Acquisition - A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach - page 73

The serial search algorithm performs two different sweeps: a frequency sweep
over all possible carrier frequencies of IF 10 kHz in steps of 500 Hz and a code

phase sweep over all 1023 different code phases. All in all, this sums up to a total
of

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2 10

000
500

,

1023 + 1 = 1023 · 41 = 41 , 943 combinations . (6.1)

code phases

frequencies

Obviously, this is a very large number of combinations. This exhausting search
routine also tends to be the main weakness of the serial search acquisition.
The implementation of the serial search acquisition method is very straight-
forward. The algorithm can be implemented directly based on the block diagram
of the method as shown in Figure 6.1.

6.2.1 PRN Sequence Generation
Figure 6.1 shows that the first task in the serial search acquisition method is to
multiply the incoming signal with the locally generated PRN sequence. This of
course involves the generation of this PRN sequence. Instead of generating PRN
sequences every time the algorithm is executed, all possible PRN sequences are
generated offline. The 32 different PRN sequences are generated by the PRN gen-
erator implemented according to Figure 2.5.
The PRN code generator is implemented using the binary values 0 and 1. How-
ever, in the signal processing algorithms it is more convenient to represent the
codes with a polar non-return-to-zero representation.
With 32 generated PRN sequences, all possible sequences originating from
GPS satellites are created. However, as mentioned in the theory of serial search
acquisition, the method involves multiplication with all possible shifted versions
of the PRN codes. That is, besides saving the 32 possible PRN codes all possible
shifted versions should also be saved. This sums up to a total of 32,736 different
PRN codes. To make the multiplication between one of the generated PRN codes
and the incoming signal possible, the code has to be sampled with 38.192 MHz,
like the received signal. This sampling converts the length of a PRN sequence
from 1023 to 38,192.

6.2.2 Carrier Generation
The second step is multiplication with a locally generated carrier wave. The car-
rier generator must generate two carrier signals with a phase difference of 90 ◦ ,
corresponding to a cosine and a sine wave. The carrier must have a frequency cor-
responding to the IF

the frequency step according to the examined frequency
area. It must be sampled with the sampling frequency of 38.192 MHz and have
a length of 1 ms. A complex signal is generated using the natural exponential
function e j 2 π f .

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