| The problem of determining the distribution and probability density function of a sum of lognormal random variables occurs in the design and study of ultra-wide bandwidth wireless systems. Many approximations have been proposed assuming that the sum distribution can be represented by another lognormal random variable. None of these approximations are valid for a wide range of parameters. A new method to calculate an approximation to the lognormal sum distribution, based on curve fitting is introduced in this thesis.;Expressions for the performance of a pulse amplitude and position modulation (PAPM) ultra-wideband (UWB) system in lognormal fading channels with maximal ratio combining (MRC) have been derived using Wilkinson's approximation. Simple expressions for the error rate performance of a diversity PAPM UWB system based on using the new approximation are derived, calculated, and compared to results obtained by using Wilkinson's approximation for the performance of MRC and equal gain combining. |
