Global Positioning System Reference
In-Depth Information
rate of the code generator in chips per second. Note that increasing the value of Q in
(6.8) improves ( C S / N 0 ) eff . Therefore, higher jamming resistance quality factor, Q ,
results in increased jamming effectiveness. Comparing (6.7) and (6.8) yields
()
2
()
Hf Sf f
R
S
−∞
Q
=
(6.9)
2
()
() ()
RHf
Sf Sf f
c
R
ι
S
−∞
To assist in the interpretation of (6.9), define the receiver transfer function to
have maximum magnitude of unity, so max
1 , which can be achieved by
multiplying the filter transfer function by a scalar without changing (6.9) in the pro-
cess. With this definition, the numerator of (6.9) is the fraction of signal power
passed by the receiver front end. (Recall that the signal power spectral density is
defined to have unit area over all frequencies.)
Then, (6.9) can be expressed succinctly as
Hf
( )
=
f
()
2
()
Hf Sf f
R
S
Q
=
−∞
(6.10)
R
κ ι
c
S
where
κ ι s is called the spectral separation coefficient (SSC) [7], which is defined as
2
()
() ()
κ ι
=
Hf SfSf f
(6.11)
S
R
ι
S
−∞
Equation (6.11) has units of reciprocal hertz or seconds. Observe that the SSC
depends on the spectrum of the desired signal as well as the spectrum of the interfer-
ence. Different interferers may have the same SSC with a given desired signal, and
when they do, the different interferers affect ( C S / N 0 ) eff the same way. It follows then
that different interferers may have a different SSC with a given desired signal. For
example, if interferer A has x dB smaller SSC with the desired signal than interferer
B, then interferer A has the same effect on ( C S / N 0 ) eff as interferer B when the power in
A is increased by x dB.
Computing Jamming Resistance Quality Factor Q
To consider interference effects further for some nominal situations, suppose that
the receive filter is very wide, so that H R ( f ) can be treated as approximately unity in
(6.9) at frequencies where the desired signal has appreciable power, and the limits
on the integrals can be approximated by infinity, so that (6.9) is approximated by
1
Q
(6.12)
() ()
RSf Sf f
c
ι
S
−∞
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