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In this paper, the problem of subspace-based blind adaptive multiuser detection in multirate direct-sequence code-division multiple-access (DS-CDMA) systems adopting short (periodic) spreading codes is considered. The solution that we propose is based on the well-known formulation of the linear minimum mean-squared error and decorrelating detectors in terms of signal subspace parameters. Since in a multirate scenario the correlation properties of the observable and, hence, the signal subspace parameters are periodically time-varying, classical subspace tracking algorithms, which assume that the subspace to be tracked is time-invariant or slowly time-varying, are shown to be not useful in this situation. A new recursive cyclic subspace tracking algorithm is thus developed. This procedure, which is based on a generalization of the PASTd algorithm, is able to capture the periodical variations of the signal subspace, and thus enables subspace-based blind adaptive multiuser detection in multirate CDMA systems. The proposed algorithm has a smaller computational complexity than the recently developed cyclic recursive-least-squares procedure, and, as numerical results confirm, is capable of providing very satisfactory performance.