1. Chapter 8: Multiplexing
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 Application: ADSL
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 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. To use the same circuit (line)
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
Time
Frequency
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 Synchronous Statistical Analog Signals
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 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
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
4 KHz f1 f2 f3 f1 f f2 f 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
Demodulator fc
(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
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 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 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 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 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
3084
8 KHz 12
Channel
Group
Super group
Master super group

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 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 Sampling Interval On the link:
Sample Number …. 6 5 4 3 2 1
Sampling Interval 4 1 5 2 6 3
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 …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)
MUXed frame
Four data channels
C C C 1
…..
Control Channel, C
010101….
…..
A data Channel
Unlikely to have …. 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: Solution - Pulse Stuffing
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)
MUXed
Frame
Source 1
Sampling
MUXed
(composite) sampling
1 s
(1/6) s X X
Source 2
Sampling
Useful data rate: 4 bps
(1/3) s
Dummy pulses
stuffed in place of blank (unused) samples

38. Example: TDM of 11 Analog and Digital Sources
3 Analog Channels
Analog to Digital Converter
PAM Analog samples
=BW=fmax
Rotation
Frequency 1 2 3 2
PCM with n = 4 bits/sample
Rotation/s 2
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:
 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
2-bit………2-bit 2-bit
16-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 = 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:
MHz for 3600 channels

42. DS & T Lines Rates Service Line Data Rate (Mbps) No. of Voice Channels
Transmission line
that supports it
Corresponding Channel Capacity
Service
Line
Data Rate (Mbps)
No. of Voice Channels
DS-1
T-1
1.544 24
DS-2
T-2
6.312 96
DS-3
T-3
44.736
672
DS-4
T-4
4032

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
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 time t2 t3
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 ) 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 Issues
Actual Aggregate I/P, bits
(= Average I/P)
(> Average I/P)
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 < a <1 )
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 < M < Peak  a < K < 1
If K = 1, this is synchronous TDM! (no longer statistical TDM)
If K < a , Capacity is below the average input data rate (Avoid)
i.e. a < 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,
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
K = a
a < K < 1
K = 1
Utilization:
r = 1
a < r < 1
r = a
Minimum Utilization
l = a R I M
R I
Larger Values
Average
Demand
Peak
Demand
Less synchronous
Greater utilization r
Larger Buffers
Poorer quality of service
More synchronous
Lower utilization r
Smaller buffers
Better quality of service

58. The Poisson Distribution of random arrivals

59. Function of r only (r has 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. Average Input load = 8,000 bps,
Frame size: 1000 bits
Buffer Size and Delay N
Frames
Average Input load = 8,000 bps,
Link Capacity = 10,000 bps
Increasing utilization increases
Buffer size required
Delay encountered
Utilization r > 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 > 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)
Service
Provider
Video, graphics
Voice,
ADSL
Upstream (upload)
Subscriber

64. FDM is used at two levels:
Use FDM to obtain three major bands:
1. POTS band: “Plain Old Telephone Service!” 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
Subscriber Loop
Telephone Exchange

67. ADSL Frequency Bands and DMT Channels
Guard bands
Between voice and data
Channel #
1 MHz
256 x 4 kHz  1 MHz
KHz 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
Serial to
Parallel
Converter 1 1
Subchannel 1 .
(Each: 4 kHz BW) 1 1 1 1 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 = 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