Global Positioning System Reference
In-Depth Information
1
p
= 1
p
= 2
p
= 4
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
−0.5
0
0.5
1
Delay [chip]
FIGURE 3.5. ACF for the BOC
(
pn
,
n
)
signal as function of delay
τ
and
p
.
and the sine integral is defined as
x
sin
(
y
)
Si
(
x
)
=
dy
.
y
0
If we plot the function
r
BOC
(
n
,
n
)
, we get a result similar to the one in Figure 3.5
for
n
4.
The BOC ACF profile results in a DLL discriminator curve that is a bit more
complicated than that of GPS. Figure 3.6 shows the ideal band-unlimited corre-
lation function for both a C/A code signal and a BOC(1,1) signal. Shown as well
are early minus late discriminator curves for a chip spacing of 0.5 chip.
We observe various facts. Both discriminator curves are linear around the cen-
ter of the ACF. In both cases the linear region extends from
=
1
,
2
,
25 chip
code offset. The slope of the BOC discriminator in the linear region is three times
the slope of the C/A discriminator. The C/A code discriminator output is used
to adjust the code NCO to align the code phase better with the incoming signal;
this adjustment will succeed for tracking errors less than 1
−
0
.
25 to 0
.
.
25 chips. The C/A dis-
1.5
1.5
Correlation
Discriminator
output
Correlation
Discriminator
output
1
1
0.5
0.5
0
0
−0.5
−0.5
−1
−1
−1.5
−1.5
−2
−1
0
1
2
−2
−1
0
1
2
Code offset [chips]
Code offset [chips]
FIGURE 3.6. C/A code and BOC(1,1) ACF and early minus late discriminator curves.
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