Acquisition of GPS C/A Code Signals - Fundamentals of Global Positioning System Receivers: A Software Approach - page 133

7.5 C/A CODE MULTIPLICATION AND FAST FOURIER
TRANSFORM (FFT)
The basic idea of acquisition is to despread the input signal and find the carrier
frequency. If the C/A code with the correct phase is multiplied on the input
signal, the input signal will become a cw signal as shown in Figure 7.1. The top
plot is the input signal, which is a radio frequency (RF) signal phase coded by a
C/A code. It should be noted that the RF and the C/A code are arbitrarily chosen
for illustration and they do not represent a signal transmitted by a satellite. The
second plot is the C/A code, which has values of ± 1. The bottom plot is a cw
signal representing the multiplication result of the input signal and the C/A code,
and the corresponding spectrum is no longer spread, but becomes a cw signal.
This process is sometimes referred to as stripping the C/A code from the input.
Once the signal becomes a cw signal, the frequency can be found from the FFT
operation. If the input data length is 1 ms long, the FFT will have a frequency
resolution of 1 kHz. A certain threshold can be set to determine whether a fre-
quency component is strong enough. The highest-frequency component crossing
the threshold is the desired frequency. If the signal is digitized at 5 MHz, 1 ms
of data contain 5,000 data points. A 5,000-point FFT generates 5,000 frequency
components. However, only the first 2,500 of the 5,000 frequency components
contain useful information. The last 2,500 frequency components are the com-
plex conjugate of the first 2,500 points. The frequency resolution is 1 kHz; thus,
the total frequency range covered by the FFT is 2.5 MHz, which is half of the
sampling frequency. However, the frequency range of interest is only 20 kHz,
FIGURE 7.1 C/A coded input signal multiplied by C/A code.