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The generalized Gaussian probability density function is shown to better approximate the probability density function of the multiple access interference in ultra-wide bandwidth systems than the Gaussian approximation and the Laplacian density approximation. Two ultra-wide bandwidth receiver structures based on this new approximation using a p-order metric receiver decision statistic are investigated for the detection of time-hopping ultra-wide bandwidth wireless signals in multiple access interference channels. The first receiver outperforms both the conventional matched filter ultra-wide bandwidth receiver and the soft-limiting ultra-wide bandwidth receiver when only multiple access interference is present in UWB channels. The second new receiver with adaptive limiting threshold outperforms the conventional matched filter ultra-wide bandwidth receiver, the soft-limiting ultra-wide bandwidth receiver, and the adaptive threshold soft limiting ultra-wide bandwidth receiver in all multiple access interference-plus-noise environments. In multipath channels, a new Rake receiver based on the p-order metric receiver is proposed for signal detection. Mathematical analysis and numerical results show that this new Rake receiver can achieve larger signal-to-interference-plus-noise ratio than the standard matched filter Rake receiver when multipath components are resolvable in UWB channels.