Chapter 8:

Multiplexing

COE 341: Data & Computer Communications (T061)Dr. Radwan E. Abdel-Aal

2

Where are we:

Physical Layer

Transmission Medium

Data Link

Chapter 4: Transmission Media

Chapter 3: Signals and their transmission over

media, Impairments

Chapter 5: Encoding: From data to signals

Chapter 7: Data Link: Flow and Error control

Chapter 6: Data Communication: Synchronization,

Error detection and correction

Chapter 8: Improved utilization: Multiplexing

3

Contents

1. Introduction

2. Two Multiplexing Techniques1. FDM

2. TDM1. Synchronous

2. Statistical

3. Application: ADSL

(Asymmetric Digital Subscriber Line)

4

Introduction Multiplexing: A generic term used when more

than one application or source share the capacity of one link

Objective is to achieve better utilization of the link bandwidth (channel capacity)

Multiplexer Demultiplexer

5

Motivation High capacity (data rate) links are cost effective.

i.e. it is more economical to go for large capacity links But requirements of individual users are usually fairly

modest…e.g. 9.6 to 64 kbps for non intensive (graphics, video applications).

Solution: Let a number of such users share the high capacity channel (Multiplexing)

Example: Long haul trunk traffic: High capacity links: Optical fiber, terrestrial microwaves, etc. Large number of channels between cities over large

distances

6

Multiplexing Types Our three resources:

Space Time Frequency Our channels must be

separated in at least one resource (can overlap in the other two)

The resource in which they are separated is “divided” between them: SDM: Separation in space TDM: Separation in time FDM: Separation in frequency

Space

FrequencyTime

TDM:Time Division Multiplexing

To use the same circuit (line)i.e. sharing space:

Use either TDM or FDM

FDM:Frequency Division Multiplexing

7

Multiplexing Types

Synchronous Statistical

FDM: Frequency Division MultiplexingTDM: Time Division MultiplexingWDM: Wavelength Division Multiplexing (a form of FDM)

Analog Signals Digital SignalsRepresentingdigital or analog data

ModulationOr shift keying

Separation in Frequency

Separation in time by interleaving

Encoding

8

Frequency Division Multiplexing (FDM)

• Channels exist on the same line (space) at the same time:• Must be separated in frequency!

f

t

9

FDM Useful bandwidth of medium exceeds required

bandwidth of channel Signal of each channel is modulated on a different

carrier frequency fc

So, channels are shifted from same base band by different fc’s to occupy different frequency bands

Carrier frequencies separated so that channels do not overlap (also include some guard bands)

Disadvantage: Channel spectrum is allocated even if no data available for transmission in channel (rigid allocation)

10

FDM

Different Frequencies

Same time

11

FDM Multiplexing Process: Time-Domain View at TX

Fc (Different for each channel)Modulator

Qty: 3

12

FDM Multiplexing Process: Frequency-Domain View at TX

All source channels are at (same) base band

ff

f1

f2

f3

0 4 KHz f1 f2 f3

Restoration at RX:3 different pass-band filters,each bracketing a channel

13

FDM De-Multiplexing Process: Time-Domain View at RX

f1

f2

f3

fcDemodulator

Low Pass Filter

Qty: 3

Demultiplexing Filters

Qty: 3

Filter pass bands

(Different for each channelSame as those used at TX)

14

FDM De-Multiplexing Process: Frequency-Domain View at RX

f1

f2

f3

0 4 KHz

All received channels restored to base band

• Guard bands prevent channel overlap• But represent wasted spectrum

f

15

FDM System – Transmitter

Subcarriers

Main CarrierAny type of modulation:AM, FM, PM

Group of channels

To meet Transmission Requirements

Individual base band channels

16

FDM System – Receiver

fc

Composite base band signal mb(t)

recovered

Individual base band channels

recovered

Subcarriers

Main Carrier

f1

f2

f3

17

FDM of Three Voice band Signals

What is the modulation type ?

3 MUXed channelUsing lower side band only

3 Subcarriers at:64, 68, and 72 KHz

Channel overlap means crosstalk!

