Chapter Four
Multiplexing
((PHYSICAL LAYER))
4.1- Introduction
Whenever the transmission capacity of a medium linking two devices is greater
than the transmission needs of the devices, the link can be shared, much as a large
water pipe can carry water to several separate houses at once. Multiplexing is the
set of techniques that allows the simultaneous transmission of multiple signals
across a single data link.
As data and telecommunications usage increases, so does traffic. We can
accommodate this increase by continuing to add individual lines each time a new
channel is needed, or we can install higher capacity links and use each to carry
multiple signals.
high-bandwidth media such as coaxial cable, optical
fiber, and terrestrial and satellite microwaves. Each of these has a carrying
capacity far in excess of that needed for the average transmission signal, if the
transmission capacity of a link is greater than the transmission needs of the
devices connected to it, the excess capacity is wasted. An efficient system
maximizes the utilization of all facilities. In addition, the expensive technology
involved often becomes cost-effective only when links are shared.
Figure (1) shows two possible ways of linking four pairs of devices. In figure (1-a),
each pair has its own link, if the full capacity of each link is not being utilized; a
portion of that capacity is being wasted. In figure (1-b), transmissions between the
pairs are multiplexed; the same four pairs share the capacity of a single link.
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1 Path
4 Channels
Figure (1-a) :No Multiplexing
Figure (1-b): Multiplexing
In a multiplexed system, n devices share the capacity of one link; Figure (1-b)
shows the basic format of a multiplexed system. The four devices on the right
direct their transmission streams to a Multiplexer (MUX) which combines them
into a single stream (lots of to one). At the receiving end, that stream is fed into a
Demultiplexer (DEMUX), which separates the stream back into its component
transmissions (one-to-many) and directs them to their intended receiving devices.
In Figure (1-b) the word Path refers to the physical link. The word Channel refers
to a portion of a path that carries a transmission between a given pair of devices.
One path can have many (n) channels.
4.2- Types of Multiplexing
Signals are multiplexed using three basic techniques:
Frequency Division Multiplexing (FDM)
Wavelength Division Multiplexing (WDM)
Time Division Multiplexing (TDM)
TDM is further subdivided into synchronous TDM (usually called TDM) and
asynchronous TDM, also called statistical TDM or concentrator (See Figure (2))
Figure (2) :Types of Multiplexing
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4.2.1- Frequency-Division Multiplexing (FDM)
Frequency-division multiplexing (FDM) is an analog technique that can be
applied when the bandwidth of a link is greater than the combined bandwidth of
the signals to be transmitted. In FDM, signals generated by each sending device
modulate with different carrier frequencies. These modulated signals are then
combined into a single composite signal that can be transported by the link. Carrier
frequencies are separated by enough bandwidth to accommodate the modulated
signal. These bandwidth ranges are the channels through which the various signals
travel. Channels must be separated by strips of unused bandwidth (guard bands) to
prevent signals from overlapping. In addition, carrier frequencies must not
interfere with the original data frequencies.
Figure (3) gives a conceptual view of FDM. In this illustration, the transmission
path is divided into three pans, each representing a channel to carry one
transmission. As an analogy, imagine a point where three narrow streets merge to
form a three-lane highway. Each of the three streets corresponds to a lane of the
highway. Each car merging onto the highway from one of the streets still has its
own lane and can travel without interfering with cars in other lanes.
Keep in mind that although Figure (3) shows the path as divided spatially into
separate channels, actual channel divisions are achieved by frequency rather than
by space.
Figure (3) :Frequency Division Multiplexing
The FDM Process:
Figure (4) is a conceptual time-domain illustration of the multiplexing process.
FDM is an analog process and we show it here using telephones as the input and
output devices. Each telephone generates a signal of a similar frequency range.
Inside the multiplexer, these similar signals are modulated onto different carrier
frequencies (f1, f2, and f3). The resulting modulated signals are then combined into
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a single composite signal that is sent out over a media link that has enough
bandwidth to accommodate it.
Figure (4) :FDM multiplexing process, time-domain
Figure 5 is the frequency-domain illustration for the same concept. (Note that the
horizontal axis of this figure denotes frequency, not time. All three carrier
frequencies exist at the same time within the bandwidth.) In FDM, signals are
modulated onto separate carrier frequencies (f1, f2 and f3) using either AM or FM
modulation.
Figure (5): FDM multiplexing process, frequency-domain
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Demultiplexing:
The demultiplexer uses a series of filters to decompose the multiplexed signal into
its constituent component signals. The individual signals are then passed to a
demodulator that separates them from their carriers and passes them to the waiting
receivers. Figure (6) is a time-domain illustration of FDM multiplexing, again
using three telephones as the communication devices. The frequency-domain of the
same example is shown in Figure (7).
