Digital Signal Processing Reference
In-Depth Information
arrive from the directions
φ
1
,
φ
2
, …,
φ
M
. The channel is an additive white Gaussian noise
(AWGN). We assume that the GPS signal is a direct line-of-sight signal with no reflection
or diffraction components [44]. The
k
th
data samples received at the horizontal element
and the vertical element of the
i
t h
antenna are denoted as
x
iH
(
k
) and
x
iV
(
k
), respectively.
hus, the 2
N
-by-1 data vector
x
(
k
) is given by
T
)] ,
x
() [
kxkxk
=
1
(
)
(
)
…
x
(
kx
)
(
k
(14 .1)
H
1
V
NH
NV
where (.)
T
denotes transpose. Let a
D
-by-1 vector
s
D
(
k
)denote the
D
complex GPS signals
at the
k
th
sample,
T
s
D
() [(),
ks ksk
=
(),
…
,
s
()].
k
(14.2)
1
2
D
Similarly, the
M
-by-1 interference vector
i
M
(
k
) represents the
M
complex interferers
at the
k
th
sample,
T
i
M
() [(),
ki kik
=
(),
…
,
i
()].
k
(14 . 3)
1
2
M
Let
a
D
(θ) denote the GPS signal 2
N
-by-
D
steering matrix,
a
()
θ θ
=
a
()
a
()
θ
…
a
(),
θ
(14 .4)
D
1
2
D
where
a
(θ
i
) is the 2
N
-by-1 steering vector of the
i
t h
GPS signal incident on the antenna
array from direction θ
i
,
H
a
()[
θ
=
a
(
θ
)
a
(
θ
)
…
a
(
θ
)
a
(
θ
)]
,
(14 . 5)
i
1
H
i
1
V
i
NHi
NV
i
where (.)
H
denotes complex conjugate transpose.
a
I
(φ) represents the interference
2
N-
by-
M
steering matrix,
a
()
ϕϕ ϕ
=
a
()
a
()
…
a
(
ϕ
) .
(14 .6)
I
1
2
M
In the above equation,
a
(φ
i
) represents the 2
N
-by-1 steering vector of the
i
t h
interference,
H
a
()[
ϕ
=
1
a
(
ϕ
)
a
(
ϕ
)
...
a
()
ϕ
a
( ].
ϕ
(14 .7)
i
H
i
1
V
i
NHi
NV
i
In GPS, two binary phase shift keying (BPSK) codes are applied to the GPS informa-
tion symbols. The coarse acquisition (C/A) code is a repeating 1 MHz pseudo random
noise (PRN) code (1,023 bits) transmitted with the carrier frequency L1 = 1,575.42 MHz
by the satellite vehicles (SVs). The precise (P) code is a very long 10 MHz PRN code
(7 days) transmitted with both L1 = 1,575.42 MHz and L2 = 1,227.60 MHz. Over one
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