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A matching pursuit followed by cancellation (MPC) algorithm is investigated for time-varying multipath channel estimation in asynchronous CDMA. The algorithm has significantly low computational complexity and consists of two steps. In the first step, a basic matching pursuit algorithm that identifies the strongest channel taps, and successively cancels them, is used. The second step of the algorithm uses the already estimated channel taps to remove interference from the received vector in order to identify the channel coefficients more accurately. The performance of the algorithm is characterized in terms of mean squared identification error (MSIE). The convergence behavior of MPC is described. A method to terminate the MP step of the algorithm successfully is proposed and is shown to perform well. Our results show that MPC achieves performance close to the Cramer-Rao lower bound (CRLB).