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A more appropriate statistical model for the multiple access interference than the generally used Gaussian approximation is proposed to reflect the heavy-tailed nature of the multiple access interference in ultra-wide bandwidth systems. Novel receiver structures which surpass the performance of the conventional matched filter receiver are studied for ultrawide bandwidth multiple access communications in both AWGN and fading multipath channels. A proposed Rake receiver is advantageous over the conventional Rake receiver when multiuser interference dominates ambient Gaussian noise and originates from a small to moderate number of interferers. Explanation is provided for the inaccuracy of a Gaussian approximation with regard to the multiple access interference, and the heavy-tailed nature of the probability density function of the multiple access interference is also discussed.