Acquisition - A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach - page 77

−40 −40

−60 −60

−80 −80

−100 −100

−120 −120

0 5 10 15 19.096 0 5 10 15 19.096

Frequency [MHz] Frequency [MHz]

(a) (b)

FIGURE 6.6. PSD plot of the incoming signal multiplied by a locally generated PRN code
sequence. (a) When multiplying with a perfectly aligned PRN code, the output will show
a peak at the carrier frequency. (b) When multiplying with a nonaligned code, the output
will not show any peaks. The IF is 9.548 MHz. The Doppler frequency is the same on IF
and RF, and thus also the difference between the IF and the peak frequency.

Like the serial search acquisition method, the implementation of the parallel
frequency space search method is straightforward. The algorithm can be imple-
mented directly based on the block diagram of the method shown in Figure 6.4.
The first part of this method is identical to the first part of the serial search
method. That is, a locally generated PRN code must be multiplied with the in-
coming signal. After the code multiplication, the signal is transformed into the
frequency domain through Fourier transform. An efficient tool for that is the fast
Fourier transform (FFT). See Oppenheim & Schäfer (1999) for details on the FFT.
After transforming the signal into the frequency domain by means of the FFT
algorithm, it becomes a complex signal. If the locally generated code is well
aligned with the code in the incoming signal, the output from the FFT will have a
peak at the IF plus Doppler offset frequency. To find the possible peak frequency
the absolute value of all components are calculated. Figure 6.7 shows the output
from the parallel frequency space search method.

6.4 Parallel Code Phase Search Acquisition

As seen from Equation (6.1), the amount of search steps in the code phase dimen-
sion is significantly larger than that of the frequency dimension (1023 compared to
41). The previous method parallelized the frequency space search eliminating the
necessity of searching through the 41 possible frequencies. If the acquisition could
be parallelized in the code phase dimension, only 41 steps should be performed
compared to the 1023 in the parallel frequency space search acquisition algorithm.
A recent method in GPS signal acquisition utilizes the before-mentioned ad-
vantage of parallelizing the code phase search. This method is simply referred to
as parallel code phase search acquisition. In the following we describe the theory
behind this method.