Interpulse Interval Distribution in the Environment of N Periodic Radars

This paper is concerned with an environment consisting of N periodic radars, each emitting a periodic pulse train. The number of radars and their periodicities are assumed known but the epoch of each pulse train is a random variable with a uniform distribution. The principal result of this paper is the expression for the probability density function of interpulse intervals of the sum of all the N pulse trains. Only absence or presence of a pulse is considered, and the amplitude distribution is not treated; i.e., any pulse emitted by any of the N radars is considered capable of initiating a new interpulse interval. The obtained result is useful in establishing the control function for the interpulse interval generator of a stochastic interference simulator.