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In this paper, we examine the uplink of a cooperative CDMA network, where users cooperate by relaying each other's messages to the base station. When spreading waveforms are not orthogonal, multiple access interference (MAI) exists at the relays and the destination, causing cooperative diversity gains to diminish. To address this issue, we adopt the multiuser detection (MUD) technique to mitigate MAI in achieving the full advantages of cooperation. Specifically, the relay-assisted decorrelating multiuser detector (RAD-MUD) is proposed to separate interfering signals at the destination with the help of preceding at the relays along with pre-whitening at the destination. Unlike the conventional zero-forcing (ZF) precoder or the decorrelating MUD, the proposed RAD-MUD experiences neither power expansion at the relays nor noise amplification at the destination. Three cooperative transmission strategies are considered on top of RAD-MUD; namely, transmit beamforming, selective relaying and distributed space-time coding. Since the reliability of each source-relay and/or relay-destination links are different, relay transmissions are weighted accordingly in our schemes to further combat MAI. The advantages of RAD-MUD over ZF precoding and other existing cooperative MUD schemes are shown through computer simulations.