Global Positioning System Reference
In-Depth Information
desired signal. In generating noise, the sampling frequency f s is important. If
the signal is sampling at 5 MHz, the input bandwidth is 2.5 MHz (5/2), which
is determined by the Nyquist sampling theory. Considering the shape of a real
filter with a bandwidth of 2 MHz, an input bandwidth of 2.5 MHz is a reasonable
value. When the input bandwidth is 2 MHz, the thermal noise, as indicated in
Section 10.2, is at about
111 dBm. If the input signal is at
130 dBm, the S / N
is at
19 dB. The amplitude of the signal can be written as
2 n st ( 10 dB/ 20 ) ( 12 . 17 )
where the 2 is for considering the power of the carrier signal and n st is the
standard deviation of the noise. In Matlab simulation, n st
amp
=
=
1 is often used and
the value dB is the desired S / N .
If the signal is sampled at a different frequency, the equivalent bandwidth
will be different from 2 MHz, which will affect the noise floor and the S / N .For
example, if the signal is sampled at 50 MHz instead of 5 MHz, the noise band-
width is about 25 MHz, and the corresponding noise floor is at about
100 dBm.
An input signal at 130 dBm will have a S / N of 30 dB instead of 19 dB.
If the noise is digitized at a higher frequency than 5 MHz, such as 50 MHz,
and an input of 3 MHz bandwidth is desirable in the simulation, the noise should
be filtered out by a 3 MHz filter before the signal is added. After the filter, the
standard deviation of the noise can be obtained and the amplitude of the signal
can be found using Equation (12.17).
The S / N problem does not exist with data collected through a hardware sys-
tem, either from the satellites or from a simulator, because the filter in the receiver
will limit the amount of noise.
12.8 ACQUISITION IMPACT OF FILTER BANDWIDTH
IN FRONT OF ADC
Because the null-to-null bandwidth of the C/A code is 2.046 MHz, it is natural
to assume that the filter bandwidth in front of the ADC will be around 2 MHz.
It is interesting to question whether the filter bandwidth has an impact on the
acquisition result. In this section, digital filters (rather than analog filters) with
different bandwidth are used to evaluate the impact, since digital filters are easy
to simulate.
The approach is to use real data collected from the GPS data collection system,
described in Section 6.8. The output IF signal is sampled at 10 MHz rather than
the 5 MHz, which is used in most examples in this topic. The reason to use
this sampling frequency is to avoid spectrum overlap. The analog filter at the
RF front end of the ADC is about 3 MHz, but it does not have a sharp cutoff
frequency response. Energy, including signals and noise, will extend over the
2.5-MHz frequency range. This energy will fold into the 2.5-MHz bandwidth
and appear at the digitized output. If the sampling frequency is 10 MHz, the
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