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The probabilistic data association (PDA) method for multiuser detection in synchronous code-division multiple-access (CDMA) communication channels is extended to asynchronous CDMA, where a Kalman filter or smoother is employed to track the correlated noise arising from the outputs of a decorrelator. The estimates from the tracker, coupled with an iterative PDA, result in impressively low bit error rates. Computer simulations show that the new scheme significantly outperforms the best decision feedback detector. The algorithm has O(K/sup 3/) complexity per time frame, where K is the number of users.