Frequency-Division Multiplexing

Frequency-division multiplexing (FDM) is an analog technique that can be applied
when the bandwidth of a link (in hertz) is greater than the combined bandwidths of
the signals to be transmitted. In FOM, signals generated by each sending device modulate
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
sufficient bandwidth to accommodate the modulated signal. These bandwidth ranges are
the channels through which the various signals travel. Channels can 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 6.3 gives a conceptual view of FDM. In this illustration, the transmission path
is divided into three parts, each representing a channel that carries one transmission.

We consider FDM to be an analog multiplexing technique; however, this does not

mean that FDM cannot be used to combine sources sending digital signals. A digital

signal can be converted to an analog signal (with the techniques discussed in Chapter 5)

before FDM is used to multiplex them.

FDM is an analog multiplexing technique that combines analog signals.

Multiplexing Process

Figure 6.4 is a conceptual illustration of the multiplexing process. Each source generates

a signal of a similar frequency range. Inside the multiplexer, these similar signals

modulates different carrier frequencies (/1,12, and h). The resulting modulated signals

are then combined into a single composite signal that is sent out over a media link that

has enough bandwidth to accommodate it.

Demultiplexing Process

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 output lines. Figure 6.5 is

a conceptual illustration of demultiplexing process.

Example 6.1

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 6.6. At the receiver, each channel receives the entire signal, using a

filter to separate out its own signal. The first channel uses a filter that passes frequencies

between 20 and 24 kHz and filters out (discards) any other frequencies. The second channel

uses a filter that passes frequencies between 24 and 28 kHz, and the third channel uses a filter

that passes frequencies between 28 and 32 kHz. Each channel then shifts the frequency to start

from zero.

Example 6.2

Five channels, each with a lOa-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 10kHz 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 x 100 + 4 x 10 =540 kHz, as shown in Figure 6.7.

Figure 6.6     Example 6.1

Example 6.3

Four data channels (digital), each transmitting at I Mbps, use a satellite channel of I MHz.

Design an appropriate configuration, using FDM.

Solution

The satellite channel is analog. We divide it into four channels, each channel having a 2S0-kHz

bandwidth. Each digital channel of I Mbps is modulated such that each 4 bits is modulated to

1 Hz. One solution is 16-QAM modulation. Figure 6.8 shows one possible configuration.

The Analog Carrier System

To maximize the efficiency of their infrastructure, telephone companies have traditionally

multiplexed signals from lower-bandwidth lines onto higher-bandwidth lines. In this

way, many switched or leased lines can be combined into fewer but bigger channels. For

analog lines, FDM is used.

In this analog hierarchy, 12 voice channels are multiplexed onto a higher-bandwidth

line to create a group. A group has 48 kHz of bandwidth and supports 12 voice channels.

At the next level, up to five groups can be multiplexed to create a composite signal

called a supergroup. A supergroup has a bandwidth of 240 kHz and supports up to

60 voice channels. Supergroups can be made up of either five groups or 60 independent

voice channels.

At the next level, 10 supergroups are multiplexed to create a master group. A

master group must have 2.40 MHz of bandwidth, but the need for guard bands between

the supergroups increases the necessary bandwidth to 2.52 MHz. Master groups support

up to 600 voice channels.

Finally, six master groups can be combined into a jumbo group. A jumbo group

must have 15.12 MHz (6 x 2.52 MHz) but is augmented to 16.984 MHz to allow for

guard bands between the master groups.

Other Applications ofFDM

A very common application of FDM is AM and FM radio broadcasting. Radio uses the

air as the transmission medium. A special band from 530 to 1700 kHz is assigned to AM

radio. All radio stations need to share this band. As discussed in Chapter 5, each AM station

needs 10kHz of bandwidth. Each station uses a different carrier frequency, which

means it is shifting its signal and multiplexing. The signal that goes to the air is a combination

of signals. A receiver receives all these signals, but filters (by tuning) only the one

which is desired. Without multiplexing, only one AM station could broadcast to the common

link, the air. However, we need to know that there is physical multiplexer or demultiplexer

here. As we will see in Chapter 12 multiplexing is done at the data link layer.

The situation is similar in FM broadcasting. However, FM has a wider band of 88

to 108 MHz because each station needs a bandwidth of 200 kHz.

Another common use of FDM is in television broadcasting. Each TV channel has

its own bandwidth of 6 MHz.

The first generation of cellular telephones (still in operation) also uses FDM. Each

user is assigned two 30-kHz channels, one for sending voice and the other for receiving.

The voice signal, which has a bandwidth of 3 kHz (from 300 to 3300 Hz), is modulated by

using FM. Remember that an FM signal has a bandwidth 10 times that of the modulating

signal, which means each channel has 30 kHz (10 x 3) of bandwidth. Therefore, each user

is given, by the base station, a 60-kHz bandwidth in a range available at the time of the call.

Example 6.4

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. The 3-kHz voice is modulated using FM, creating 30 kHz of modulated

signal. 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. We discuss AMPS in greater detail in Chapter 16.

Implementation

FDM can be implemented very easily. In many cases, such as radio and television

broadcasting, there is no need for a physical multiplexer or demultiplexer. As long as

the stations agree to send their broadcasts to the air using different carrier frequencies,

multiplexing is achieved. In other cases, such as the cellular telephone system, a base

station needs to assign a carrier frequency to the telephone user. There is not enough

bandwidth in a cell to permanently assign a bandwidth range to every telephone user.

When a user hangs up, her or his bandwidth is assigned to another caller.