We develop a novel distributional upper bound on the interference created in an ultra-wideband wireless communication systems under two general assumptions: the first is that there is an unknown number of interferers who are distributed according to a homogeneous Poisson point process randomly in space; and the second is that the frequency bands occupied by the unknown number of interferers is also a random variable in an ultra-wideband setting. Then given these two general assumptions, we derive a distributional upper bound representation of the total interference.