In this paper, we develop a statistical characterization of the multipath interference in an Impulse Radio (IR)-UWB system, considering the standardized IEEE 802.15.4a channel model. In such systems, the chip length has to be carefully tuned as all the propagation paths located beyond this limit can cause interframe/intersymbol interferences (IFI/ISI). Our approach aims at computing the probability density function (PDF) of the power of all multipath components with delays larger than the chip time, so as to prevent such interferences. Exact analytical expressions are derived first for the probability that the chip length falls into a particular cluster of the multipath propagation model and for the statistics of the number of paths spread over several contiguous clusters. A power delay profile (PDP) approximation is then used to evaluate the total interference power as the problem appears to be mathematically intractable. Using the proposed closed-form expressions, and assuming minimal prior information on the channel state, a rapid update of the chip time value is enabled so as to control the signal to interference plus noise ratio.