Approximation for a Sum of On-Off Log-Normal Processes With Wireless Applications

In this paper, a log-normal approximation is proposed for the sum of log-normal processes weighted by binary processes. The analytical approach moves from the method earlier proposed by Wilkinson for approximating first-order statistics of the sum of log-normal components, and extends to incorporate second-order statistics and the presence of both time-correlated random binary weights and cross-correlated log-normal components in moments´ matching. Since the sum of weighted log-normal processes models the signal-to-interference-plus-noise ratio of wireless systems, the method can be applied to evaluate in an effective and accurate way the outage occurrence rate and outage duration for different wireless systems of practical interest. In a frequency-reuse-based cellular system, the method is applied to various propagation scenarios, characterized by different shadowing correlation decay distances and correlations among shadowing components. A further case of relevant interest is related to power-controlled wideband wireless systems, where the random weights are binary random variables denoting the activity status of each interfering source. Finally, simulation results are used to confirm the validity of the analysis for the considered cases of practical interest.