563489578934

394
AM, FM, and Digital Modulated Systems Chap. 5
under the curves are unity because the powers of m(t) and c(t) are unity. (They both have only
;1 values.) From Eq. (5–121), g(t) is obtained by multiplying m(t) and c(t) in the time
domain, and m(t) and c(t) are independent. Thus, the PSD for the complex envelope of the
BPSK-DS-SS signal is obtained by a convolution operation in the frequency domain:
g (f) = A c 2 m (f) * c (f)
(5–129)
This result is shown in Fig. 5–41c for the approximate PSDs of m(t) and c(t). The bandwidth
of the BPSK-DS-SS signal is determined essentially by the chip rate R c , because R c R b . For
example, let R b = 9.6 kbitss and R c = 9.6 Mchipss. Then the bandwidth of the SS signal is
B T ≈ 2R c = 19.2 MHz.
From Fig. 5–41, we can also demonstrate that the spreading has made the signal less
susceptible to detection by an eavesdropper. That is, the signal has LPI. Without spreading
[i.e., if c(t) were unity], the level of the in-band PSD would be proportional to A 2 c (2R b ), as
seen in Fig. 5–41a, but with spreading, the in-band spectral level drops to A 2 c (2R c ), as seen in
Fig. 5–41c. This is a reduction of R c R b . For example, for the values of R b and R c just cited,
the reduction factor would be (9.6 Mchipss)(9.6 kbitss) = 1,000, or 30 dB. Often, the
eavesdropper detects the presence of a signal by using a spectrum analyzer, but when SS is
used, the level will drop by 30 dB. This is often below the noise floor of the potential eavesdropper,
and thus, the SS signal will escape detection by the eavesdropper.
Figure 5–39c shows a receiver that recovers the modulation on the SS signal. The
receiver has a despreading circuit that is driven by a PN code generator in synchronism with
the transmitter spreading code. Assume that the input to the receiver consists of the SS signal
plus a narrowband (sine wave) jammer signal. Then
r(t) = s(t) + n(t) = A c m(t)c(t) cos v c t + n j (t),
(5–130)
where the jamming signal is
n j (t) = A J cos v c t
(5–131)
Here, it is assumed that the jamming power is A 2 J2 relative to the signal power of A 2 c 2 and
that the jamming frequency is set to f c for the worst-case jamming effect. Referring to Fig.
5–39c, we find that the output of the despreader is
y 1 (t) = A c m(t) cos v c t + A J c(t) cos v c t
(5–132)
since c 2 (t) = (;1) 2 = 1. The BPSK-DS-SS signal has become simply a BPSK signal at the
output of the despreader. That is, at the receiver input the SS signal has a bandwidth of 2R c ,
but at the despreader output the bandwidth of the resulting BPSK signal is 2R b , a 1,000:1
reduction for the figures previously cited. The data on the BPSK despread signal are recovered
by using a BPSK detector circuit as shown.
Now we show that this SS receiver provides an antijam capability of 30 dB for the case
of R b = 9.6 kbitss and R c = 9.6 Mchipss. From Eq. (5–132), it is seen that the narrowband
jammer signal that was present at the receiver input has been spread by the despreader, since
it has been multiplied by c(t). It is this spreading effect on the jamming signal that produces
the antijam capability. Using Eq. (5–132) and referring to Fig. 5–39c, we obtain an input to
the LPF of