Figure (6) :FDM demultiplexing process, time-domain
Figure (7) :FDM demultiplexing process, frequency-domain
A familiar application of FDM is cable television. The coaxial cable used in a
cable television system. Today, a new and more efficient method is being
developed to implement FDM over fiber-optic cable. Called Wavelength Division
Multiplexing (WDM), it uses essentially the same concepts as FDM but
incorporates the range of frequencies in the visible light spectrum.
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Example:
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 multiplexer process and de multiplexer process in frequency
domain(configuration using the frequency domain). Assume there are no guard
bands.
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Example
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 as shown in Figure below.
5 × 100 + 4 × 10 = 540 kHz,
Example:
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 a 250-kHz bandwidth. Each digital channel of 1 Mbps is modulated such
that each 4 bits is modulated to 1 Hz. One solution is 16-QAM modulation. The
Figure below shows one possible configuration.
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4.2.2- Time-Division Multiplexing (TDM)
Time-division multiplexing (TDM) is a digital process that can be applied when
the data rate capacity of the transmission medium is greater than the data rate
required by the sending and receiving devices. In such a case, multiple
transmissions can occupy a single link by subdividing them and interleaving the
portions.
Figure (8) gives a conceptual view of TDM. Note that the same link is used as in
the FDM. Here however, the link is shown sectioned by time rather than
frequency.
In the TDM figure, portions of signals 1,2, 3, and 4 occupy the link sequentially.
As an analogy, imagine a ski lift that serves several runs. Each run has its own line
and the skiers in each line take turns getting on the lift as each chair reaches the top
of the mountain, the skier riding it gets off and skis down the run for which he or
she waited in line.
Figure (8): Time Division Multiplexing
TDM can be implemented in two ways: synchronous TDM and asynchronous
TDM.
a) Synchronous TDM
In time-division multiplexing, the term synchronous has a different meaning from
that used in other areas of telecommunications. Here synchronous means that the
multiplexer allocates exactly the same time slot to each device at all times, whether
or not a device has anything to transmit. Time slot A, for example, is assigned to
device A alone and cannot be used by any other device. Each time its allocated
time slot comes up, a device has the opportunity to send a portion of its data. If a
device is unable to transmit or does not have data to send, its time slot remains
empty.
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Time slots are grouped into frames. In a system with n input lines, each frame
has at least n slots. With each slot allocated to carry data from a specific input line.
If all the input devices sharing a link are transmitting at the same data rate, each
device has one time slot per frame. However, it is possible to accommodate
varying data rates. A transmission with two slots per frame will arrive twice as
quickly as one with one slot per frame.
In Figure (9), we show three input lines multiplexed onto a single path using
synchronous TDM. In this example, all of the inputs have the same data rate, so the
number of time slots in each frame is equal to the number of input lines.
Figure (9): Synchronous TDM
Example:
Four channels are multiplexed using TDM. If each channel sends 1kbits/s
and we multiplex 1 bit per channel Find
(a) The input bit duration,
(b) The output bit duration,
(c) The output bit rate,
(d) The output frame rate.
Solution
We can answer the questions as follows:
a. The duration of 1 bit before multiplexing is 1/1 kbps, or 0.001 s (l ms).
b. The rate of the link is 4 times the rate of a connection, or 4 kbps.
c. The duration of each time slot is one-fourth of the duration of each bit
before multiplexing, or 1/4 ms or 250us.
Note that we can also calculate this from the data rate of the link, 4 kbps.The
bit duration is the inverse of the data rate, or 1/4 kbps or 250 us.
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 us, or1 ms.
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Example:
Four channel synchronous TDM with a data stream for each input 1mbps and 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=1/input bit rate=1/1mps=1 s.
b. The output bit duration =1/number of input channel=1/4 s.
c. The output bit rate =number of channel*rate of channel=1mbps*4=4
mbps
or it is the inverse of the output bit duration or 1/(4 s) or 4 Mbps.
d. The frame rate is always the same as any input rate =1 mbps.
Example:
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 of the link.
Solution
The multiplexer is shown in Figure (10). Each frame carries 1 byte from each
channel. So the size of each frame is 4 bytes or 32 bits. Because each channel is
sending 100 bytes per second and a frame carries 1 byte from each channel, the
frame rate must be 100 frames per second. The duration of a frame is therefore
1/100 s. the link is carrying 100 frames per second, and each frame contains 32
bits, so the bit rate is 100×32 or 3200 bps. This is actually 4 times the bit rate for
each channel, which is 100×8=800 bps.