Guard bandsTo reduce channel spectrum overlap

BW, allocated: 0 – 4000 Hz

BW, actual : 300 – 3400 Hz

fc

Assume we will keep only the lower side band

for each channel

18

Analog Carrier Systems One-go Vs Hierarchical:

…. Channel ….

Group ….

Master super group

Super group ….

4000 channels 4000 channels

... ...

• Modular approach• Easier to implement• Also, not all channels may be available at one place

Stages

….

….

19

Analog Carrier Systems Devised by AT&T (USA) Hierarchy of FDM schemes: MUXing in stages Group: AM, Lower Side band

12 voice channels = 12 x 4 kHz = 48 kHz BW 12 sub carriers: 64 kHz – 108 kHz in 4 KHz intervals Frequency range for group: 60 kHz – 108 kHz = 48 kHz (lower side band)

Super group: FM 5 groups = 5 x 48 kHz = 240 kHz BW 5 sub carriers: 420 kHz - 612 kHz at 48 KHz intervals (No GBs bet. groups) Frequency range: 312 kHz – 552 kHz = 240 kHz

Master group: FM 10 super groups = 10 x 240 kHz = 2400 kHz BW 10 sub carriers: 1116 kHz - 3396 kHz (Min of 8 KHz GBs between SGs) BW of 2.52 MHz (> 10 x 240 KHz = 2.4 MHz due to GB between SGs)

Jumbo group: FM

6 master groups i.e. total of 6 x 10 x 5 x 12 = 3600 voice channels BW of 16.984 MHz (> 3600 x 4 KHz due to gaud bands between super groups)

Each channel is 300 to 3400 = 3100 Hz. 4000 Hz provides 900 Hz guard band

20

Analog Carrier Systems

12

8 KHz

GroupChannel Super group Master super group

3084

21

Analog FDM Hierarchy

0.24 x 10 Vs 2.52

22

FDM characteristic problems Two potential problems characterize FDM and

all broadband applications Crosstalk:

- Due to overlap between channel spectra and the use of non-ideal filters to separate them

- Use gurdbands

Inter modulation noise:

- Nonlinearities in amplifiers ‘mix’ channels

- This generates spurious frequency components (sum, difference) which fall within channel BWs!

23

Waveform Division MUXing (WDM) A form of FDM used with optical fibers Lasers of different colors (different wavelengths)

are used simultaneously in the same fiber Each beam carries a separate data channel 256 such beams @ 40 Gbps each 10 Tbps

over 100 km

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Usually uses synchronous transmission,

but asynchronous is also possible Data rate of medium exceeds data rate of digital

signals to be transmitted for one channel Digital signals of multiple channels interleaved in time Interleaving may be:

At bit level At block level (e.g. bytes)

Two types: Synchronous TDM (Fixed rotation on channels) Statistical or asynchronous TDM (More efficient utilization of

the time slots)

Time Division Multiplexing (TDM)

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Time Division Multiplexing

300 Hz Channels occupy the same frequency band(Base band)

Channels must go on the link atdifferent times

3400 Hz

26

Time Division Multiplexing (TDM)

BasebandSignals

Ts = 1/2fmax

Channel sampling interval

Note: MUXing and DeMUXingare transparent to the end stations.Each pair ‘think’ they have a dedicated link !

Time

27

TDM Frames

Channel sampling interval = 3TFor each channel, data rate is 1 sample/3T

1

2

3

4

5

6

123456….Sample Number

On the link: Data is sent at a rate of 1 sample/TData rate is 3 times the channel data rate

Sampling Interval

Sampling Interval

28

Interleaving may be: At bit level: Suitable for synchronous transmission At block level (e.g. bytes): Suitable for asynchronous

transmission Synchronous TDM: (Fixed channel scan arrangement)

Time slots pre-assigned to sources and fixed Disadvantage: Time slots allocated even if no data available

(channel capacity waste, as with BW waste in FDM) But simple to implement, e.g. No need to send ID of source

channel We could assign more than time slot per scan for faster sources-

but on a permanent basis Could use both synchronous and asynchronous transmission

