Approximation for a sum of on-off log-normal processes with wireless applications

This paper proposes a log-normal approximation for the sum of on-off log-normal processes. An analytical approach is developed, that moves from the method early proposed by Wilkinson for approximating first order statistics of a sum of log-normal components, and extends to incorporate second order statistics and the presence of random weights in moments´ matching. As a relevant application, the method is used to calculate in an effective and accurate way the parameters of the signal-to-(noise+interference) ratio (S I N R) in a power-controlled wideband wireless system, where the random weights are binary RVs and denote the activity status of each interfering source. A collection of numerical results is presented, where performance predicted by the analysis is compared to that obtained from simulation.