Bounds on the distribution of a sum of independent lognormal random variables

The distribution function of a sum of lognormal random variables (RVs) appears in several communication problems. Approximations are usually used for such distribution as no closed form nor bounds exist, Bounds can be very useful in assessing the performance of any given system. In this letter, we derive upper and lower bounds on the distribution function of a sum of independent lognormal RVs, These bounds are given in a closed form and can be used in studying the performance of cellular radio and broadcasting systems.