Time Division Multiplexing (TDM)

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Synchronous TDM – Transmitter

Scanning and link data rate: high enough to prevent channel buffers overflowing

N channels,Sampling rate R sample/s Minimum link

capacity = N R sample/s

Analog Signal

Digital Signalor

Transmitted frames consist of interleaved channel data

Time Slot, T Channel dwell time

T Should be enough to

empty a channel buffer

Channel 2

Bit stream

Channel Buffers

Sample data fills buffer

30

TDM System – Receiver

Bit stream

31

Data Link Control with Sync TDM Frames on the link consist of interleaved channel frames

They will not have headers and trailers of their own Data rate on the link (multiplexed line) is fixed and MUX

and DEMUX must operate at it Data link control protocol not needed on the MUXED line Flow control Channel based

If one channel receiver is not ready to receive data, other channels will carry on

Channel-based flow control would then halt corresponding source channel

This causes transmission of empty slots for that channel in the MUXED data

Error control Channel based Errors are detected and handled by individual channel systems

32

Data Link Control with TDM

Channel 1 Frame

This is what goes on the linkEverything is mixed up, even FCS bytesFCS applies only to channel framesChannel frames get reassembled at RX

Start of “1” Frame

MUXed stream can not be considered as an HDLC frames!

33

Framing in TDM So far, no flag or SYNC characters bracketing

composite (MUXED) TDM frames on the link Must provide frame synchronization to allow RX

to keep ‘in step’ with TX Two approaches:

Frame-by-Frame: A synch pattern at the beginning of each assembled frame (similar to the preamble flag)

Frame-to-Frame: Additional control channel with a unique frame-to-frame pattern that can be easily identified by RX (can be just 1 bit, and extends across frames, so less overhead)This is called “added digit framing”

34

Framing in TDM Added digit framing

One control bit added to each TDM frame as an additional “control channel”

Carries an identifiable known bit pattern in time (frame to frame) e.g. alternating 01010101…unlikely to occur on a normal data channel

RX searches frame-to-frame for this pattern until it finds it. This establishes frame sync. Will keep locked to it

35

Frame-to-Frame Sync (added digit framing)

C 1 2 3 4 C 1 2 3 4 C 1

0 1 0

Four data channels

Control Channel, C010101….

…..

A data ChannelUnlikely to have 010101…. over successive frames

Once the position of this control channel is established, RX knows where the channel sequence starts and sync is established with TX

…..

MUXed frame

RX knows the size of the MUXed frame

It can check each frame bit frame-to-frame for the special pattern until it finds it!

36

Pulse Stuffing Other Practical Problems:

Different sources (channels) may require sampling at different rates

Different sources may be using different clocks and you would like to standardize them on a common (higher rate) clock

Solution - Pulse Stuffing Make outgoing data rate higher than the sum of incoming rates

and an exact multiple of each to allow uniform sampling Stuff extra dummy bits (pulses) into incoming channel signals to

satisfy the higher data rate Stuffed pulses inserted at fixed locations in frame by TX MUX

and removed by RX deMUX

37

Pulse Stuffing Example:

Source 1: 1 bps

Source 2: 3 bps

MUXed data rate 1+3 = 4 bps take as 6 bps

(divides both rates)

(1/6) s1 sSource 1

Sampling

Source 2Sampling (1/3) s

X X

MUXed (composite) sampling

Dummy pulses stuffed in place of blank (unused) samples

MUXedFrame

Useful data rate: 4 bps

38

Example: TDM of 11 Analog and Digital Sources

=BW=fmax

Now channel 2 is sampled uniformly and at the correct rate

221 2 3

PCM with n = 4 bits/sample

PAM Analog samples

PCM

Sys

tem

3 Analog Channels

Digital Signals:64 kbps

Analog to Digital Converter

RotationFrequency

8 D

igit

al I

nput

s

Sampling rate = 2 fmax = 4K sample/s

64 kbps

Sampling rate:2 fmax = 8K sample/s

= MUXed data rate

Satisfies the two requirements:• 64 + 8 x 8 128 kbps• Divides 64kbps, 8 kbps exactly

