8/16/20021 Modems Key Learning Points Fundamentals of modulation and demodulation Frequency Domain Representation Time Domain Representation M-ary Modulation.

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Modems

Key Learning Points

• Fundamentals of modulation and demodulation

• Frequency Domain Representation

• Time Domain Representation

•M-ary Modulation and Bandwidth Efficiency

• BER vs bit/second

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2.5 Public Carrier Circuits

for Limited Geographic Span: use privately owned resources• e.g. Local Area Network, Routers, Hubs

for Larger Geographic Span:

• Line of Sight (LOS) uwave

• satellite links

• public carriers (e.g. Sprint, MCI, …)

- analog PSTN using modems

- digital leased lines: T1, T3, ISDN

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2.5.1: Analog PSTN Circuit

• designed for analog voice transmission (mixed audio frequencies )

• Bandwidth ranges 400-3000Hz

- DC power supply will not pass low frequency signals (1111… or 0000…)

- 2 voltage levels for different signals won’t work (0 output for 1111… or 0000…)

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Binary Data Transmission over PSTN Requires Modem

Modulator: Convert binary data into from compatible with

PSTN at transmitter

Demodulator: Convert signal back, recover data at receiver

2 options for conventional PSTN modem connection:

1. short-term switched path: dialing & setting up ~ phone call

2. leased line: bypass normal switching equipment (switch exchanges)

- set-up on long-term basis- economical only if utilization is high

- operating characteristics accurately quantified higher signal rates

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Modulation: three general types which can be combined

(i) Amplitude Shift Key,

(ii) Frequency Shift Key,

(iii) Phase Shift Key

binary data requires at least 2 signal levels• as binary data keys between 1 and 0• signal shifts between 2 levels

different methods require different amounts of BW

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(1) carrier signal: vc(t) = cos wct (assume unity amplitude)

• carrier frequency, fc: (Hz) or wc = 2fc (rads)

• fc selected within PSTN Bandwidth (1000Hz-2000Hz)

(2) binary data signal, vd(t)

fundamental frequency of data signal: w0 = 2f0

mathematically modulation is vc(t) vd(t)

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1. Amplitude Shift Key (ASK) Principal of Operation:

- amplitude of audio tone (fc) switched between 2 levels

- bit rate of transmitted binary signal determines switching rate & bandwidth

- binary data is effectively carried by carrier signal

unipolar periodic data signal given by:

...5cos

5

13cos

3

1cos

2

2

1000 twtwtw

vd(t) =

vASK(t) = vc(t) vd(t)

modulated signal given by

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....3coscos3

1coscos

2cos

2

100

twtwtwtwtw ccc =

vASK(t) = vc(t) vd(t)

= twwtwwtw ccc )cos()cos(1

cos2

100

*2cosA cosB = cos(A-B) + cos(A+B)

twwtww cc )3cos()3cos(3

100

...)5cos()5cos(5

100 twwtww cc

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vASK(t) =

00 ))12(cos(

12

11cos

2

1

icc twiw

itw

vASK(t) consists of original data signal vd(t)

• translated in frequency by wc (wc ± w0, wc ± 3w0, wc ± 5w0) …

• DC component translated to sinusoidal component at wc

• 2 frequency components for fundamental & each harmonic

- frequency components are equally space on either side of fc

- spectral components are known as sidebands

- each bandpass component at ½ power of original baseband sidebands

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fc–3f0 fc–f0 fc fc+f0 fc+3f0 f

signal power

6f0

2f0ASK – frequency domain

digital signal

carrier signal 1 0 1 0 1 0

+V0

ASK – time domain

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Recall from discussion of Limited Bandwidth:

• higher channel bandwidth received signal is closer to transmitted

• given data rate = R, minimum channel bandwidth for satisfactory performance in the worst case

- f0 of “101010…” (shortest period highest f0)

- f0 = ½ R

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• minimum channel bandwidth for ASK

- to receive only f0 bandwidth, B = 2f0 = R

- to receive f0 and 3rd Harmonic bandwitdh = 6f0 = 3R,

• component at carrier frequency is present in received signal, contains no information (inefficient)

- Nyquist: maximum achievable data rate for ideal channel

C = 2 B

Alternatively, let B = 2f0 max data rate R = B =22f0

• both primary sidebands used to compute minimum BW• either contains required signal, f0

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Single Side Band (SSB)

• use band pass filter on transmitter lower required bandwidth to B = f0 (Nyquist rate)

- limit pass band- remove lower sidebands: (fc - f0)

e.g. limit pass band to fc + (fc + 5f0)

• primary sideband signal power cut in ½ relative to vc (t )

