Global Positioning System Reference
In-Depth Information
FIGURE 7.2
Acquisition with C/A code and frequency analysis.
complex and can be represented by
e
jωt
. The local code is obtained from the
product of the complex RF and the C/A code, thus, it is also a complex quan-
tity. Assume that the L1 frequency (1575.42 MHz) is converted to 21.25 MHz
and digitized at 5 MHz; the output frequency is at 1.25 MHz as discussed in
Section 6.8. Also assume that the acquisition programs search the frequency
range of 1
,
250
10 kHz in 1 kHz steps, and there are a total of 21 frequency
components. The local code
l
si
can be represented as
±
l
si
=
C
s
exp
(j
2
πf
i
t)
(
7
.
1
)
where
subscript
s
represents
the
number
of
satellites
and
subscript
i
=
1
,
2
,
3
...
21,
C
s
is the C/A code of satellite
S
,
f
i
=
−
−
1
,
250
10, 1
,
250
9,
−
+
1
,
250
10 kHz. This local signal must also be digitized at 5 MHz
and produces 5,000 data points. These 21 data sets represent the 21 frequencies
separated by 1 kHz. These data are correlated with the input signal. If the
locally generated signal contains the correct C/A code and the correct frequency
component, the output will be high when the correct C/A phase is reached.
Figure 7.3 shows the concept of such an acquisition method. The operation
of only one of these 21 sets of data will be discussed because the other 20 have
the same operations. The digitized input signal and the locally generated one are
multiplied point by point. Since the local signal is complex, the products obtained
from the input and the local signals are also complex. The 5,000 real and imag-
inary values of the products are squared and added together and the square root
of this value represents the amplitude of one of the output frequency bins. This
process operates every 200 ns with every new incoming input data point. After
the input data are shifted by 5,000 points, one ms of data are searched. In 1 ms
there are 5,000 amplitude data points. Since there are 21 local signals, there are
overall 105,000 (5
,
000
×
21) amplitudes generated in 1 ms. A certain threshold
can be set to measure the amplitude of the frequency outputs. The highest value
among the 105,000 frequency bins that also crosses the threshold is the desired
frequency bin. If the highest value occurs at the
k
th input data point, this point
is the beginning of the C/A code. If the highest peak is generated by the
f
i
frequency component, this frequency component represents the carrier frequency
of the input signal. Since the frequency resolution is 1 kHz, this resolution is not
8
,...
1250
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