Global Positioning System Reference
In-Depth Information
Since the input has been down converted to base band, the peak output is usually
very close to the direct current (dc) component. Figure 11.9a shows the output
of the 1000 frequency components. Figure 11.9b shows the 100 components
near dc, which is obtained by plotting points from 951 to 1000 and 1 to 50 of
Figure 11.9a. This operation shifts the outputs from near zero in Figure 11.9a to
near the center in Figure 11.9b.
In general, the input frequency does not fall on a frequency bin. Under this
condition, the frequency is spread into several frequency bins, as shown in
Figure 11.9b. One can improve the frequency reading from the two adjacent
frequency bins with the highest outputs as
(
1
)
A(
1
)
A(
0
)
f
del
=
(
11
.
5
)
+
A(
1
)
where
f
del
is a shift frequency with resolution less than 1 Hz from the peak
output,
A
(0) is the highest amplitude in Figure 11.9b, and
A
(1) is the higher one
of the two adjacent frequency bins of
A
(0). By this equation, the frequency can
be adjusted to less than 1 Hz. The direction of the true frequency lies toward the
higher neighboring bin. With this process, a very accurate carrier frequency can
be obtained.
11.8 CALCULATING SIGNAL-TO-NOISE RATIO (S/N)
This operation is not essential to the tracking program; however, it is nice to
have a
S
/
N
estimation every second. Once the frequency bins are calculated, the
power of the signal can be calculated. If the noise power and the signal power are
obtained, the
S
/
N
can be calculated. Theoretically the noise of the signal can be
obtained from either the frequency or the time domain. From Figure 11.9a one
can take a portion of the spectrum that does not include the signal to represent
the noise power. The noise measured this way, however, varies from second to
second by about 1 dB based on real data. This may be caused by the nonuniform
distribution. A closer examination of the noise in Figure 11.9a reveals that the
noise is slightly higher around bins 200 and 900. The noise of additional real
data will be discussed in Section 10.15.
The noise power obtained from 1 ms of data in time domain every second
varies much less than 1 dB. Therefore the noise power is measured in the time
domain with 1 ms of data. In this operation the signal is included in the noise
calculation. Because the nominal signal is about
−
19 dB under the noise in
a 2 MHz bandwidth system, the error caused by including the signal can be
neglected. The total noise power in one second can be obtained by multiplying
the measured noise by 1000 because there are 1000 frequency bins. The noise
power per second
P
n
is
P
n
=
var
(x
i
)
×
1000
(
11
.
6
)
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