mobasseri 26 04/20/23

FALL BACK RATE

If conditions demand, transmission falls back

to 8-QAM at 7200 bps. Bit Q1 is permanently

set to zero limiting the amplitudes.

0

90

180

270

45135

225 315

33

3

2

32

©1997 BG Mobasseri 27 04/20/23

V.33

V.33 is a transmission standard at 14,400 bps.

Modulation is 128-QAM constellation

Carrier frequency is 1800 Hz.

Signaling rate is 2400 baud.

©1997 BG Mobasseri 28 04/20/23

V.34

Adopted in September 94.

Signaling at 28.8 kbps.

Baud rate at 3200 symbols/sec

Constellation size: 768 points