563489578934

Sec. 5–13 Spread Spectrum Systems 393
r n = d
1
N 2 , n = 0
a N + 1
N 2 b a sin(pn>N)
pn>N b, n Z 0
(5–128)
This PSD is plotted in Fig. 5–40b.
Now let us demonstrate that the bandwidth of the SS signal is relatively large compared
to the data rate R b and is determined primarily by the spreading waveform c(t), and not by the
data modulation m(t). Referring to Fig. 5–39, we see that the PSDs of both m(t) and c(t) are of
the [(sin x)x] 2 type, where the bandwidth of c(t) is much larger than that of m(t) because it is
assumed that the chip rate R c = 1T c is much larger than the data rate R b = 1T b . That is,
R c R b . To simplify the mathematics, approximate these PSDs by rectangular spectra, as
shown in Figs. 5–41a and 5–41b, where the heights of the PSD are selected so that the areas
p m (f)
1
2R b
(a) Approximate PSD for m(t)
R b
p c (f)
R b
f
1
2R c
R c R c
f
(b) Approximate PSD for c(t)
A c
2
2
p g (f)=A c p m (f) * p c (f)
R b
2R c
Figure 5–41
R c
R c
t
(c) Approximate PSD for Complex Envelope of the SS Signal
Approximate PSD of the BPSK-DS-SS signal.