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We present a blind array beamforming method for the detection of aperiodic CDMA signals in the presence of an unknown carrier drift. This method employs a differential array beamforming algorithm (DABA), which utilizes the known spreading code of the desired user to estimate the signal subspace under carrier drift. Successful beamforming enables better carrier drift estimation before detecting user data symbols. Simulations are performed in order to compare this method with an existing subspace technique, as well as two baseline (Weiner filter and single element matched filter) detectors.