Page 189 - Fundamentals of Communications Systems

Amplitude Modulation 6.11

Assuming that the negative peaks of the message signal are at about the same
level as the positive peaks and using Eq. (6.10) and the definition of PAPR given
in Chapter 5, the MCPR can be approximated with
1
MCPR ≈ (6.13)
PAPR m
Consequently, the smaller the PAPR of the message signal the easier it is to
put a larger percentage of the transmitted power into the message signal. It
should be noted that most signals of interest in analog communications have a
PAPR > 10, so typically MCPR < 10%. Later after the impacts of noise are
evaluated on LC-AM demodulation it will be shown that the MCPR is directly
related to the achieved transmission efficiency of LC-AM.

EXAMPLE 6.4
Affine modulation with
β 2 β 2
m(t) = β sin(2π f m t) G m (f ) = δ( f − f m ) + δ( f + f m )
4 4
produces
√
x c (t) = A c (1 + aβ sin(2π f m t)) 2 cos(2π f c t)
and
2 2 2
A a β
c
(f ) = [δ( f − f m − f c ) + δ( f + f m − f c ) + δ( f − f m + f c )
G x c
8
A 2 c
+δ( f + f m + f c )] + [δ( f − f c ) + δ( f + f c )]
2
The transmitted power is
a β
2 2
= A 2
c
P x c 1 +
2
To maintain x I (t) > 0 implies that a < 1/β. The mesage signal and the output modulated
√
time domain signal are plotted in Figure 6.12(a) for f c = 20 f m , a = 1/β, and A c = 1/ 2.
Note that both the message signal and the modulated signal are periodic with a period
of T = 1/f m . The plot of the energy spectrum of the message and the modulated signals
√
are plotted in Figure 6.12(b) for f c = 20 f m , a = 1/β, and A c = 1/ 2. It should be noted
= 0.75 and MCPR = 50%.
that P x z = P r z
EXAMPLE 6.5
The computer-generated voice signal given in Chapter 2 (W = 2.5 kHz) is used to LC-AM
modulate a 7-kHz carrier. A short time record of the scaled complex envelope and the
resulting output modulated signal is shown in Figure 6.13(a). Note, the minimum value
of the voice signal is -3.93 so the modulation coefficient was set to a = 0.25. Figure 6.13(a)