The multiple-user interference (MUI) in time-hopped impulse-radio ultrawide bandwidth (UWB) systems is impulse-like and poorly approximated by a Gaussian distribution. Therefore, conventional matched filter receiver designs, which are optimal for Gaussian noise, are not fully efficient for UWB applications. Several alternative distributions for approximating the MUI process and the MUI-plus-noise process in UWB systems are motivated and compared. These distributions have in common that they are more impulsive than the Gaussian approximation, with a greater area in the tails of the probability density function (pdf) compared to a Gaussian pdf. The improved MUI and MUI-plus-noise models are utilized to derive new receiver designs for UWB applications, which are shown to be superior to the conventional matched filter receiver. Multipath propagation is abundant in UWB channels and is exploited by a Rake receiver. A Rake receiver uses multiple fingers to comb the multipath rays with a conventional matched filter implemented in each finger. Rake structures utilizing the new receiver designs that are suitable for reception of UWB signals in multipath fading channels are provided. An optimal performance benchmark, based on an accurate theoretical model for the interference that fully explains the features of the MUI pdf, is also presented. Analysis and simulation results are shown for the novel receivers, which demonstrate that the new designs have superior performance compared to the conventional linear receiver when MUI is significant. Several adaptive receivers are shown to always match or exceed the performance of the conventional linear receiver in all MUI-plus-noise environments. Parameter estimation for the new receivers also is discussed.