Figure (10)
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4.2.3 Interleaving
Synchronous TDM can be compared to a very fast rotating switch. As the switch
opens in front of a device, that device has the opportunity to send a specified
amount (x-bits) of data onto the path. The switch moves from device to device at a
constant rate and in a fixed order. This process is called interleaving. Interleaving
can be done by bit, by byte, or by any other data unit.
At the receiver, the demultiplexer decomposes each frame by discarding the framing bits and extracting each character in turn. As a character is removed from a
frame, it is passed to the appropriate receiving device. Figure (11) illustrate the
interleaving process.
Figure (11): Interleaving
Figure (11) also point out the major weakness of synchronous TDM. By assigning
each time slot to a specific input line, we end up with empty slots whenever not all
the lines are active.
Example:
Multiplexer combines four 100-kbps channels using a time slot of 2 bits. Show the
output with four arbitrary inputs. What is the frame rate? What is the frame
duration? What is the bit rate? What is the bit duration?
Solution
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The Figure shows the output for four arbitrary inputs.
The link carries 50,000 frames per second since each frame contains 2 bits per
channel.
The frame duration is therefore 1/50,000 s or 20 us.
The frame rate is 50,000 frames per second,
since each frame carries 8 bits; the bit rate is 50,000 x 8 =400,000 bits or 400 kbps.
The bit duration is 1/400,000 s, or 2.5u.s. Note that the frame duration is 8 times
the bit duration because each frame is carrying 8 bits.
4.2.4 Empty Slots
Synchronous TDM is not as efficient as it could be. If a source does not have data
to send, the corresponding slot in the output frame is empty. Figure 7 shows a case
in which one of the input lines has no data to send and one slot
in another input line has discontinuous data.
Figure 7 empty slots in synchronous TDM The first output frame has three slots
filled, the second frame has two slots filled, and the third frame has three slots
filled. No frame is full. We learn in the next section that statistical TDM can
improve the efficiency by removing the empty slots from the frame.
4.2.5 Synchronization
Implementing a TDM is not an easy process as FDM. Synchronization between
multiplexers and demultiplexers is a major issue. If the multiplexer and the
demultiplexer are out of synchronization, a bit belonging to one channel may be
received by the wrong channel. For this reason, one or more synchronization bits
are usually added to the beginning of each frame, these bits, called framing bits.
Because the time slot order in a synchronous TDM system does not vary from
frame to frame, very little overhead information needs to be included in each
frame.
In most cases, this synchronization information consists of one bit per frame,
alternating between 0 and 1, as shown in Figure (12).
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Figure (12): Framing bits
Example:
We have four sources, each creating 250 characters per second. If the interleaved
unit is a character and 1 synchronizing bit is added to each frame, find (a) the data
rate of each source, (b) the duration of each character in each source, (c) the frame
rate, (d) the duration of each frame, (e) the number of bits in each frame, and (f)
the data rate of the link.
Solution
a- The data rate of each source is 250 × 8 = 2000 bps = 2 kbps.
b- Each source sends 250 characters per second; therefore, the duration of a
character is 1/250 s, or 4 ms.
c- Each frame has one character from each source, which means the link needs
to send 250 frames per second to keep the transmission rate of each source.
d- The duration of each frame is 1/250 s, or 4 ms. Note that the duration of
each frame is the same as the duration of each character coming from each
source.
e- Each frame carries 4 characters and 1 extra synchronizing bit. This means
that each frame is 4 × 8 + 1 = 33 bits.
f- The data rate of the link is 250 frames/second × 33 bits/frame = 8250 bps, or
4 × 2000 bps + 250 synchronization bps= 8250 bps.
4.3- Bit Padding
It is possible to multiplex data from devices of different data rates. For example,
device A could use one time slot, while the faster device B could use two. The
number of slots in a frame and the input lines to which they are assigned remain
fixed throughout a given system, but devices of different data rates may control
different numbers of those slots. Remember, the time slot length is fixed. For this
technique to work, therefore different data rate must be integer multiples of each
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other. When the speeds are not integer multiples of each other, they can be made to
behave as if they were, by a technique called Bit Padding. In bit padding, the
multiplexer adds extra bits to a device
relationship among the various devices into integer multiple of each other. For
example, if we have one device with a bit rate 2.75 times that of the other device,
we can add enough bits to raise the rate to 3 times that of the others. The extra bits
are then discarded by the demultilpexer.
Example:
Two channels, one with a bit rate of 100 kbps and another with a bit rate of 200
kbps, are to be multiplexed. How this can be achieved? What is the frame rate?
What is the frame duration? What is the bit rate of the link?
