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In this paper, we propose a novel criterion for the detection of weak m-ary signals. In the sense of minimizing the error probability, the proposed criterion is optimal when the signal strength approaches zero. Based on the proposed criterion, a detection scheme for ultrawideband multiple access systems is proposed and analyzed in the presence of impulsive interference. Numerical results show that the proposed detector requires less complexity than, and possesses almost the same performance as, the maximum likelihood detector. In impulsive interference, the proposed detector also offers significant performance improvement over the detector optimized for a Gaussian environment.