- reduces Signal to Noise Ration increases BER

SSB-ASK

fc–5f0 … fc–f0 fc fc+f0 …. fc+5f0 f

filter

power passband

filter

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Demodulation: Recover transmitted Signal – at receiver• assume ideal channel - no noise, distortion, attenuation• practically, problem is more difficult

received signal = vASK(t)

...)3cos(

3

1)cos(

1cos

2

100 twwtwwtw ccc

vASK(t) =

...)3cos(cos

3

1)cos(cos

1coscos

2

100 twwtwtwwtwtwtw cccccc

...)32cos(3

13cos

3

1)2cos(cos

2

1)2cos()0cos(

4

1

00

00

twwtw

twwtwtwt

c

cc

receiver multiplies vASK(t) by vc (t) vd(t) v2c(t)

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Produces 2 versions of received signal

• each at ½ original power

• both with data contained in sidebands

• one is centered at 2fc (high frequency component )

• other is at baseband (fc - fc) = 0

0

00

12

)12(2cos

12

)12(cos2

2

1)2cos()0cos(

4

1

i

cc i

twiw

i

twitwt

collecting terms yields:

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Select baseband signal with Low Pass filter:

• Low pass filter output = bandwidth limited version of vd(t)

• pass only 0, f0 3f0, (assume 3rd harmonic used )

filter all components < 3f0

0

00

12

)12(2cos

12

)12(cos2

2

1)2cos()0cos(

4

1

i

cc i

twiw

i

twitwt

hi frequency components completely filtered

00 3cos3

1cos

1

4

1ww

Recovered Signal =

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000 cos

1...3cos

3

1cos

1

4

1nw

nww

Recovered Signal after low pass filtering, fcutoff = 3fn

Original Data Signal

...5cos

5

13cos

3

1cos

2

2

1000 twtwtw

vd(t) =

Modulated Signal

vASK(t) =

00 ))12(cos(

12

11cos

2

1

icc twiw

itw

Demodulated Signal

0

00

12

)12(2cos

12

)12(cos2

2

1)2cos()0cos(

4

1

i

cc i

twiw

i

twitwt

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vd(t)

f0 3f0 f

fc–3f0 fc–f0 fc fc+f0 fc+3f0 f

vASK(t)

2 fc–3f0 2fc–f0 2fc 2fc+f0 2 fc+3f0 f0 3f0

demodulated

f0 3f0

filtered and recovered

Ideal ASK Modulation – Frequency Domain

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vd‘(t)PSTN

cos(wct)

vd(t)

cos(w’ct)

vASK (t)

More Practically• if attenuation is included 10-30dB attenuation common• if noise is included received power > noise floor (SNR)• if distortion is included must use equalizers, match filter, etc

• if carriers aren’t synchronized phase noise wc(t)-w’c(t) = (t)

• receiver must synchronize sampling interval to recover signal

Fantasy: Received Signal = ½ power of Transmitted Signal

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ASK is simple to implement, not used in early, low rate modems

- PSTN long haul switching & transmission systems were analog

- voice & data signals transmitted & switched as analog signals

- ASK sensitive to resulting variable signal attenuation

More recently PSTN long haul switching & transmission systems are digital

- source signal is analog only to local exchange- converted digital signal retains form thru-out network

- significant improvement in electrical characteristics of PSTN ckts

ASK & PSK used to in higher rate modems

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data-rate 300bps 1200bps 4800bpscomponent

f0 150Hz 600Hz 2400Hz

3f0 450Hz 1800Hz 7200Hz

ie: Estimate BW to transmit f0 & 3f0 using ASK for data rates: (without SSB)

baseband

14400Hz3600Hz900Hz6f0

4800Hz1200Hz300Hz2 f0

Required BW4800bps1200bps300bpsdata-rate

bandpass

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2. Frequency Shift Key (FSK): used in early low rate modems

Principal of Operation

• use 2 fixed amplitude carrier signals, vc1 (t), vc2 (t) to avoid reliance on amplitude variance

• modulation is equivalent to summing 2 ASK modulators- one carrier uses original data signal, vd(t)- other carrier uses compliment of data signal, v’d(t)

- 2 data signals: vd(t) and vd’(t) = 1- vd(t)

• 2 carrier frequencies fc1 , fc2 frequency shift: fs = fc2 - fc1

vFSK(t) = vc1(t) vd(t) + vc2(t) vd’(t)

= cos(wc1t) vd(t) + cos(wc2t) vd’(t)

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1 0 1 0 1 0 data vd(t)

carrier vc1(t)+V

-V

+V

-V

0 1 0 1 0 1 inverted data v’d(t)

carrier vc2(t)

