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In this paper, the results of ultra wide band (UWB) measurements carried out in indoor environments are presented and a statistical propagation model for the UWB channel covering the frequency band from 3.1 to 10.6 GHz is proposed. The measurements have been performed in the time domain by exciting the channel with very short pulses of 50 ps width. Both line-of-sight (LOS) and non-line-of-sight (NLOS) propagation with a maximum distance of 10 m are considered. Inspection of measured data after processing shows that the multipath components of the UWB channel tend to arrive in clusters. Therefore, the Saleh-Valenzeula (S-V) model has been adopted as starting point for our modelling analysis. Important channel parameter statistics of the model are extracted from the measured data. The obtained results show some discrepancies with respect to the IEEE channel model. The results presented here illustrate that the conventional single Poisson process is not sufficient to model the cluster and ray arrival times. Therefore, a Gamma distribution is proposed to model the cluster inter-arrival times and a mixture of two Poisson processes to model the ray intra-arrival times. It is found that the amplitude fading statistics can be modelled by the log-normal distribution with a standard deviation decreasing linearly with the excess delay. Other parameters like cluster and ray power decay constants are determined to complete the statistical UWB channel model.