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We consider an ultra wide band impulse radio multiple access scheme based on time-hopping code under a realistic multipath channel model. As a novelty, we provide a closed-form expression for the variance of the multiuser interference at the output of the rake receiver of the user of interest. That enables us to characterize the optimal time-hopping codes minimizing the multiuser interference variance. Finally we observe through simulations that minimizing the multiuser interference variance translates into better performance by significantly decreasing the error probability.