Global Positioning System Reference
In-Depth Information
12.6 STRONG AND WEAK SIGNAL CONDITIONS
(
4-6
)
Many satellite signals are blocked by tall buildings in an urban area crowded with
high rise buildings. Only a few satellites can reach a GPS receiver directly. This
is why signals at the receiver consist of both strong and weak signals. The strong
signal referenced here is a signal at nominal power level and the weak signal is
weaker than the nominal power level. Let us assume that
S
1
is a strong signal and
S
2
is a weak signal. During acquisition, the strong signal can be found easily. In
order to find the weak signal, C/A code of
S
2
must be used for acquisition. If the
frequency of
S
2
is not known, one must search within the anticipated frequency
range. However, the C/A codes are not true orthogonal but near orthogonal with
each other. The autocorrelation peak of a C/A code is 1023, and the largest cross-
correlation peak is
−
65, as discussed in Section 5.7. The cross-correlation peak
is about
−
23.94 dB (20
×
log
(
65
/
1023
)
) below the autocorrelation peak. Thus,
if the weak signal is about
20 dB below the strong one, the cross-correlation
peak with the strong signal is comparable to the autocorrelation peak of the weak
signal. One approach to locating the weak signal is to find all the strong signals
and subtract them from the input data set.
Before the strong signal is removed, the effect of the strong signal on the weak
signal acquisition will be shown. Suppose that the received GPS signal consists
of a strong signal
S
1
, a weak signal
S
2
, and noise
n
,then
−
=
S
1
+
S
2
+
y
n
(
12
.
3
)
The noise ratios of the strong and weak signals are
S
N
10 log
P
1
N
0
S
N
10 log
P
2
N
0
1
=
2
=
(
12
.
4
)
where
P
1
is the strong signal power,
P
2
is the weak signal power, and
N
0
(vari-
ance of
n
) is the noise power. The basic process used to find the weak signal is
to correlate the input signal
y
with the locally generated C/A code (C
2
)ofthe
weak signal
S
2
.Since
y
also contains the strong signal, for the purpose of the
discussion, the strong signal can be represented as
S
1
=
A
1
C
1
,P
1
=
A
1
(
12
.
5
)
where
A
1
and
C
1
are the amplitude and the C/A code of the strong signal,
respectively.
The basic idea of this approach is to treat the cross correlation between the
C/A codes:
C
1
of the strong signal and the locally generated
C
2
as equivalent
noise power. The equivalent noise power
N
e
can be then written as
S
1
)
2
]
=
A
1
E
[
(C
2
⊗
C
1
)
2
]
=
N
e
=
E
[
(C
2
⊗
P
1
K
and
(
12
.
6
)
C
1
)
2
]
K
≡
E
[
(C
2
⊗
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