The Distribution of Sums of Path Gains in the IEEE 802.15.3a UWB Channel Model

When multipath arrival times and gains are specified by the IEEE 802.15.3a ultra-wideband (UWB) channel model, formulas are derived for the characteristic function of the sum of gains arriving in a given time window. These formulas are first used to determine structural properties of the corresponding distributions and densities. The formulas are then used to compute the distribution and density functions by numerically inverting the characteristic function. For small time windows, the densities of the path-gain sums are bimodal and therefore highly non-Gaussian