Rotation/s

39

Example: TDM of 11 Analog and Digital Sources

16-bit Buffer

2-bit Buffer

2-bit Buffer

2-bit Buffer

Suggested framing and buffering arrangement

64 kbps 16-bit2-bit………2-bit 2-bit

32-bit MUXed frames

64 kbps

No. of frames/s= 128 kbps/32bpframe= 4 k frames/s= Rotation rate

Time slot, enough to empty buffer8 kbps

This is also the rate of emptying any ofThe MUXed buffers: 4 k buffers/s

Rate of filling the buffers should not exceed the rate of emptying them

Rate of filling this buffer= 64 kbps/16 bpbuffer= 4 k buffers/s

4 k rotations/s

Frame bits are allocated to Scanned sources in proportion to their data rates

40

Digital Carrier Systems Hierarchy for TDM (as with FDM!) USA/Canada/Japan use one system ITU-T use a similar (but different) system US system based on DS format, for example DS-1 (similar to a group in FDM):

Multiplexes 24 PCM voice channels digitized with n = 8 bits + a framing bit (a control channel for frame-to-frame synchronization)

Frame takes a sample of each channel So, frame size is 24 x 8 +1 = 193 bits Channels must be sampled at 2 x 4000 = 8000 sample/s This gives a data rate = 8000 x 193 = 1.544 Mbps for DS-1

Note: FDM Group needed 48 KHz for 12 channels

41

The DS Hierarchy

42 x 96 = 4032 DS-0(4032 voice channels)

DS-0 is a PCM voice channel:8000 sample/s x 8 b/sample= 64 kbps

Transmission lines used should support the progressivelyincreasing data rate (channel capacity) requirement

FDM Jumbo group: 16.984 MHz for 3600 channels

Which one uses BW more efficiently ?

42

DS & T Lines Rates

Service LineData Rate

(Mbps)No. of Voice

Channels

DS-1DS-1 T-1T-1 1.5441.544 2424

DS-2DS-2 T-2T-2 6.3126.312 9696

DS-3DS-3 T-3T-3 44.73644.736 672672

DS-4DS-4 T-4T-4 274.176274.176 40324032

Transmission line that supports it Corresponding Channel Capacity

43

DS-1 Digital Carrier Systems For voice, each channel contains one byte of digitized

data (PCM, 8000 samples per sec) Data rate 8000 MUXed frames/s x (24x8+1) bits/frame =

1.544Mbps Five out of every six frames have 8 bit PCM user data samples

for each channel Sixth frame has (7 bit PCM user data + 1 signaling bit) for each

channel Signaling bits form a stream for each channel containing

control (e.g. error and flow) and routing info Same format for digital data

23 channels of data 7 bits per frame plus indicator bit for data or systems control

24th channel is for signaling DS-1 can carry mixed voice and data signals

44

DS-1 Transmission Format

Frame

(frame-to-frame)

125/193

(8000 x 7 bits = 56 kbps)

45

T1

Due to 1 framing bitPer frame

46

T1 Frames

Framing bit

1 second

47

SONET/SDH SONET: Synchronous Optical Network (ANSI) SDH: Synchronous Digital Hierarchy (ITU-T) They utilize the large channel capacity of

optical fibers They are Compatible

48

Statistical (Asynchronous) TDM In Synchronous TDM many time slots may be wasted

since not all channels will have data all the time Statistical TDM allocates time slots to channels

dynamically based on demand Multiplexer scans input lines and collects data available

from all channels to fill a MUXed frame and sends it: Skips ‘empty’ channels

Must specify source of data since MUX rotation is no longer fixed

Data rate on MUXed line can be made lower than the aggregate peak rate on input lines This saves on channel capacity (and bandwidth)

A calculated risk!

49

Statistical TDM

t1 t2 t3 t4Time slots wasted: Couldserve a higher user demand

using same link capacity!

We could use a lower data rate for sending same data Reduce channel capacity (BW requirement)!

Penalty: Should specify source generating the data. More overhead!

