Global Positioning System Reference
In-Depth Information
(a)
(b)
Fig. 5.
α
max
vs.
C
/
N
0
and different integration windows: (a) with data wipe-off;
(b) without data wipe-off
α
mean
and
.
α
mean
is constant for low
C
/
N
0
values because at such a noise level,
R
floor
is a zero-mean
Gaussian random variable and for most of
R
[
k
,
m
]
samples:
Var
2
2
|
R
floor
|
≤
E
{|
R
floor
|
}
+
η
{|
R
floor
|
2
}
(20)
where
η
is an arbitrary constant. Then:
Var
{|
R
floor
|
2
}
2
{|
R
floor
|
}
max
α
mean
=
=
1
+
η
(21)
{|
R
floor
|
2
}
{|
R
floor
|
2
}
E
E
2
Since
R
floor
is complex and Gaussian distributed, then
|
R
floor
|
=
R{
R
floor
}
+
I{
R
floor
}
is
2
distributed (2 degrees of freedom) and thus the ratio of mean and variance is constant
(Kreiszig, 1999). In Fig. 5(b), it can be seen that without data wipe-off the CAF envelope
behaves as if it is made of noise only, even at the highest values of
C
/
N
0
.
χ
3.3.2 Doppler effects on carrier and code
The Doppler effect observed at the receiver location is caused by the time-variant propagation
delay of the transmitted signal along its path toward the receiver. This delay changes over
time even in case of a low-dynamics user (e.g. pedestrians, etc.), as at least the SV is
moving along its own orbit. Even if the rate of change is relatively slow, when long coherent
integration windows are used, it can be shown that it impacts on the acquisition sensitivity.
Let (22) be the general expression of the received RF signal (noiseless for simplicity):
)=
√
2
Cc
(
[
− τ
(
)]
{
[
− τ
(
)]
}
s
RX
t
t
t
cos
2
π
f
RF
t
t
(22)
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