Multiplexing l7

Multiplexing Techniques
 What /Why Multiplexing ?198 pc 161 bk
 Basic multiplexing approaches
 Frequency Division Multiplexing (FDM)
•Wavelength Division Multiplexing (WDM)
 Time Division Multiplexing (TDM)
•Synchronous
•Asynchronous
Inverse TDM

Why Multiplexing?
Observation?
 Most individual data-communication devices typically
require modest data rate.
 Communication media usually have much higher
bandwidth.
 Two communicating stations do not utilize the full
capacity of a data link.
 The most cost effective transmission facility is
achieved at the higher data rate.

When the bandwidth of a medium is greater than
individual signals to be transmitted through the channel,
a medium can be shared by more than one channel of
signals by using Multiplexing.
For efficiency, the channel capacity can be shared
among a number of communicating stations.
Most common use of multiplexing is in long-haul
communication using coaxial cable, microwave and
optical fiber.
When multiplexing ?
(Sharing: Sharing of BW between multiple users)

Dividing a link into channels, TDM

Frequency-division multiplexing (FDM)

FDM is an analog multiplexing technique that
combines analog signals.
It uses the concept of modulation.

6.10
FDM demultiplexing example

6.11
FDM
Applications of FDM:
Transmission of AM / FM radio signal
TV Broadcasting
Cable Television

Assume that a voice channel occupies a bandwidth of 4 kHz. We
need to combine three voice channels into a link with a bandwidth
of 12 kHz, from 20 to 32 kHz. Show the configuration, using the
frequency domain. Assume there are no guard bands.
Solution
We shift (modulate) each of the three voice channels to a different
bandwidth, as shown in Figure 6.6. We use the 20- to 24-kHz
bandwidth for the first channel, the 24- to 28-kHz bandwidth for the
second channel, and the 28- to 32-kHz bandwidth for the third one.
Then we combine them as shown in Figure
Example

6.14
Five channels, each with a 100-kHz bandwidth, are to be
multiplexed together. What is the minimum bandwidth of
the link if there is a need for a guard band of 10 kHz
between the channels to prevent interference?
Solution
For five channels, we need at least four guard bands. This means
that the required bandwidth is at least
5 × 100 + 4 × 10 = 540 kHz,
as shown in Figure 6.7.
Example 6.2

Four data channels (digital), each transmitting at 1
Mbps, use a satellite channel of 1 MHz. Design an
appropriate configuration, using FDM.
Solution
The satellite channel is analog. We divide it into four
channels, each channel having 1M/4=250-kHz bandwidth.
Each digital channel of 1 Mbps must be transmitted over a
250KHz channel. Assuming no noise we can use Nyquist to
get:
C = 1Mbps = 2×250K×log2 L -> L = 4 or n = 2 bits/signal
element.
One solution is 4-QAM modulation.
Example 6.3

6.18
Figure 6.9 Analog hierarchy

6.20
The Advanced Mobile Phone System (AMPS) uses two
bands. The first band of 824 to 849 MHz is used for
sending, and 869 to 894 MHz is used for receiving. Each
user has a bandwidth of 30 kHz in each direction. How
many people can use their cellular phones
simultaneously?
Solution
Each band is 25 MHz. If we divide 25 MHz by 30 kHz, we
get 833.33. In reality, the band is divided into 832
channels. Of these, 42 channels are used for control, which
means only 790 channels are available for cellular phone
users.
Example 6.4

6.21
WDM is an analog multiplexing technique to combine
optical signals.

6.22
Figure: Wavelength-division multiplexing (WDM)

6.23
Prisms in wavelength-division multiplexing
and demultiplexing

6.24
TDM is a digital multiplexing technique for
combining several low-rate digital
channels into one high-rate one.

6.25
Figure 6.13 Synchronous time-division multiplexing

6.30
In synchronous TDM, the data rate
of the link is n times faster, and the unit duration
is n times shorter.

In Figure 6.13, the data rate for each one of the 3 input
connection is 1 kbps. If 1 bit at a time is multiplexed (a unit
is 1 bit), what is the duration of (a) each input slot, (b)
each output slot, and (c) each frame?
Solution
a. The data rate of each input connection is 1 kbps. This
means that the bit duration is 1/1000 s or 1 ms. The
duration of the input time slot is 1 ms (same as bit
duration).
Example 6.5

6.32
Figure 6.13 Synchronous time-division multiplexing

6.33
b. The duration of each output time slot is one-third of the
input time slot. This means that the duration of the
output time slot is 1/3 ms.
c. Each frame carries three output time slots. So the
duration of a frame is 3 × 1/3 ms, or 1 ms.
Note: The duration of a frame is the same as the duration
of an input unit.
Example 6.5 (continued)

