Global Positioning System Reference
In-Depth Information
Input data down converted to base band
50,000 pts
Multiply
10-ms C/A code 50,000 pts
Shift 2 samples each time by moving
2 samples from the front to the end
250
50,000 pts
sum
200 pts
Perform FFT
FIGURE 12.4
Acquisition on 10 ms C/A code signal.
1 pt
3. Summing 250 points into one point produces an output of 200 points.
4. The input frequency is found by performing FFT on the 200 data points.
Figure 12.4 shows one of the 2500 operations. If the local C/A matches the
C/A code in the input signal, the output from the FFT has a strong single peak.
If the local C/A code and the C/A code in the input do not match, the output is
noiselike. Under this condition the reference C/A code is shifted two samples by
moving the first two data points to the end. The same operations are performed
from 2 to 4 until the correct initial C/A code is found. Because the C/A is
repetitive over 1 ms time, the local signal is only needed to shift 2500 times
instead of 25,000 times. The overall outputs from 10 ms of data are 50,000 points
(200 in frequency domain and 2500 in time domain.) This operation is easy to
understand but computationally intensive. The following method can accomplish
the same goal with less calculation.
The circular correlation by partition method provides a simple way to perform
the operation above. The down-converted input signal is divided into 250-point
sections, and there are 200 sections in 10 ms. The objective is to locally generate
10 ms of C/A code and divide it into 200 250-point sections. The circular corre-
lation of each section is illustrated in Figure 12.5. In this figure only the first two
sections are shown. One section of local C/A code will circular correlated with
two consecutive sections of input to guarantee that the portion of the C/A code is
contained in the input. The 250-point C/A code must be padded with 250 zeros
to match the length of the input signal. In this figure the shaded area represents
the portion of C/A code in the input signal. The circular correlation on the two
sets of 500 points of data can be performed the same as described in Sections 7.8
and 7.9. The details of the operation are as follows: First, FFTs are performed
on both the input and the local C/A code to change them into frequency domain
results. Since the down-converted input signal is complex, the spectrum will be
like the one shown in Figure 7.5, where most of the information is in the first
half of the spectrum. After the FFT the first 250 points are retained, since this is
where the information in the input signal is concentrated. Next, multiply the input
frequency domain data with the complex conjugate of the C/A code frequency
domain data and take the inverse FFT of the result to generate the desired output.
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