A novel analytical method is introduced for exact statistical modeling of multiple access interference (MAI), in time hopping pulse position modulation and pulse amplitude modulation (TH-PPM and TH-PAM) ultra wideband (UWB) systems operating in additive white Gaussian noise (AWGN) channels. Based on this method, exact bit error rates (BER) are expressed in simple formulas. In a similar fashion, the exact BER of direct sequence (DS) UWB is also derived for PAM modulation. The proposed modeling of MAI considers complete asynchronism in user access, and is also suitable for accurately modeling the MAI components contributed by individual paths in channels with Poisson arrivals, based on the time variables. We further extend this method to derive general expressions for the BER performance in log-normal fading multi-path channels. In the course of these derivations, we also introduce a more accurate numerical approach to evaluate the characteristic function (CF) of a lognormal random variable