Chapter 6
Digital Modulation
From
Introduction to Communication Systems
Copyright by Upamanyu Madhow, 20082010
+1
BittoSymbol Map
0
+1
1
1
...
Pulse
Modulation
...0110100...
...
+1
1
1
+1
T
Symbol interval
1
+1
Figure 6.1: Running example: Binary antipodal signaling using a timelimited pulse.
Digital modulation is the process of translating bits to analog waveforms that can be sent over
a physical channel. Figure 6.1 shows an example of a baseband digitally modulated waveform,
where bits that take values in
{
0
,
1
}
are mapped to symbols in
{
+1
,
−
1
}
, which are then used
to modulate translates of a rectangular pulse, where the translation corresponding to successive
symbols is the symbol interval
T
. The modulated waveform can be represented as
u
(
t
) =
summationdisplay
n
b
[
n
]
p
(
t
−
nT
)
(6.1)
where
{
b
[
n
]
}
is a sequence of
symbols
in
{−
1
,
+1
}
, and
p
(
t
) is the
modulating pulse.
This
is an example of a widely used form of digital modulation termed
linear modulation,
where
the transmitted signal depends linearly on the symbols to be sent.
Our treatment of linear
modulation in this chapter generalizes this example in several ways. The modulated signal in
Figure 6.1 is a baseband signal, but what if we are constrained to use a passband channel (e.g., a
wireless cellular system operating at 900 MHz)? One way to handle this to simply translate this
baseband waveform to passband by upconversion; that is, send
u
p
(
t
) =
u
(
t
) cos 2
πf
c
t
, where the
carrier frequency
f
c
lies in the desired frequency band. However, what if the frequency occupancy
of the passband signal is strictly constrained? (Such constraints are often the result of guidelines
from standards or regulatory bodies, and serve to limit interference between users operating in
adjacent channels.)
Clearly, the timelimited modulation pulse used in Figure 6.1 spreads out
significantly in frequency. We must therefore learn to work with modulation pulses which are
better constrained in frequency.
We may also wish to send information on both the I and Q
1
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components. Finally, we may wish to pack in more bits per symbol; for example, we could send
2 bits per symbol by using 4 levels, say
{±
1
,
±
3
}
.
Plan:
We first develop an understanding of the structure of linearly modulated signals, using the
binary modulation in Figure 6.1 to lead into variants of this example corresponding to different
signaling constellations which can be used for baseband and passband channels. We discuss how
to quantify the bandwidth of linearly modulated signals by computing the power spectral density.
Since the receiver does not know the bits being sent, they can be modeled as random, which
implies that the modulated signal is a random process. We compute the power spectral density for
this random process in order to determine how bandwidth depends on the choice of modulation
pulse and the statistics of the transmitted symbols. With these basic insights in place, we turn
to a discussion of modulation for bandlimited channels, treating signaling over baseband and
passband channels in a unified framework using the complex baseband representation. We note,
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 Fall '08
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 Bandwidth, pulse, sinc Pulse

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