Gaussian mixture (GM) receivers have been recently introduced in the context of ultra wide band (UWB) impulse radio (IR) as a robust alternative to commonly employed techniques. By statistically modeling interference as a GM, as opposed to the ordinary AWGN assumption, such receivers are able to mitigate the effect of multiple user interference (MAI). However, this is achieved at the cost of an increased complexity, commonly thought as an high complexity. In this paper we prove that a suitable reformulation of the GM approach leads to a receiver which is low complexity, while providing the same performance of standard GM. Hence, the GM paradigm is a usable, and welcome, technique for IR applications.