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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 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 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+Noise) Ratio (SINR) 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.
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