Global Positioning System Reference
In-Depth Information
Table 4.1
Autocorrelation Function Characteristics for BOC Modulations
Number of Positive
and Negative Peaks
in Autocorrelation
Function
Delay Values
of Peaks (Seconds)
Autocorrelation Function
Values for Peak at
Modulation
jT
S
/2
j even
j odd
1)
(|
j
|−1)/2
/(2
k
BOC
s
(
m
,
n
)
2
k
−
1
=
jT
S
/2,
(
−
1)
j
/2
(
k
−
|
j
/2|)/
k
(
−
)
−
2
k
+
2
≤
j
≤
2
k
−
2
BOC
c
(
m
,
n
)
τ =
jT
S
/2,
1)
j
/2
(
k
1)
(|
j
|+1)/2
/(2
k
2
k
+
1
(
−
−
|
j
/2|)/
k
(
−
)
−
2
k
+
1
≤
j
≤
2
k
−
1
2
π
f
f
f
f
2
sin
4
(
)
s
4
T
sinc
2
π
f T
,
k
even
c
c
π
cos
2
)
()
s
S
f
=
(4.18)
(
BOC
m n
,
2
c
π
f
f
2
sin
(
)
cos
2
π
fT
4
c
s
4
T
,
k
odd
c
(
)
2
π
f
f
π
fT
c
cos
2
s
A binary coded symbol (BCS) modulation [4] uses a spreading symbol defined
by an arbitrary bit pattern {
c
m
} of length
M
as:
M
−
∑
0
1
()
(
)
gt
=
c
p t
−
TM
(4.19)
BCS
m
TM
c
c
m
=
where
pt
TM
c
/
()is a pulse taking on the value 1/
T
c
over the interval [0,
T
c
/
M
) and
zero elsewhere. The notation BCS([
c
0
,
c
1
, ...,
c
M
−1
],
n
) is used to denote a BCS modula-
tion that uses the sequence [
c
0
,
c
1
, ...,
c
M
−1
] for each symbol and a chipping rate of
R
c
=
n
1/
T
c
. As shown in [4], the autocorrelation function for a BCS([
c
0
,
c
1
, ...,
c
M
−1
],
n
) modulation with perfect spreading code is a piecewise linear function
between the values:
×
1.023 MHz
=
1
M
−
∑
1
(
)
R
TM
M
=
cc
(4.20)
c
m
m
−
n
BCS
m
=
0
where
n
is an integer with magnitude less than or equal to
M
and where it is under-
stood that
c
m
=
0 for
m
∉
[0,
M
−
1]. The power spectral density is:
2
1
M
−
∑
1
()
(
)
Sf
=
T
M
ce
−
j
2
π
mfTM
sinc
2
π
fT M
(4.21)
c
BCS
c
m
c
m
=
0
Given the success of BPSK-R modulations, why consider more advanced modu-
lations like BOC or BCS? Compared to BPSK-R modulations, which only allow the
signal designer to select carrier frequency and chip rate, BOC and BCS modulations
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