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We establish a statistical model for the ultra-wide bandwidth (UWB) indoor channel based on an extensive measurement campaign in a typical modern office building with 2-ns delay resolution. The approach is based on the investigation of the statistical properties of the multipath profiles measured in different rooms over a finely spaced measurement grid. The analysis leads to the formulation of a stochastic tapped-delay-line (STDL) model of the UWB indoor channel. The averaged power delay profile can be well-modeled by a single exponential decay with a statistically distributed decay constant. The small-scale statistics of path energy gains follow Gamma distributions whose parameters m are truncated Gaussian variables with mean values and standard deviations decreasing with delay. The total received energy experiences a lognormal shadowing around the mean energy given by the path-loss power law. We also find that the correlation between multipath components is negligible. Finally, we propose an implementation of the STDL model and give a comparison between the experimental data and the simulation results.