High Sensitivity Techniques for GNSS Signal Acquisition - Global Navigation Satellite Systems: Signal,Theory and Applications - page 9

As described, once P fa and P d are known, the others can be easily computed. These two
probabilities are also used to plot the Receiver Operational Characteristic (ROC) curve (see
Fig. 3(b)) depicting the behaviors of the P fa versus P d for different values of V . This curve is
useful for performance comparison among different acquisition strategies.

2.3.2 Peak-to-floor ratios

Theoretical assessment of acquisition performance is not always possible, since it requires
also the knowledge of the pdf of the decision variables. For such a reason Monte-Carlo
simulation are often employed. In such a case, in order to have suitable confidence in the
results, each simulated value of the ROC curve (as in in Fig. 3(b)) has to be the result of
the average of million of simulated cases. Therefore, if the sensitivity of a single acquisition
scheme in different conditions has to be assessed, it is also useful to consider easy-to-compute
parameters, named peak-to-floor ratios, ( α max , α mean ). They are defined as:

S peak S peak

2 2

E

2

α max =

2 ;

α mean = (14)

max S floor S floor

where S peak is the maximum of the CAF magnitude and S floor is the floor of the
CAF magnitude (i.e outside the main correlation peak which is 2 chips wide). These
metrics highlight the overall trend of post-correlation Signal-to-Noise Ratio (SNR), avoiding
time-consuming calculations or simulations. Anyhow, it is important to point out that the
comparison of different acquisition schemes based on the peak-to-floor ratios may be not fair
if their decision variables show different statistical properties (Ta et al., 2008).

2.3.3 Mean acquisition time

Let us consider a search-space with N c columns and N f rows as in Fig. 2(a), and denote A
as a successful detection of a serial acquisition engine (Fig. 1) after some miss-detections and
false-alarms. The mean duration from the beginning of the process to the instant when A
happens is named mean acquisition time, and can be written as (Park et al., 2002)

2 P d

2 P d +

−

T d
P d

T A =( N c N f − 1

)(

T d + T fa P fa ) (15)

with T d and T fa being the dwell time and the penalty time respectively.

Equation (15) shows that T A depends on the values of :
- The false-alarm ( P fa ) and detection ( P d ) probabilities at a single cell.

×

- The search space size N c N f

- The penalty time T fa and the dwell time T d . In fact, T fa is represented through T d and the

penalty coefficient k p , T fa

=

k p T d . Obviously, T d depends on each strategy.

Therefore, T A can be seen as the performance parameter taking into account both the
computational complexity and the sensitivity of a strategy.