Detection of the existence of a desired user is considered in this paper. We assume that the signal to noise ratio is high enough to ignore the effects of noise compared with those of the interference by other users. The inter-user interference and user signals are modeled by the Nakagami model. We observation model for this situation is proposed, the locally optimum test statistic is derived under the model, and the asymptotic performance of the test statistic is compared with that of the envelope detector. We show that the locally optimum detector has performance better than the conventional envelope detector. (C) 1997 Published by Elsevier Science B.V.