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The huge potential of ultra wide band impulse radio (UWB IR) with multiple access was initially evaluated using the standard Gaussian approximation which assumed that multi user interference could be approximated as classical Gaussian noise. Later the standard Gaussian approximation has been proved to be invalid in several cases. Thus the performance of the classical UWB IR correlation receiver dramatically reduces. We show in this paper how the non Gaussianity of the multi user interference can be exploited, turning the non Gaussianity into an advantage, increasing the performance with respect to the Gaussian interference case which was supposed to be too optimistic until now.