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.