Global Positioning System Reference
In-Depth Information
12
β
2
r
() ()
∫
SfS fdf
ι
S
−
β
2
σ
≅
σ
1
+
r
NELP,D
→
0
CELP D
,
→
0
2
β
2
r
()
∫
TC
S
f df
S
S
(6.36)
−
β
2
r
12
κ
1
σ
1
+
+
ι
S
CELP D
,
→
0
T
C
N
T
C
C
S
S
2
η
η
0
ι
where
η
is the fraction of signal power passed by the precorrelation bandwidth,
β
2
r
()
−
∫
η
=
Sf f
S
(6.37)
β
2
r
κ
ι
S
is the SSC describing the effect of interference on correlator output SNR,
defined in (6.11).
Clearly, quantifying the effect of interference on code tracking accuracy is dif-
ferent and more complicated than evaluating its effect on signal acquisition, carrier
tracking, and data demodulation. Not only does the effect depend on the spectra of
signal and interference and on the precorrelation filter, but also on details of the
discriminator design and the bandwidth of the code tracking loop.
As an example, consider narrowband interference centered at
and
±
f
ι
, whose spec-
trum is modeled as
S
(
f
)
(·) is the Dirac function hav-
ing infinite amplitude, vanishing width, and unit area. Substituting for this
interference power spectral density in the code tracking SSC (6.34), assuming the
interference is within the precorrelation bandwidth, yields
=
0.5[
δ
(
f
+
f
)
+ δ
(
f
−
f
)], where
δ
()
2
χ
ι
=
fS f
(6.38)
S
ι
S
ι
The lower bound on code tracking accuracy with narrowband interference is
obtained by substituting the interference spectrum into (6.30), yielding
B
n
σ
≅
LB
β
2
C
N
r
()
−
∫
2
2
π
S
fS fdf
(6.39)
S
0
β
2
r
B
CN
1
=
n
2
πβ
S
S
0
This result shows that optimal code tracking in narrowband interference produces
the same code tracking error as with no narrowband interference. It is readily shown
that this processing is closely approximated by narrowband excision followed by
CELP with very small early-late processing.
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