Minimum duration outage for cellular systems: a level crossing analysis

Traditionally, studying outage for cellular systems has been based on the signal level (or, more precisely, the signal-to-interference ratio (SIR)) falling below a required threshold. In real cellular environments, it is not the instantaneous drop of the signal strength below the threshold that determines outage. It is, in fact, the duration of time below a threshold that determines outage for cellular systems. Moreover, the static analysis of outage precludes the time correlation in the signals which is important in real systems owing to mobility, fading and power control. We analyse “minimum duration” outages for such systems, where outage is defined as an excursion of the SIR below a level for a certain minimum duration. We formulate the outage condition as a level crossing problem and extend asymptotic results from the theory of level crossings to derive analytical results for the probability of outage. This method enables us to include the time correlation of signals in the analysis as well. The validity of the asymptotic results is verified using some exact results as well as simulations. These “minimum duration” outages have implications in redefining user capacity and handoff performance