Acquisition - A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach - page 81

TABLE 6.1. Execution time for each of the three implemented acquisition algorithms

Algorithm Execution Repetitions Complexity

time

Serial search 87 41,943 Low

Parallel frequency space search 10 1023 Medium

Parallel code phase search 1 41 High

As mentioned earlier, the navigation data are transmitted with a rate of 50 bps.
This results in possible data bit transitions every 20 ms. If, for instance, 10 ms of
data is used for the acquisition algorithm, it might include a bit transition. In fact,
there is almost a 50% possibility that it does include a bit transition. (Not exactly
50% because two consecutive data bits might have identical values.) However, if
acquisition is performed on two consecutive sequences, each with the length of
10 ms, at least one of the sequences will not include a data transition.
The second issue to consider when selecting the data size used for acquisition
is the probability of making a successful acquisition. This issue can be discussed
from the idea that the probability of detecting the correct parameters for a certain
satellite increases with the amount of analyzed data.
The third issue is the computational demands as a function of the length of
data to be analyzed. This is actually the counterpart to the previous issue, as the
computations get slower when the sequence gets longer.
The choice of data size used for acquisition has to be a compromise based
on the three issues just described. If the issue with data transitions have to be
considered it might be necessary to run the acquisition algorithm twice for each
acquisition. To ensure good probability of successful acquisition, the data length
cannot be too short. However, it cannot be too long because this will cause the
computations to be too heavy and time-consuming.
A compromise that will be used involves a data length of 1 ms for the acquisi-
tion algorithms. One ms corresponds exactly to the length of one complete C/A
code, so it also simplifies the algorithm, making it unnecessary to duplicate the
code. The data length can hardly be shorter, because this would involve correlation
with an incomplete code. It could be longer, but as mentioned this would decrease
the computational performance of the algorithm. To ensure that satellites will be
acquired even though a data bit transition occurs in the analyzed data sequence,
the algorithm can be run a second time if the first acquisition is unsuccessful.

6.6 Execution Time

As mentioned in the theory behind the acquisition methods, the theoretical per-
formance regarding the computational demands are different between the three
methods. So the execution time for each of the three implemented methods will