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The problem of blind adaptive suppression of both multiple-access interference (MAI) and intersymbol interference (ISI) in a high-rate dispersive CDMA network is considered. The dispersive CDMA channel is first cast within a multiple-input multiple-output (MIMO) model. It is then shown that the linear MMSE receiver can be expressed in terms of the signal subspace components of an augmented received signal, the desired user's signature waveform and its channel response. The signal subspace components can be adaptively estimated using subspace tracking techniques. Moreover, it is shown that the desired user's dispersive channel can also be estimated using a constrained adaptive filtering method. The proposed adaptive receiver employs a subspace tracker and a channel estimator, and forms the linear MMSE detector in closed-form based on the estimated subspace components and the channel response.