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FSK – time domain

vFSK(t) = cos wc1t

...)5cos

5

13cos

3

1(cos

2

2

1000 twtwtw

+ cos wc2t

...)5cos

5

13cos

3

1(cos

2

2

1000 twtwtw

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sign

al p

ower

FSK – frequency domain

fc1–3f01 fc1–f01 fc1 fc1+f01 fc1+3f01

6f01

2f01

fc2–3f02 fc2–f02 fc2 fc2+f02 fc2+3f02

frequency shift: fs = fc2 – fc1

6f02

2f02

...)3cos(

3

1)cos(

1cos

2

102022 twwtwwtw ccc

...)3cos(

3

1)cos(

1cos

2

101011 twwtwwtw ccc

vFSK(t)

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FSK bandwidth requirements

• fc1 modulates ‘1’ and fc2 modulates ‘0’ - minimum bandwidth for each carrier is ½ R - highest fundamental freq component of each carrier ½ of ASK

• assume just f0 component received (no harmonics)

- let fs = fc2-fc1 total bandwidth for FSK is 2f0-FSK + fs

- since f0-FSK ½ f0-ASK total BW f0-ASK + fs

- with 3rd harmonic: 6f0 ASK+ fs

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fc1 fc2

-3 -2 -1 0 1 2 3frequency = 1/Tb

Sunde FSK MSK

Attn

(dB)

0-10-20-30-40

• choice of fs is significant - naïve choice vs efficient choice

• spectrum of simple FSK vs CPFSK techniques- Sunde FSK- MSK

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simple FSK system with phase jumps

switch

cos w2t

cos w1tinput data phase jumps

VCO

cos wct

input data

continuous phase FSK (CPFSK) with VCO based oscillator

Implementation of FSK

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ie: EIA for Bell 103, ITU-T for V.21 - FSK modems, full-duplex links

• f0 = 75 Hz R = 150 bps

• 2f0 = 150 Hz R = 300 bps

• fs = 200Hz, separation between primary sidebands = 50Hz

space = binary 0, mark = binary 1

DTE DTE

modemmodulator

‘0’ = 1070 Hz‘1’ = 1270 Hz

demodulator’0’ = 2025 Hz ‘1’= 2225 Hz

modem

demodulator‘0’ = 1070 Hz‘1’ = 1270 Hz

modulator’0’ = 2025 Hz’1’ = 2225 Hz

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3. PSK: phase shifts in carrier encode bits in data stream• carrier frequency & amplitude are constant (constant envelope)

phase coherent‘1’‘0’

i. phase coherent PSK: 2 fixed carriers 180° phase shift represents ‘1’ or ‘0’

• One signal is simply inverse of other

• Disadvantage: requires reference carrier signal at receiver- received phase signal is compared to local reference carrier- more complex demodulation circuitry

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differential90° = ‘0’270° = ‘1’’

270° phase shift relative to current signal next bit = ‘1’

ii. differential PSK: phase shift at each bit transition• irrespective of whether ‘111…’ or ‘000…’ transmitted

90° phase shift relative to current signal next bit = ‘0’

• demodulation: determine magnitude of each phase shift (not absolute value)

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PSK Bandwidth requirement: represent data in bi-polar form

• negative signal level results in 180° phase change in carrier• assume unity amplitude, fundamental freq = w0

...)5cos5

13cos

3

1(cos

4000 twtwtw

V

vd(t) =

vc(t) = cos wct

vPSK(t) = vd(t)vc(t)

...5coscos

5

13coscos

3

1coscos

4000 twtwtwtwtwtw ccc

vPSK(t) =

...)5cos(

51

)3cos(31

)cos(2

000 twwtwwtww ccc

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fc–3f0 fc–f0 fc fc+f0 fc+3f0 f

signal power 6f0

2f0

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PSK BW Requirements

- same bandwidth as ASK, no carrier component, coswct at wc

- assume 10101… w/ only f0 to be received min BW = 2 f0

-absence of carrier component means more power to sidebands - sidebands contain data more resilient to noise than FSK, ASK

with band pass filter on transmitter band limit transmitted signal to fc

• achieve nyquist rate for minimum bandwidth required ½ R = f0

(~ ASK)

• no component at wc all received power in data carrying signal, fc ± f0, …

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Phase Diagram• 2 axis: in-phase, I & quadrature, Q• represents carrier as vector, length = amplitude• vector rotates CCW around axis angular frequency, w

- ‘1’ represented as vector in phase with carrier- ‘0’ represented as vector 180° out of phase with carrier

Q (quadrature)

180 = 0 0 =1 I (in-phase)

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4. Multilevel Modulation

• Advanced modulation techniques higher bit rates- multi-level signaling- mix of basic schemes (PSK, ASK)- more complex (cost), higher bit error rate

• Used in all digital PSTN (switching & transmission)

Multi-Level Signal (use amplitude, phase, or frequency)

• use n signal levels each signal represents log2n data bits

- 4 signal levels 2 bits/signal element

- 8 signal levels 3 bits/signal element

- 16 signal levels 4 bits/signal element

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Q (quadrature)

