In this paper, a multiple-access transmission scheme based on random permutations is studied. This scheme provides both a spectrum spreading and a time spreading, combined with a chip interleaving. One considers asynchronous transmissions on frequency-selective and time-varying channels. It is assumed that the channel coeffcients are unknown by the receiver, and that only vague estimates of the minimum and maximum delays are available. In such a context, an LMS algorithm is used to solve the bit detection problem. Theoretical performance results are given. Moreover, this random permutation-based scheme is compared with the DS-CDMA system, for which an equivalent LMS detector is developed in the same context.