Automatic addressing by fixed rotation time

time

Same data rate

Lower data rate

50

Statistical TDM Frame FormatsStation

Channel

Channel Channel

• Source address and length of data (if variable) for each channel have to be specified• To reduce overhead:

- Use relative addressing (e.g. relative the previous source), or - Use a single address bit map (e.g. 10010010) indicating which channels are sending

51

Performance Issues Use a data rate that is less than peak aggregate

input rate from individual sources (channels) to improve utilization (economize)

But this may cause problems during peak periods when all channels suddenly transmit and you get peak demand!

52

Performance Issues Solution:

MUX should keep a buffer of adequate size for holding excess data from arriving during peak times

Buffer size is determined by data rate allowed for the MUXed data (on the link) in relation to the aggregate average data rate from sources: The closer the data rate used to the average demand the

more economical the link is, but the larger the buffer size required to handle the expected large backlog during peaks

Larger buffers slow down system response: increase waiting time by sources for service (MUX will be busy sending backlog in buffer first!)

Compromise between required link capacity (economy) and source waiting time (user satisfaction)!

53

Example A system serves:

10 sources, each with a peak data rate of 1000 bps But on average, data from the sources will be produced

at 50% of the maximum rate Examine system performance and determine

minimum buffer size for: A link capacity = average aggregate input data rate

(5000 bps) A link capacity > average aggregate input data rate

(= 7000 bps) We are given the following information on actual

aggregate input data rate at twenty 1ms time intervals:

54

Performance IssuesA

ctua

l agg

rega

te in

put (

bits

) ov

er tw

enty

1 m

s in

terv

als

Average = 5 bits/ms = 5000 bps

MUXed link capacity = 5000 bpsMin buffer size = ?

MUXed link capacity = 7000 bpsMin buffer size = ?

(= Average I/P) (> Average I/P) Actual Aggregate I/P, bits

55

Statistical Performance I = number of (identical) input sources R = maximum data rate for each source, bps

(when a source sends, it sends at this maximum rate) Peak data rate from all sources combined = R I = mean fraction of time over which a source

transmits (0 < <1 ) Average input data rate from all sources combined () = R I

M = effective capacity of multiplexed line, bps (excluding overhead)

K = M / (IR)= ratio of multiplexed line capacity to the maximum input data rate= measure of compression achieved by multiplexer (=1 for synch TDM)

(link capacity reduction over synchronous TDM)

For Statistical TDM Average< M < Peak < K < 1 If K = 1, this is synchronous TDM! (no longer statistical TDM) If K < , Capacity is below the average input data rate (Avoid) i.e.< K < 1

56

Performance A queuing theory model: Data sources queue for service

by the MUX Event (request for service): A bit generated by a source Service: MUX sends that bit Assume random (Poisson) arrivals and fixed service time Average event arrival rate = Rate of requesting service, I R bit arrivals/s (Demand rate) Rate of providing the service = M bits sent/s (Service

rate) Service time Ts:

Link utilization, (fraction of total line capacity utilized): = Average rate of sources requesting service/Rate of MUX

providing it

MTs

1

1 be will ,K with , KM

IRT

M s

57

Choice of M for a statistical TDM

RI

MK

= R I

Average Demand

Peak Demand

R I

Less synchronousGreater utilization Larger BuffersPoorer quality of service

M

< K < 1 K = 1K =

K

M

More synchronousLower utilization Smaller buffersBetter quality of service

< < 1 =

Synchronous

Minimum Utilization

Utilization:

Larger Values

58

The Poisson Distribution of random arrivals

e-1

!)(

a

meaP

am

59

A measure of the buffer size needed (in frames)

Average delay suffered by a request

Function of only ( has M)

Function of both and M

(MUX)

What happens as approaches 1?

