The generalized normal-Laplace (GNL) distribution is employed to reflect the heavy-tailed and impulsive nature of the multiple access interference (MAI) plus AWGN noise in ultra-wideband (UWB) systems. To accurately represent the impulsive feature of the MAI-plus-noise while keeping longer tails, the kurtosis matching (KM) method combined with the method of moments estimation (MME) is proposed for the parameter estimation for time-hopping UWB multiple access communications in AWGN channels. The GNL based UWB receiver using the KM approach outperforms the conventional matched filter receiver, the soft-limiting receiver, the Gaussian-Laplace mixture receiver, and the MME-based GNL receiver in high SNR ranges.