PROBABILISTIC CHARACTERISTICS OF THE SYNC DETECTION ALGORITHM BASED ON THE SELECTION OF AN ADJACENT PAIR OF SEGMENTS WITH THE MAXIMUM TOTAL COUNT
Abstract
An algorithm for detecting sync signals based on the selection of an adjacent pair of segments
with the maximum total count is proposed. This algorithm takes into account the shortcomings
of an alternative algorithm for detecting a sync signal based on comparing the sum of samples
from an adjacent pair of segments with a threshold level, consisting in the need to know the level of background and noise influence, which determines the threshold level and the probability
of erroneous detection of a signal pair of segments. The dependence of the probability of an error
in detecting a sync pulse on the average number of signal photons in a sync pulse is studied for
various values of the number of segments in a time frame. Thus, the probability of erroneous detection
of a sync pulse during a frame decreases significantly as the average number of photons in
a sync pulse increases. For example, by increasing the average number of signal photons in a sync
pulse from 1 to 5, the probability of a sync detection error is reduced by a factor of 37. It should
be noted that the number of pairs of segments has a weak effect on the probability of erroneous
detection, which indicates a weak effect of dark current pulses on the probabilistic characteristics
of the proposed algorithm for detecting sync signals. Analytical expressions are obtained for accurate
and express calculation of probabilistic characteristics of detection, taking into account the
probability of finding a sync pulse at the boundary of two adjacent segments due to the equality of
the duration of the sync pulse and the time segment. The results of calculation using exact expressions
for the probability of detecting a sync pulse showed that when the signal-to-noise ratio is
equal to 10 and higher, the influence of noise pulses on the probability of detecting a sync pulse
can be neglected. It has been noted that the greater the number of recorded events, or, in other
words, the greater the sum of the average numbers of signal photons and dark current pulses, the
greater the detection probability. The calculation of the probability of detecting a sync pulse using
simplified expressions shows a slight deviation from calculations using exact formulas, which does
not exceed 5,3%, and the calculation using approximate expressions gives an underestimated result.
The resulting approximate analytical expressions can be used for express calculation of the
probability of detecting a sync pulse in a pair of segments.
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