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AM, FM, and Digital Modulated Systems Chap. 5
0
5
MSK
[p y (f)] =10 log
dB
cos 2 (∏f/R)
[1-(4 f/R) 2 ] 2 sin(∏f/R)
10
GMSK (BT b =0.3)
15
QPSK or OQPSK
[p y (f)] =10 log
dB
(
∏f/R
(
2
Power spectral density (dB)
20
25
30
35
40
0 0.5R R 1.5R 2R 2.5R 3R
f
Figure 5–35 PSD for complex envelope of MSK, GMSK, QPSK, and OQPSK, where R is the bit rate
(positive frequencies shown).
Thus, the PSD for the complex envelope of an MSK signal is
g (f) = 16A c 2 T b
(5–115)
p 2 a cos 2 2pT b f
[1 - (4T b f) 2 ] 2b
where the normalized power in the MSK signal is A 2 c > 2 . The PSD for MSK is readily obtained
by translating this spectrum up to the carrier frequency, as described by Eq. (5–2b). This complex-envelope
PSD for MSK is shown by the solid-line curve in Fig. 5–35.
Example 5–14 PSD FOR A MSK SIGNAL
Compute and plot the PSD for an MSK signal. See Example5_13.m for the solution. Compare
this result with that shown in Figure 5–35.