Global Positioning System Reference
In-Depth Information
second-half spectrum lines contain very little information. Thus the acquisition
through the circular correlation method can be modified as follows:
1. Perform the FFT on the 1 ms of input data x ( n ) and convert the input into
frequency domain as X ( k )where n = k = 0 to 4,999 for 1 ms of data.
2. Use the first 2,500 X ( k )for k
= 0 to 2,499. Take the complex conjugate
and the outputs become X(k) .
3. Generate 21 local codes l si ( n )where i
1 , 2 ,... 21, using Equation (7.1)
as discussed in the previous section. Each l si ( n ) has 5,000 points.
4. Perform the FFT on l si ( n ) to transform them to the frequency domain as
L si ( k ).
5. Take the first half of L si ( k ), since the second half of L si ( k ) contains very
little information. Multiply L si ( k )and X(k) point by point and call the
result R si ( k )where k
=
= 0 2499.
6. Take the inverse FFT of R si ( k ) to transform the result back into time domain
as r si ( n ) and find the absolute value of the
|
r si (n)
|
. There are a total of
52,500 (21 × 2 , 500) of | r si (n) | .
7. The maximum of |
| is the desired result, if it is also above a prede-
termined threshold. The i th frequency gives the carrier frequency with a
resolution of 1 kHz and the n th location gives the beginning point of C/A
code with a 400 ns time resolution.
8. Since the time resolution of the beginning of the C/A code with this method
is 400 ns, the resolution can be improved to 200 ns by comparing the
amplitudes of n th location with (n
r si (n)
1 ) and (n
+
1 ) locations.
In this approach from steps 5 through 7 only 2,500 point operations are per-
formed instead of the 5,000 points. The sorting process in step 7 is simpler
because only half the outputs are used. Step 8 is very simple. Therefore, this
approach saves operation time. Simulated results show that this method has
slightly lower signal-to-noise ratio, about 1.1 dB less than the regular circular
correction method. This might be caused by the signal loss in the other half of
the frequency domain.
7.10 DELAY AND MULTIPLY APPROACH ( 3-5 )
The main purpose of this method is to eliminate the frequency information in the
input signal. Without the frequency information one need only use the C/A code
to find the initial point of the C/A code. Once the C/A is found, the frequency
can be found from either FFT or DFT. This method is very interesting from a
theoretical point of view; however, the actual application for processing the GPS
signal still needs further study. This method is discussed as follows. First let us
assume that the input signal s ( t ) is complex, thus
C s (t)e j 2 πf t
s(t)
=
( 7 . 13 )
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