Acquisition - A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach - page 76

Incoming signal

Local PRN code

Result of
multiplication

FIGURE 6.5. PRN code demodulation. At the top the PRN code is modulated onto the
carrier wave. In the middle is a perfectly aligned PRN sequence. At the bottom we recover
the continuous wave after multiplying the incoming signal with the perfectly aligned PRN
sequence.

peak will be located at the frequency index corresponding to the frequency of the
continuous-wave signal and thereby the frequency of the carrier wave signal.
The accuracy of the determined frequency depends on the length of the DFT.
The length corresponds to the number of samples in the analyzed data. If 1 ms of
data is analyzed, the number of samples can be found as 1 / 1000 of the sampling

frequency. That is, if the sampling frequency is f s = 10 MHz, the number of

samples is N 000.

With a DFT length of 10,000, the first N

= 10 ,

/ 2 output samples represent the fre-

f s
2

quencies from 0 to Hz. That is, the frequency resolution of the output is

f s / 2 f s

N .

f =

2 =

(6.2)

N /

With a sampling frequency of f s = 10 MHz the resulting frequency resolution is

10 MHz
10

f =

000 =

1kHz . (6.3)

,

In this case, the accuracy of the estimated carrier frequency is 1 kHz compared
to the accuracy of 500 Hz in serial search acquisition.
Figure 6.6 shows the output as two power spectral density (PSD) plots. The
PSD algorithm is using FFT for the acquisition. Figure 6.6a is the output of the
Fourier transform with a perfectly aligned code phase. This can be noticed from
the peak in the plot. Figure 6.6b shows the PSD plot for a not aligned code phase.
Note the absence of a peak in the plot.
Where the serial search acquisition method steps through possible code phases
and carrier frequencies, the parallel frequency space search acquisition only steps
through the 1023 different code phases. This comes with the cost of a frequency
domain transformation with each code phase. Depending on the implementation
of the frequency domain transformation, it should be possible to make a faster
implementation of this method compared to the serial search acquisition method.