In this paper, we propose a novel detection criterion for weak M-ary signal detection. In the sense of minimizing the error probability, the proposed novel detection criterion is optimum when the signal strength approaches zero. Based on the proposed novel detection criterion, a new detector for ultra wideband multiple access systems is proposed in the presence of impulsive interference modeled with the bivariate isotropic symmetric α-stable distribution. Numerical results show that the proposed detector possesses less complexity than and about equal performance to the detector optimized for the Cauchy distribution. In impulsive interference, the new detector also offers substantial performance improvement over the detector optimized for the Gaussian distribution.