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This paper addresses multiuser detection and diversity combining for frequency selective fading code-division multiple access (CDMA) channels. It is well known that the decorrelating detector is an effective technique for separating signals of different users in bandwidth-efficient CDMA. For a general asynchronous CDMA channel, the output of the decorrelator for each user can be characterized by an equivalent single-user system with multiuser (MAI)-induced intersymbol interference (ISI). We investigate diversity combining techniques for this equivalent single-user channel using differential phase shift keying (DPSK) detection. This method does not require tracking of rapidly changing fading parameters. To improve the performance of the DPSK combiner, it can be beneficial to weigh the signals associated with different paths. We consider several criteria for choosing these weights. For the synchronous (ISI-free) channel, we show that the bit error rate (BER) of the optimal combiner can be closely approximated by a combination of two decorrelating detectors (with either noise whitening or signal whitening filters). We also discuss this "hybrid" approach for asynchronous channels with MAI-induced ISI. Finally, a minimum mean square error (MMSE) combiner is analyzed and compared to other techniques.