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In this contribution we propose and study a multicarrier direct-sequence code-division multiple-access (MC DS-CDMA) scheme, which employs both time (T)-domain and frequency (F)-domain spreading. We investigate the achievable detection performance in the context of synchronous TF-domain spread MC DS-CDMA, when communicating over an additive white Gaussian noise (AWGN) channel. The performance of three different detection schemes is investigated, which include the single-user correlation based detector, the joint TF-domain MMSE multiuser detector (MUD) and the separate TF-domain MMSE/decorrelating MUD. Our simulation results show that the separate TF-domain MMSE/decorrelating MUD scheme is capable of achieving a bit error rate (BER) performance that is similar to that of the significantly more complex joint TF-domain MMSE MUD schemes.