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We consider multiple users in an asynchronous DS-CDMA system operating in a multipath environment. The received cyclostationary spread signal sampled at the chip rate is converted to a stationary vector signal, leading to a linear multichannel model. Linear receivers for multiple access interference (MAI) suppression are studied with emphasis on computationally simple algorithms. The desired user channel estimate is obtained by a new blind technique using the spreading sequence properties and second-order statistics. A blind MMSE-ZF receiver is subsequently obtained. Equivalence to the anchored MOE receiver is shown. Since the blind receiver relies on the inversion of the signal covariance matrix RYY, a consistent estimate of which requires a large number of data points if a large number of users are concurrently active, a semi-blind alternative for the estimation of the interference cancelling filter is presented. Iterative improvements of this estimate based upon exploitation of the finite-alphabet are investigated. Performances of different interference cancellation schemes are compared in terms of the output signal-to-interference-plus-noise ratio (SINR)