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A robust receiver is proposed for time-hopping pulse-position-modulation impulse radio systems transmitting over frequency-selective ultra-wideband channels, which aims to remove large-amplitude outliers that occur due to impulsive noise. The proposed system contains a rake structure for collecting the signal energy, which is dispersed over a large number of paths as a result of the wide channel bandwidth. Before the paths are merged via maximal ratio combining, they are passed through nonlinearities to trim the outlier noise components. The robust receiver so designed is shown to outperform the conventional linear rake receiver that consists of only matched filters at its fingers.