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An exact mathematical model which explains the important characteristics of the Probability Density Function (PDF) of the Multiple Access Interference (MAI) in Time-Hopping UWB (TH-UWB) systems is discussed. The proposed model accurately foresees impulses, singularities, and heavy tails found in the distribution of the MAI. Also, it discloses precisely why a Gaussian approximation for the MAI in TH-UWB systems is highly inaccurate even in the presence of a large number of interferers. Then, using the Maximum A Posteriori (MAP) receiver rule and based on the obtained model for the PDF of the MAI, the optimal achievable BER performance of binary TH-UWB receivers is numerically determined.
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