Probability and Distribution in Time of Pulse Overlap in Periodic Settings

Periodic pulse trains can represent the emissions of a pulsed source or the \look" pattern of a scanning receiver. The distribution in time of pulse overlaps is considered for two strictly periodic pulse trains. The probability of at least one pulse overlap within a given time is found for a periodic pulse train with a staggered or jittered pulse train. These questions are important in understanding when a receiver will fail to correctly record data. TABLE OF NOTATION Symbol Meaning PRI pulse repetition interval TOA time of arrival PoI probability of intercept T i PRI of train i i pulse duration of train i R PRI ratio combined pulse duration S number of pulses from one train n c number of clusters n 0 number of pulses before cluster merger advancement of pulses in a cluster q max number of pulses at any point in a cluster