563489578934

Sec. 5–10 Multilevel Modulated Bandpass Signaling 375
where T s = T b . That is, there are l bits representing each allowed multilevel value. For
symmetrical (polar type) signaling—for example, as illustrated in Fig. 5–32 for the case of
M = 16—with equally likely multilevels, the mean value of c n is
m c = c n = 0
(5–101a)
and the variance is
s c 2 = c n c n * = |c n | 2 = C
(5–101b)
where C is a real positive constant. Substituting Eqs. (5–100) and (5–101) into Eq. (6–70d), we
find that the PSD for the complex envelope of MPSK or QAM signals with data modulation of
rectangular bit shape is
g (f) = Ka sin pf/T 2
b
b , for MPSK and QAM
pf/T b
(5–102)
where K = CT b , M = 2 is the number of points in the signal constellation, and the bit rate is
R = 1T b . For a total transmitted power of P watts, the value of K is K = 2PT b , since
1 q
- q P s(f) df = P. This PSD for the complex envelope is plotted in Fig. 5–33. The PSD of
the MPSK or QAM signal is obtained by simply translating the PSD of Fig. 5–33 to the
carrier frequency, as described by Eq. (5–2b). For = 1, the figure gives the PSD for BPSK
0
–5
Power spectral density (dB)
–10
–15
–20
[p g (f)] dB
=10 log
(
sin(∏f/R)
∏f/R
(
2
–25
–30
0
R
2R
3R
4R
Figure 5–33 PSD for the complex envelope of MPSK and QAM with rectangular data pulses, where
M = 2 , R is the bit rate, and R = D is the baud rate (positive frequencies shown). Use = 2 for PSD
of QPSK, OQPSK, and p4 QPSK complex envelope. (See Example5_12.m.)
5R
6R
7R
8R
f