For direct-sequence code-division multiple-access (DS/CDMA) systems, the multiuser and multipath interferences are always present. When the demodulation is coherent, a coherent carrier reference must be generated prior to demodulation. The generation of coherent reference at low signal-to-interference-and-noise ratio (SINR) is difficult. In the downlink CDMA communications, numbers of active Users transmit information simultaneously by different signature waveform. However. the multipath channel and multiple-access interference (MAI) limit the system capacity. Adaptive single-user receivers do not require knowledge of MAI parameters and need fewer computations. In this paper. we propose adaptive receivers with decision-feedback differential detection (DF-DD) and compare variations of the receiver structure proposed in Schrober's paper for noncoherent channels. In the absence of knowledge of the carrier phase, we derive the minimum mean square error (MMSE) of the proposed receivers to show that the performances of the proposed receivers with M-ary differential phase-shift keying (MDPSK) signals approach that of the coherent receiver with MPSK signal. Some simulation examples are given to demonstrate the effectiveness and compare the performances of the proposed adaptive receivers. Copyright (C) 2008 John Wiley & Sons, Ltd