Global Positioning System Reference
In-Depth Information
80
d
=1.0
d
= 0.5
d
= 0.1
60
40
20
0
−20
−40
−60
−80
0
100
200
300
400
500
Multipath delay
δ
[m]
FIGURE 7.17. Multipath error envelope for noncoherent early/late detector for C/A code,
α
=
0
.
5. The positive multipath error corresponds to constructive interference while nega-
tive multipath error corresponds to destructive interference.
approximated as
exp
j
)
D
y
±
(
t
)
≈
A
1
R
C
(τ
1
−
τ
±
δ)
D
(
t
−
τ
1
)
+
A
2
R
C
(τ
2
−
τ
±
δ)
ψ(
t
(
t
−
τ
2
)
A
1
R
C
(τ
1
−
τ
±
δ)
+
D
A
2
exp
j
R
C
(τ
2
−
τ
±
δ)
≈
ψ(
t
)
(
t
−
τ
1
).
With
=
τ
1
−
τ
, the envelope of
y
±
(
t
)
is
)
R
C
+
(τ
2
−
τ
1
)
±
δ
.
A
2
exp
j
|
y
±
(
t
)
|=
A
1
R
C
(
±
δ)
+
ψ(
t
(7.27)
The output of the envelope discriminator is
(
t
)
=|
y
−
(
t
)
|−|
y
+
(
t
)
|
.
(7.28)
As mentioned before, the amplitude of the sum signal depends on the relative
phase
between the direct and the reflected signal components. We consider
the two special cases of constructive and destructive interference:
Constructive interference
In this case exp
j
ψ(
t
)
)
=
ψ(
t
1and
|
y
±
(
)
|=
A
1
R
C
(
±
δ)
+
A
2
R
C
(
+
τ
2
−
τ
1
±
δ).
t
(7.29)
Destructive interference
Here, exp
j
)
=−
ψ(
t
1 and, therefore,
|
y
±
(
t
)
|=
A
1
R
C
(
±
δ)
−
A
2
R
C
(
+
τ
2
−
τ
1
±
δ).
(7.30)
v
1
=
v
2
and the relative phase
changes over time. Therefore, the envelope of the received signal will fluctuate
If the receiver is moving, it is very likely that
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