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We present a novel nonparametric multiuser detector for non-Gaussian channels that is based on the signed-rank norm for linear regression. Analytical and simulation results show that the proposed detector offers similar or better performance as compared to the minimax robust detector, but without requiring any a priori information on the noise. The complexity of this detector is lower than that of the pseudo-norm nonparametric detector stated previously by the authors. This is due to the fact that in contrast to the latter, it is not necessary to compute the intercept parameter for the signed-rank detector proposed in this correspondence. We analyze the behavior of the blind version of this detector and show that it outperforms the blind minimax detector. We also show that this detector has a bounded influence function and hence it is robust.