The Poisson clumping heuristic and outage duration calculations in wireless systems

An outage has been defined by Mandayam, Chen, and Holtzmann (see Journal of Wireless Personal Communications, 1998) as the signal to interference ratio (SIR) going below a threshold and staying there longer than a certain minimum duration. That paper also contains asymptotic calculations of average durations of such outages for the case of log-normal fading, based on the theory of level crossings, for the case when the signal is assumed to be a stationary stochastic process with smooth sample paths, i.e., its autocorrelation function is assumed to have a second derivative at the origin. In this work, we consider the popular autocorrelation function proposed by Gudmundson (1991) for lognormal shadow fading, for which the smoothness assumption above does not hold. Under some general assumptions, we show that the Poisson clumping heuristic (PCH) can be applied to provide approximations to the distribution of the outage time for both kinds of autocorrelation functions, thereby enabling us to obtain more general results than before.