Networking Reference

In-Depth Information

X
n

S
(
t
)

r
(
t
)

X
n

+

Demodulator

Modulator

A
(
t
)

n
(
t
)

Figure 2.1
Generic channel model of modulation of digital signals.

modulate one bit at a time; or we can have
M

4 symbols (00, 01, 10, and 11) where we

modulate two bits at a time, and so on. An
M
-ary modulator takes as an input one of the
M

symbols and produces one of
M
analog waveforms that can be transmitted over the physical

media. There are many functions needed to be incorporated in the physical layer in order

to make modulation work effectively to include frequency conversion, signal amplification,

and transducers.

Figure 2.1 presents a generic channel model which focuses on modulation and demod-

ulation of a digital signal. In this model, we start with
M
symbols and have a signaling

rate of
T
S
. That is, every
T
S
seconds, the modulator gets an input
S(T )
which represents

one of the
M
symbols. At any given time
t
, the output of the modulator
S(t)
is one of

M
waveforms.
S(t)
can be expressed as
S(t)
=
S
X
n
(t)
. The waveform
S(t)
can be a set

of voltages or currents (over a wire), a set of optical signals (over an optical medium), a

set of electric field intensities (over the air), and so on. In many cases,
S(t)
is limited to

a time interval bounded by
T
S

=

seconds.
2
Simply, the modulator emits signals at a rate of

symbols per second. Note:
M
is a power of two in most cases.
3

R
S
=

1
/T
S

If the symbol

rate of this channel model is
R
S
, then the bit rate is
mR
S
or
m/T
S
bps.

In the model presented in Figure 2.1, the modulated signal is distorted by attenuation, fad-

ing, noise, and other interference.
A(t)
expresses attenuation and fading while
n(t)
expresses

added noise. The received signal, in most cases, is very different from the transmitted signal.

Communications references use models for attenuation and fading such as Rayleigh, Rician,

and log-normal models. One of the most common noise models implemented in the field

is the additive white Gaussian noise (AWGN) model. Reference [1] is known as a classic

textbook example of noise models. Although these models help engineers design excellent

demodulators, there are some caveats that accompany them. For starters, some of these

models are linear, while channels are not. For example, signal amplifiers are non-linear; this

is especially true for high power signals such as satellite communications where the channel

non-linearity characteristics can considerably deviate from the models used in the design.

Models could be time-invariant, while in reality channel gain is time variant. Another issue

in channel modeling is the difficulty in accounting for frequency dispersion in a channel

model. The AWGN model commonly used is often far from reality. With tactical radios,

we need to consider the fact that the enemy could use sophisticated jammers that introduce

noise patterns as far away from AWGN as possible; in such a case, the AWGN model seems

2
In some waveforms, spectrum management techniques call for pulse overlap - detection and estimation of mod-

ulated signals is an interesting field of study that you can reference. Simply remember that a pulse is not an

even-shaped pulse and the leading and tail ends of it can have low spectrum density. The tradeoff between pulse

overlap and pulse energy at the receiver is an interesting area of study.

3
For one bit per symbol, M
=
2 (0 or 1). For two bits per symbol, M
=
4 (00, 01, 10, 11). For three bits per

symbol, M

8 (000, 001, 010, 011, 100, 101, 110, 111), and so on. The
T
1 example presented in this section

shows an unusual case where we have two digital symbols and three modulated signals.

=

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