= /M = Utilization

= /M

60

Buffer Size and Delay

Increasing utilization increases Buffer size required Delay encountered

Utilization > 0.8 is undesirable

Frame size: 1000 bits

,

Average Input load = 8,000 bps,Link Capacity = 10,000 bps

Increasing link capacity, M reduces delay time for same

Frame size: 1000 bits

N

Tr

,

Frames

ms

N does not depend on Mdirectly

61

Probability of Buffer overflow Vs Buffer Size

For a given buffer size, higher utilization increases probability of overflow

For a given utilization , Increasing buffer size drastically reduces probability of overflow, particularly for low

Again, utilization > 0.8 is highly undesirable

62

Asymmetric Digital Subscriber Line (ADSL) ADSL is an asymmetric communication technology designed for residential users over ordinary telephone twisted pair wires

High speed digital data transmission Existing subscriber lines (local loops) were installed for

base band speech (0 – 4 kHz), but can actually provide bandwidths of up to 1 MHz (short distances)

ADSL is an adaptive technology, using different data rates based on the condition of the local loop line

Ranges up to 5.5 km (95% of subscriber lines in USA) Two main technologies: - Multi-level encoding, e.g. QAM

- Discrete Multitone (DMT) by FDM

Shorterdistance,Higherdata rates

Q. What is the BE for 2.5 km lines?

63

ADSL Design

Asymmetric: Providing higher capacity down stream (to customer) than upstream (from customer)

Originally targeting the video-on-demand market Now being used for Internet traffic Uses Frequency Division Multiplexing (FDM) in a novel

way to utilize the 1 MHz BW of twisted pair wires

ServiceProvider

Video, graphics

Voice, e-mailADSLSubscriber

Downstream (download)

Upstream (upload)

64

FDM is used at two levels:

Use FDM to obtain three major bands:

1. POTS band: “Plain Old Telephone Service!” 0 - 20 kHz

2. Upstream band:

25 – 200 kHz

3. Downstream band:

250 – 1000 KHz

4

DMT: Further FDM inside the upstream and the downstream bands: Single fast bit stream is split into multiple bit streams traveling at lower data rates in parallel (simultaneously) in subchannels at different subbands within the upstream and downstream bands.

65

ADSL Using Echo Cancellation Echo cancellation is a signal

processing method that allows overlapping the upstream and downstream bands

Advantages: Allows more of the downstream

band to fall in the lower frequency region Lower attenuation and larger distances

Gives flexibility in defining the width of the upstream band to suit user requirements

66

ADSL Hardware Home

Telephone Exchange

Subscriber Loop

67

ADSL Frequency Bands and DMT Channels

Guard bandsBetween voice and data

Channel #

256 x 4 kHz 1 MHz

1 MHz

- 256 4KHz sub channels- DMT distributes data rate load on sub channels, non uniformly

68

Discrete Multitone (DMT) Multiple subchannels (each 4 KHz wide) within the upstream

and downstream bands Subchannels are modulated with subcarriers

of different frequencies (FDM) (hence “multitone”) Bit stream to be transmitted is split into a number of streams

that travel in parallel at a lower data rate on a number of these limited BW subchannels

1

1011010011Serial to Parallel

Converter

Subchannel 1

Subchannel 5

.

.

1

0

1

1

0

1

0

0

1

1

Data rate for each channel:R/5 bpsOverall data rate: R bps

Data rate R bps

(Each: 4 kHz BW)

15

69

Discrete Multitone (DMT): Adaptive ADSL adaptive property:

Not all subchannels run at the same data rate! Each subchannel can carry from 0 to 60 kbps DMT modem sends out test signals on various

subchannels to determine SNR (expected lower for subchannels located at higher frequencies due to larger attenuation)

Then faster data rates are assigned to subchannels having better signal transmission conditions

.

.

1

1

70

Discrete Multitone (DMT) Uses QAM (Quadrature Amplitude Modulation)

multilevel modulation allowing up to 15 bits/baud (L = 15 bits/signal level)

(4 KHz B D = 4 kbauds (if filtering coefft. r = 0) R max = 4 kbauds x 15 = 60 kbps per channel)

Ideally, 256 x 60 kbps = 15.36 Mbps maximum (if uniform)

Not uniform, not maximum in practice due to various transmission impairments

Practical system operate at 1.5 to 9 Mbps depending on distance and line quality

.

.

1

1

71

DMT

72

DMT

Demodulators

Modulators