Multiplexing

1
COE 341 Data Computer Communications
(T061)Dr. Radwan E. Abdel-Aal

• Chapter 8
• Multiplexing

2
Where are we
Chapter 7 Data Link Flow and Error control
Data Link
Chapter 8 Improved utilization Multiplexing
Physical Layer
Chapter 6 Data Communication Synchronization,
Error detection and correction
Chapter 4 Transmission Media
Transmission Medium
Chapter 5 Encoding From data to signals
Chapter 3 Signals and their transmission over
media, Impairments
3
Contents

• Introduction
• Two Multiplexing Techniques
• FDM
• TDM
• Synchronous
• Statistical
• 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 modeste.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
Frequency
Time
FDM Frequency Division Multiplexing
TDM Time Division Multiplexing
To use the same circuit (line) i.e. sharing
space Use either TDM or FDM
7
Multiplexing Types
Modulation Or shift keying
Encoding
Representing digital or analog data
Analog Signals
Digital Signals
Separation in Frequency
Separation in time by interleaving
FDM Frequency Division Multiplexing TDM Time
Division Multiplexing WDM Wavelength Division
Multiplexing (a form of FDM)
Synchronous
Statistical
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 fcs 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
Same time
Different Frequencies
11
FDM Multiplexing Process Time-Domain View at TX
Qty 3
Fc (Different for each channel)
Modulator
12
FDM Multiplexing Process Frequency-Domain View
at TX
0
4 KHz
f2
f1
f3
f1
f
f
f2
f3
All source channels are at (same) base band
Restoration at RX 3 different pass-band
filters, each bracketing a channel
13
FDM De-Multiplexing Process Time-Domain View at
RX
Filter pass bands
f1
f2
f3
Demultiplexing Filters
Low Pass Filter
fc
Demodulator
(Different for each channel Same as those used at
TX)
Qty 3
Qty 3
14
FDM De-Multiplexing Process Frequency-Domain
View at RX

• Guard bands prevent channel overlap
• But represent wasted
• spectrum

f1
f
f2
0
4 KHz
f3
All received channels restored to base band
15
FDM System Transmitter
Subcarriers
To meet Transmission Requirements
Main Carrier
Any type of modulation AM, FM, PM
Group of channels
Individual base band channels
16
FDM System Receiver
f1
f2
Subcarriers
fc
Main Carrier
f3
Composite base band signal mb(t) recovered
Individual base band channels recovered
17
FDM of Three Voice band Signals
Guard bands To reduce channel spectrum overlap
BW, allocated 0 4000 Hz
BW, actual 300 3400 Hz
Assume we will keep only the lower side band for
each channel
fc
What is the modulation type ?
3 MUXed channel Using lower side band only
3 Subcarriers at 64, 68, and 72 KHz
Channel overlap means crosstalk!
18
Analog Carrier Systems

• One-go Vs Hierarchical

.
Master super group
Stages
.
Super group
.
.
Group
Channel
.
...
.
...
4000 channels
4000 channels

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

19
Analog Carrier Systems

• Devised by ATT (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 (gt 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 (gt 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
3084
8 KHz
12
Super group
Master super group
Group
Channel
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 _at_ 40 Gbps each ? 10 Tbps over 100
  km

24
Time Division Multiplexing (TDM)

• 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)

25
Time Division Multiplexing
3400 Hz
Channels must go on the link at different times
300 Hz
Channels occupy the same frequency band (Base
band)
26
Time Division Multiplexing (TDM)
Note MUXing and DeMUXing are transparent to the
end stations. Each pair think they have a
dedicated link !
Baseband Signals
Time
Ts 1/2fmax
Channel sampling interval
27
TDM Frames
Sampling Interval
Sample Number
.
1
2
3
4
5
6
Sampling Interval
4
1
2
5
3
6
On the link Data is sent at a rate of 1
sample/T Data rate is 3 times the channel data
rate
Channel sampling interval 3T For each channel,
data rate is 1 sample/3T
28
Time Division Multiplexing (TDM)

• 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

29
Synchronous TDM Transmitter
Scanning and link data rate high enough to
prevent channel buffers overflowing
Sample data fills buffer
Analog Signal
N channels, Sampling rate R sample/s
Minimum link capacity N R sample/s
Bit stream
or
Digital Signal
Channel Buffers
T Should be enough to empty a channel buffer
Time Slot, T Channel dwell time
Channel 2
Transmitted frames consist of interleaved
channel data
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
Start of 1 Frame
Channel 1 Frame
MUXed stream can not be considered as an HDLC
frames!
This is what goes on the link Everything is mixed
up, even FCS bytes FCS applies only to channel
frames Channel frames get reassembled at RX
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
  01010101unlikely 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)
MUXed frame
Four data channels
C 1 2 3 4 C 1
2 3 4 C 1
0
0
1
..
Control Channel, C 010101.
..
A data Channel Unlikely to have 010101. over
successive frames
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!
Once the position of this control channel is
established, RX knows where the channel sequence
starts and sync is established with TX
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 ? 13 4 bps ? take as 6 bps
• (divides both rates)

