This paper deals with the problem of blind multiuser detection in multirate direct-sequence code division multiple access (DS-CDMA). Direct-Sequence Spread Spectrum (DS-SS) signals are well-known for their low probability of interception: their statistics are similar to that of a noise; furthermore, they are usually transmitted below the noise level. We tackle here the theoretical performances, in terms of probability of detection and false alarm of the method based on the fluctuations of autocorrelation estimators. Numerical results will illustrate the efficiency of the method.