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An iterative blind self-synchronizing MMSE receiver with a J-element antenna array for asynchronous DS-CDMA signals is developed in this paper. The primary requirement is knowledge of the desired user's signature sequence. A computationally efficient IIR-filter version of the proposed receiver is developed that utilizes a correlation-subtraction architecture based on the multistage reduced-rank Wiener filter introduced by Goldstein and Reed. This technique eliminates the tasks of an explicit estimation of the covariance matrix and its inversion. Moreover, this multistage scheme achieves a rapid adaptive convergence and improves the tracking ability at a relatively small amount of observed data. These features contribute significantly to the reduction of the computational cost and make possible practical realization.