Acquisition of Weak Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 237

10.9 OUTPUT SAMPLING RATE

The concept of output sampling rate will be discussed here. The overall Doppler
frequency is 10 kHz (from − 5 to 5 kHz) caused by the satellite motion, as
discussed in Section 3.6. This is the bandwidth the acquisition must search. In
order to cover this bandwidth, the sampling speed must be 20 kHz for real input
and 10 kHz for complex input. However, the input signal is sampled at 5 MHz
to accommodate the 2.046 MHz input bandwidth. If the C/A code is stripped off
from the input signal, the input becomes a cw signal with a frequency range of
10 kHz caused by the Doppler effect.
The input signal can be down converted into baseband and stripping the C/A
code by the following operation:

s b (t) = s(t)C(t) exp (j 2 πf 0 t) ( 10 . 15 )

while s b (t) , s(t) ,and C(t) are the baseband, the input and the C/A code signals,
respectively, and f 0 = 1 . 25 MHz is the center frequency of the input signal after
down conversion, as discussed in Section 7.1. From this equation one can see that
the baseband signal is a complex quantity because of the operator exp( j 2 πf 0 t ).
The s b (t) has two output frequencies: the sum and difference between the input
frequency and f 0 . The sum frequency can be referred to as the high-output
frequency. The difference frequency is often called the baseband frequency with
a bandwidth of 10 kHz. For a complex signal with 10 kHz bandwidth, one can
sample at 10 kHz.
In order to differentiate the two sampling frequencies, the 5 MHz sampling
is referred to as the input sampling rate, and the 10 kHz sampling as the output
sampling rate. There can be different input and output sampling rates. To convert
from the input to the output sampling rate, one can sum many input points into
one output point. For example, to change from 5 MHz to 10 kHz, 500 input data
points can be summed into one output point because 5 × 10 6 / 10 × 10 3 = 500.

The summation process is equivalent to a low-pass filter, which can filter out the
high-output frequency in s b (t) .

10.10 COHERENT INTEGRATION FOR PERIODIC SIGNAL

This acquisition method only applies to periodic signal; therefore it applies only
to C/A code, not to the P code signal. A more general acquisition that can
process both the C/A and P code signals will be discussed in Section 12.4. Since
the acquisition presented in this section is simpler than the general acquisition
method, it is actually used in finding weak signals.
Only the coherent integration will be discussed in this section. The noncoherent
integration operation will be discussed in the next two sections. The coherent
method is similar to the modified circular correlation in Section 7.9. It can be
considered an extension of the modified circular correlation acquisition. Ten ms