Interference, Multipath, and Scintillation - Understanding GPS: Principles and Applications - page 273

6.2.2.7 Effects of RF Interference on Code Tracking
The effect of RF interference on code tracking is different from its effect on signal
acquisition, carrier tracking, and data demodulation. While the latter three func-
tions depend on the output SNIR at the output of a prompt correlator, as described
in Section 6.2.2.5, code tracking relies on the difference between an early correlator
and a late correlator, as described in Section 5.2.
The interference considered here is modeled as Gaussian and zero-mean, but
not necessarily having a white (flat) spectrum. The analysis assumes that the
receiver front end does not saturate or respond nonlinearly in some other way to the
interference, as discussed in Section 6.2.2.1, and that there is no multipath, so that
code tracking errors are caused by noise and interference. While the effects of white
noise on code tracking error are considered in Section 5.6.3, this section evaluates
the effect of nonwhite interference, which produces additional random, zero-mean,
code tracking error. The effect of interference is quantified in terms of the standard
deviation of the code tracking error.
As described in Section 5.4, there are many different designs for discriminators
and tracking loops, and interference may have different effects on each. However, a
lower bound on the code tracking error has been developed that is independent of
code tracking circuit design, yet is a tight bound in the sense that it provides reason-
ably accurate predictions of code tracking performance for well-designed tracking
circuits. This lower bound (in units of seconds) is given by [10]:

B

n

σ ≅ (6.30)

LB

()

β 2

Sf

r

S

∫

2

2 π f df

− 1

C
N

C
C

− β 2

()

r

S ι

+ Sf

ι

0 s

where the code-tracking loop has a (one-sided) equivalent rectangular bandwidth of
B n Hz that is much smaller than the reciprocal of the correlation integration time,
the power spectral density of white noise, and any spectrally flat interference is N 0
W/Hz, and the nonwhite component of the interference has power spectral density
C ι S ι ( f ) W/Hz, with normalized power spectral density

∞

∫

Sfdf
ι

() = 1and interfer-

−∞

ence power over infinite bandwidth of C ι W (the aggregate interference carrier
power and power spectral density may result from the aggregation of multiple inter-
fering signals). The signal has power spectral density S S ( f ) normalized to unit
power over infinite bandwidth,

∞

∫

() 1, and C S is the recovered desired sig-
nal power, also defined over an infinite bandwidth, so that the signal has a carrier
power to noise density ratio of C S / N 0 Hz, in white noise. The ratio of interfer-
ence power to signal power is C ι / C S . It is assumed that the power spectral densities
are symmetric about f

Sfdf
ι

=

−∞

0. Precorrelation filtering in the receiver is approximated
by an ideal filter with linear phase and rectangular passband having total band-
width

=

β r Hz.