180o= 00 0o = 11 I (in-phase)

90o = 00

270o = 10

QPSK (4-PSK):

• 4 signals (0°, 90°, 180°, 270°) 2 bits/signal

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QAM – (quad amplitude modulation) Combine ASK & PSK• QAM-16 levels per signal element 4-bits per symbol

- 12 phase levels- 4 amplitudes levels- different amplitude associated with adjacent phases - 48 total signal levels possible bits/symbol = 5

2(t)

1(t)

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using 16 of 48 possible signals makes recovery less prone to errors- same amplitude levels have large phase variation- same phase angles have large amplitude variation- extra bit can be used for forward error correction

practical limits to M-level signalling:

• more phase/amplitude levels difference between unique signal

symbols is reduced

• increases impact of channel impairments (noise distortion, attenuation• scheme’s robustness depends on proximity of adjacent points in constellation• complexity rises cost, risk, rate of failures rise

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received signal region bit error unlikely

8 signals 3 bits/signalQ (quadrature)

0o = 010

270o = 111

I (in-phase)180o= 100

90o = 001

45o = 011

225o =101 300o= 110

135o = 111

received signal region bit error likely

reduce error rate: maximize distance between adjacent points grey coding – adjacent symbols differ by 1 bit offset phase angles for adjacent amplitude

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All modulation schemes scramble & descramble

• reduces probability that consecutive bits in sequence are in adjacent bit positions

- at transmitter: bit stream scrambled using pseudo random sequence- at receiver: bit stream descrambled restore bit stream- used in V.29 modems (fax machines @ 9600 bps)

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trellis–code modulation (TCM) - another redundancy scheme

- use all 32 amplitude –phase alternatives

- resulting 5 bit symbols contain only 4 data bits

- 5th bit generated using convolutional encoder, used for error correction

• at transmitter: each 4-bit set in source stream converted to 5 bits • at receiver: most likely 4 data bits determined

- with no bit errors correct 4 bit set collected- with bit errors some probability that correct 4 bits selected

used inV.32 for rates up to 14.4kbpsV.34 fast modems rates up to 19.2k, 24k, & 28k

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type bps modulation protocol bell 103 0-300 FSK async bell 202 1200 FSK async V.22 1200/600 QPSK/FSK synch/async V.26 2400 QPSK sync V.27 4.8002400 8DQPSK/QDPSK sync V.29 9600 16-APK sync V.32 9600 32 QAM 16QAM sync V.33 14.4k 32 QAM svnc V.34 33.6k >1024 QAM sync V.90 56k >1024 QAM sync

different types of PSTN Modems

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2.5.1a. Cable Modems (CM) • Connection speed 3-50 Mbit/s • Distance can be 100 km or more• Master-Slave Topology (CATV is traditionally simplex)• CATV networks are Hybrid Fibre-Coax (HFC) networks

- fiber-optic cables from the Head-End to locations near the subscriber

- the signal is converted to coaxial cables to subscriber premises.

• CMTS: Cable Modem Termination System

- connects cable TV network to data network

- CMTS can drive 1-2000 simultaneous CMs on 1 TV channel

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Cable Modem 4Cable Modem 3

Cable Modem 2

CMTS (head)

Upstream DemodulatorQPSK/16-QAMcarrier freq. 5-65MHzBW: 2MHzData Rate: 3Mbps

Downstream Modulator64 QAM/256QAMcarrier freq: 65-850MHzBW: 6-8MHzData Rate: 27-56Mbps

Cable Modem 1

Upstream ModulatorQPSK/16-QAMcarrier freq: 5-65ZMHzBW: 2MHzData Rate: 3Mbps

Downstream Demodulator64 QAM/256QAMcarrier freq: 65-850MHzBW: 6-8MHzData Rate: 27-56Mbps

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OSIDOCSIS

(Data Over Cable Service Interface Specification)

Higher Layers ApplicationsDOCSIS Control Messages

Transport Layer TCP/UDP

Network Layer IP

Data Link Layer IEEE 802.2

Physical Layer

Upstream Downstream

TDMA 5 - 42 MHzQPSK/16-QAM

TDMA42 - 850 MHz64/256-QAMITU-T J.83 Annex B

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2.5.1.b Digital Subscriber Line (DSL) – up to 52Mbps over traditional phone lines

• uses carrier frequencies between 25KHz .. 1MHz• always on – no need to dial Internet Service Provider (ISP)• dedicated connections (not shared with your neighbors)• voice & data over a single line

more expensive, additional hardware required• special DSL modem at your computer• DSL Multiplexer (DSLAM) at central office

- separates voice/data streams- sends voice stream to phone company & data stream to ISP

limited availability• connection speed is dependent on distance from phone company • data rate is lowered to reduce distortion • DSL link must be within 2 miles of central office