Solution
We can allocate one slot to the first channel and two slots to the second channel.
Each frame carries 3 bits. The frame rate is 100,000 frames per second because it
carries 1 bit from the first channel. The bit rate is 100,000 frames/s × 3 bits per
frame, or 300 kbps.
b) Asynchronous TDM
Synchronous TDM does not guarantee that the full capacity of a link is used. In
fact, it is more likely that only a portion of the time slots is in use at a given
instant. Because the time slots are pre-assigned and fixed whenever a connected
device is not transmitting the corresponding slot is empty and that much of the path
is wasted. For example, imagine that we have multiplexed the output of 20
identical computers onto a single line. Using synchronous TDM, the speed of that
line must be at least 20 times the speed of each input line. But what if only 10
computers are in use at a time? Half of the capacity of the line is wasted.
Asynchronous time-division multiplexing, or statistical time-division multiplexing,
is designed to avoid this type of waste. As with the term synchronous, the term
asynchronous means something different in multiplexing than it means in other
areas of data communications. Here it means flexible or not fixed.
Like synchronous TDM, asynchronous TDM allows a number of lower speed
input lines to be multiplexed to a single higher speed line. Unlike synchronous
TDM, however, in asynchronous TDM the total speed of the input lines can be
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greater than the capacity of the path. In a synchronous system, if we have n input
lines, the frame contains a fixed number of at least n time slots. In an
asynchronous system, if we have n input lines, the frame contains no more than m
slots, with m less than n (see Figure (13) below). In this way, asynchronous TDM
supports the same number of input lines as synchronous TDM with a lower
capacity link. Or given the same link, asynchronous TDM can support more
devices than synchronous TDM.
The number of time slots in an asynchronous TDM frame (m) is based on a
statistical analysis of the number of input lines that are likely to be transmitting at
any given time. Rather than being pre-assigned, each slot is available to any of the
attached input that has data to send. The multiplexer scans the input line, accept
portions of the data until a frame is filled, and then sends the frame to link. If there
are not enough data to full all the slots in a frame, the frame is transmitted only
partially filled; thus full link capacity may not be used 100 percent of the time.
Frame n
Frame 2
Frame 1
...
Figure (13) :Asynchronous TDM
Figure (14) shows a system where five computers are sharing a data link using
asynchronous TDM. In this example, the frame size is three slots. The figure
shows how the multiplexer handles three levels of traffic. In the first case, only
three of the five computers have data to send (the average scenario for this system,
as indicated by the fact that a frame size of three slots was chosen). In the second
case, four lines are sending data, one more than the number of slots per frame. In
the third case (statistically rare), all lines are sending data. In each case, the
multiplexer scans the devices in order.
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Figure (14): Asynchronous TDM Farmes
In cases 2 and 3, if the speed of the line is equal to three of the input lines, then
the data to be transmitted will arrive faster than the multiplexer can put it on the
link. In that case, a buffer is needed to store data until the multiplexer is ready for
it.
Addressing and Overhead Cases 2 and 3 in the above example illustrate a major
weakness of asynchronous TDM: How does the demultiplexer know which slot
belongs to which output line? In synchronous TDM, the device to which the data
in a time slot belong is indicated by the position of the time slot in the frame. But
in asynchronous TDM, data from a given device might be in the first slot of one
frame and in the third of the next.
In the absence of fixed positional relationships, each time slot must carry an
address telling the demultiplexer how to direct the data. This address, for local use
only, is attached by the multiplexer and discarded by the demultiplexer once it has
been read. In Figure (14), the address is specified by a digit.
Adding address bits to each time slot increases the overhead of an asynchronous
system and somewhat limits its potential efficiency. To limit their impact,
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addresses usually consist of only a small number of bits and can be made even
shorter by appending a full address only to the first portion of a transmission, with
abbreviated versions to identify subsequent portions.
The need for addressing makes asynchronous TDM inefficient for bit or byte
interleaving. Imagine bit interleaving with each bit carrying an address: one bit of
data plus. Say, three bits of address. All of a sudden it takes four bits to transport
one bit of data. Even if the link is kept full, only a quarter of the capacity is used to
transport data the rest is overhead. For this reason, asynchronous TDM is efficient
only when the size of the time slots is kept relatively large.
Variable Length Time Slots Asynchronous TDM can accommodate traffic of
varying data rates by varying the length of the time slots. Stations transmitting at a
faster data rate can be given a longer slot. Managing variable-length fields requires
that control bits be appended to the beginning of each time slot to indicate the
length of the coming data portion. These extra bits also increase the overhead of
the system and, again, are efficient only with larger time slots.
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