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In this letter we propose and investigate a cooperative downlink transmission scheme for direct-sequence code-division multiple-access (DS-CDMA) systems, in order to achieve relay diversity. Transmitter zero-forcing (TZF)-based preprocessing is employed at the base-station (BS) of our proposed scheme for suppressing the downlink multiuser interference (MUI). At the mobile terminals (MTs) the signals are combined based on the maximal ratio combining (MRC) principles. As a benefit of TZF, the BS decontaminates the relayed signals from MUI without requiring any information from the relays. Furthermore, only low-complexity signal processing is necessary at the relays for forwarding information to the destination MTs (DMTs), while achieving the relay diversity by only exploiting the knowledge of the DMTs' spreading sequences.