MUXed Frame
MUXed (composite) sampling
Source 1 Sampling
1 s
(1/6) s
X
X
Useful data rate 4 bps
Source 2 Sampling
(1/3) s
Dummy pulses stuffed in place of blank (unused)
samples
38
Example TDM of 11 Analog and Digital Sources
Analog to Digital Converter
3 Analog Channels
PAM Analog samples
Rotation Frequency
BWfmax
1
2
3
PCM with n 4 bits/sample
Rotation/s
PCM System
Now channel 2 is sampled uniformly and at the
correct rate
Sampling rate 2 fmax 8K sample/s
Digital Signals 64 kbps
Sampling rate 2 fmax 4K sample/s
64 kbps
8 Digital Inputs
MUXed data rate

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

39
Example TDM of 11 Analog and Digital Sources
Suggested framing and buffering arrangement
Rate of filling this buffer 64 kbps/16
bpbuffer 4 k buffers/s
Frame bits are allocated to Scanned sources in
proportion to their data rates
16-bit Buffer
64 kbps
Time slot, enough to empty buffer
8 kbps
64 kbps
16-bit
2-bit2-bit 2-bit
2-bit Buffer
32-bit MUXed frames
2-bit Buffer
No. of frames/s 128 kbps/32bpframe 4 k
frames/s Rotation rate
4 k rotations/s
2-bit Buffer
This is also the rate of emptying any of The
MUXed buffers 4 k buffers/s
Rate of filling the buffers should not exceed the
rate of emptying them
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
DS-0 is a PCM voice channel 8000 sample/s x 8
b/sample 64 kbps
Transmission lines used should support the
progressively increasing data rate (channel
capacity) requirement
42 x 96 4032 DS-0 (4032 voice channels)
Which one uses BW more efficiently ?
FDM Jumbo group 16.984 MHz for 3600 channels
42
DS T Lines Rates
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 (24x81)
  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
125/193
Frame
(frame-to-frame)
(8000 x 7 bits 56 kbps)
45
T1
Due to 1 framing bit Per 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
Automatic addressing by fixed rotation
t1
t4
t2
t3
time
Same data rate
Time slots wasted Could serve a higher user
demand using same link capacity!
Lower data rate
Penalty Should specify source generating the
data. More overhead!
time
We could use a lower data rate for sending same
data ? Reduce channel capacity (BW requirement)!
50
Statistical TDM Frame Formats
Station
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 gt 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 Issues
( Average I/P)
(gt Average I/P)
Actual Aggregate I/P, bits
Actual aggregate input (bits) over twenty 1 ms
intervals
Average 5 bits/ms 5000 bps
MUXed link capacity 5000 bps Min buffer size
?
MUXed link capacity 7000 bps Min buffer size
?
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
• a mean fraction of time over which a source
  transmits (0 lt a lt1 )
• Average input data rate from all sources combined
  (l) a 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 lt M lt Peak ? a
  lt K lt 1
• If K 1, this is synchronous TDM! (no longer
  statistical TDM)
• If K lt a , Capacity is below the average input
  data rate (Avoid)
• i.e. a lt K lt 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,
• l a I R bit arrivals/s (Demand rate)
• Rate of providing the service M bits sent/s
  (Service rate)
• Service time Ts
• Link utilization, r (fraction of total line
  capacity utilized)
• Average rate of sources requesting
  service/Rate of MUX
  providing it

57
Choice of M for a statistical TDM
Synchronous
a lt K lt 1
K 1
K a
Utilization
a lt r lt 1
r a
r 1
Minimum Utilization
l a R I
M
R I
Larger Values
Peak Demand
Average Demand
More synchronous Lower utilization r Smaller
buffers Better quality of service
Less synchronous Greater utilization r Larger
Buffers Poorer quality of service
58
The Poisson Distribution of random arrivals
e-1
59
1/M
(MUX)
l/M Utilization
Function of r only (r has M)
A measure of the buffer size needed (in frames)
Function of both r and M
Average delay suffered by a request
What happens as r approaches 1?
60
Buffer Size and Delay
Frame size 1000 bits
N
Frames
Average Input load 8,000 bps, Link Capacity
10,000 bps

• Increasing utilization increases
• Buffer size required
• Delay encountered
• Utilization r gt 0.8
  is undesirable

N does not depend on M directly
, r
Frame size 1000 bits
Tr
ms
Increasing link capacity, M reduces delay time
for same r
, r
61
Probability of Buffer overflow Vs Buffer Size

• For a given buffer size, higher utilization
  increases probability of overflow
• For a given utilization r, Increasing buffer size
  drastically reduces probability of overflow,
  particularly for low r
• Again, utilization r gt 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

Shorter distance, Higher data 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

Downstream (download)
Subscriber
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

• 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
Subscriber Loop
Telephone Exchange
67
ADSL Frequency Bands and DMT Channels
Guard bands Between voice and data
1 MHz
Channel
256 x 4 kHz ? 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
1
1
Subchannel 1
Serial to Parallel Converter
0
0
. .
(Each 4 kHz BW)
0
1
1011010011
1
1
1
0
1
Subchannel 5
5
Data rate for each channel R/5 bps Overall data
rate R bps
Data rate R bps
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
Modulators
Demodulators