Global Positioning System Reference
In-Depth Information
increase slightly due to the satellite antenna array gain pattern. In other words, the
received signal power and antenna gain combination tends to be lower by about
−
3 dB near the elevation mask angle of 5º and higher by about 1.5 dB at zenith with
a fluctuation range of more than 4.5 dB in the approximately hemispherical gain
coverage region of a typical FRPA. Antenna tilt can significantly increase this gain
fluctuation range. In this example, the antenna is assumed to have (
15dB
gain toward the SV to allow for the higher SV signal levels that exist most of the
time, counting the gains of both the receiver antenna and the SV antenna. The
implementation loss is assumed to be 2 dB (
L
dB
=
G
SVi
)
=
.
dB
2) for a high-quality receiver design
and A/D converter. Using these assumptions in (6.23), the total recovered signal
power is (
C
s
)
dB
=−
158.5
+
1.5
−
2
=−
159.0 dBW. Next assume that the receiver
noise figure (
N
f
)
dB
=
490.5 K. Assuming
that the antenna noise temperature is 100K, then the thermal noise can be computed
as
N
0
4.3 dB at 290 K, so
T
amp
=
290
×
(10
0.43
−
1)
=
=
10 log
10
[
k
×
(100
+
490.5)]
=−
200.9 dBW. Therefore, the unjammed
(
C
S
/
N
0
)
dB
=−
41.9 dB-Hz.
Note that the unjammed (
C
S
/
N
0
)
dB
in (6.23) accounts for the antenna gain in the
direction of the satellite as well as the implementation loss of the receiver. Similarly,
if the antenna gain in the direction of the jammer, (
G
J
)
dB
, is accounted for in (6.22),
then
159.0
+
200.9
=
(
)
(
)
(
)
CC
=
C
−
C
ι
S
l
S
dB
dB
dB
()
( )
() ( ) ( )
C
=+
J
GL
−
ι
dB
J
dB
dB
(6.24)
dB
(
)
C
=
C
+
G
−
LS
=
+
G
−
L
S
Ri
SVi
dB
dB
SVi
dB
dB
dB
dB
dB
(
(
)
)
(
)
(
)
()
(
)
CC
=−+
J
S
G
−
G
=
JS
+
G
−
G
ι
S
dB
dB
J
SVi
J
SVi
dB
dB
dB
dB
dB
dB
where (
J
/
S
)
dB
is the jamming to signal power ratio at the antenna input in decibels.
Substituting this into (6.22)
(
)
CN
(
)
CN
S
0
eff
,
dB
S
0
dB
() ( )
(
)
−
−
JS
=
G
−
G
+
10
log
QR
10
−
10
(6.25)
10
10
SVi
J
10
c
dB
dB
dB
From (6.25), the receiver (
J
/
S
)
dB
performance can be computed for a given
QR
c
using the unjammed (
C
S
/
N
0
)
dB
from (6.23) and obtaining the value of (
C
S
/
N
0
)
eff,dB
by
simply equating it to the receiver tracking threshold as determined from the approx-
imation methods presented in Chapter 5. Recall that the carrier tracking threshold
(
C
S
/
N
0
)
eff,dB
is the weak link for an unaided GPS receiver and even for an externally
aided receiver if the carrier loop is closed.
As a computational example of (6.24) using the unjammed C/A code example
where (
C
S
/
N
0
)
dB
=
41.9 dB-Hz, assume the antenna gain toward the jammer, (
G
J
)
dB
,is
−
3 dB. Note that the jammer signal may or may not be RHCP. If RHCP, then the
antenna gain toward the jammer would be the same as its gain in that direction for
an SV. But if the jammer is linearly polarized, then an additional 3-dB loss or more
must be included in the gain toward the jammer, depending on the polarization mis-
match of the GPS antenna. Since the desired signal is C/A code with a BPSK-R(1)
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