Figure 6.14 shows synchronous TDM with four 1Mbps
data stream inputs and one data stream for the output. The
unit of data is 1 bit. Find (a) the input bit duration, (b) the
output bit duration, (c) the output bit rate, and (d) the
output frame rate.
Solution
a. The input bit duration is the inverse of the bit rate:
1/1 Mbps = 1 s.μ
b. The output bit duration is one-fourth of the input bit
duration, or ¼ s.μ
Example 6.6

6.35
c. The output bit rate is the inverse of the output bit
duration or 1/(4 s) or 4 Mbps. This can also beμ
deduced from the fact that the output rate is 4 times as
fast as any input rate; so the output rate = 4 × 1 Mbps
= 4 Mbps.
d. The frame rate is always the same as any input rate. So
the frame rate is 1,000,000 frames per second. Because
we are sending 4 bits in each frame, we can verify the
result of the previous question by multiplying the frame
rate by the number of bits per frame.

Four 1-kbps connections are multiplexed together. A unit is
1 bit. Find (a) the duration of 1 bit before multiplexing, (b)
the transmission rate of the link, (c) the duration of a time
slot, and (d) the duration of a frame.
Solution
a. The duration of 1 bit before multiplexing is 1 / 1 kbps,
or 0.001 s (1 ms).
b. The rate of the link is 4 times the rate of a connection, or
4 kbps.
Example 6.7

6.38
c. The duration of each time slot is one-fourth of the
duration of each bit before multiplexing, or 1/4 ms or
250 s. Note that we can also calculate this from theμ
data rate of the link, 4 kbps. The bit duration is the
inverse of the data rate, or 1/4 kbps or 250 s.μ
d. The duration of a frame is always the same as the
duration of a unit before multiplexing, or 1 ms. We can
also calculate this in another way. Each frame in this
case has four time slots. So the duration of a frame is 4
times 250 s, or 1 ms.μ

Interleaving
The process of taking a group of bits from each
input line for multiplexing is called interleaving.

Four channels are multiplexed using TDM. If each
channel sends 100 bytes /s and we multiplex 1 byte per
channel, show the frame traveling on the link, the size of
the frame, the duration of a frame, the frame rate, and the
bit rate for the link.
Solution
The multiplexer is shown in Figure 6.16. Each frame
carries 1 byte from each channel; the size of each frame,
therefore, is 4 bytes, or 32 bits. Because each channel is
sending 100 bytes/s and a frame carries 1 byte from each
channel, the frame rate must be 100 frames per second.
The bit rate is 100 × 32, or 3200 bps.
Example 6.8

Data Rate Management
• Not all input links maybe have the same data rate.
• Some links maybe slower. There maybe several
different input link speeds.
• There are three strategies that can be used to
overcome the data rate mismatch: multilevel,
multislot and pulse stuffing

Data rate matching
• Multilevel: used when the data rate of the input
links are multiples of each other.
• Multislot: used when there is a GCD (greatest
common divisor) between the data rates. The
higher bit rate channels are allocated more slots
per frame, and the output frame rate is a multiple
of each input link.
• Pulse Stuffing: used when there is no GCD between
the links. The slowest speed link will be brought up
to the speed of the other links by bit insertion, this
is called pulse stuffing.

Figure 6.19 Multilevel multiplexing

Figure 6.20 Multiple-slot multiplexing

Synchronization
• To ensure that the receiver correctly reads the
incoming bits, i.e., knows the incoming bit
boundaries to interpret a “1” and a “0”, a known
bit pattern is used between the frames.
• The receiver looks for the anticipated bit and
starts counting bits till the end of the frame.
• Then it starts over again with the reception of
another known bit.
• These bits (or bit patterns) are called
synchronization bit (s).
• They are part of the overhead of transmission.

Asynchronous / Statistical / Intelligent TDM: TDM
time Slots are allocated dynamically in demand.

6.51
Inefficient use of Bandwidth
• Sometimes an input link may have no data to
transmit.
• When that happens, one or more slots on the
output link will go unused.
• That is wasteful of bandwidth.

Figure 6.26 TDM slot comparison

Figure 6.24 T-1 line for multiplexing telephone lines

Figure 6.25 T-1 frame structure

Inverse TDM takes the data stream from one high-
speed line and breaks it into portions that can be
sent across several low-speed line simultaneously
Inverse TDM
Number of channels of smaller bandwidth
Bandwidth on demand (more cost effective use of bandwidth)
Let, Voice = 64 Kbps, Data = 128 Kbps, and Video = 1.544 Mbps

Multiplexing l7

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