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We consider signal reception in a multicarrier code division multiple access (MC-CDMA) system with an antenna array in time-varying frequency-selective fading channels. The use of subspace-based detectors with spatial diversity is proposed to recover the transmitted user symbols. The channel parameters are adaptively estimated using a blind subspace-based technique which requires only the knowledge of the user spreading code and the number of paths of the multipath channel. The signal subspace is tracked adaptively using the low cost NOOja (normalized orthogonal Oja) algorithm (Attallah, S. and Abed-Meraim, K., IEEE Sig. Processing Lett., vol.8, no.7, p.203-6, 2000). Simulation results show that the use of an antenna array considerably improves the performance of adaptive blind subspace-based detectors.