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In this paper, the performance of the cooperative multiuser direct-sequence code-division multiple-access (DS-CDMA) system is analyzed in the asymptotic regime where both the spreading codes and the number of users grow unboundedly large with the same ratio. Assuming that each terminal is paired with another user which, in addition to transmitting its own data, estimates and relay the information transmitted from its partner, a simple approximate signal-to-interference-plus-noise ratio (SINR) expression is derived that is independent from the spreading codes and explicitly accounts for the effects of the multiple-access interference (MAI) and the relay noise. The so-obtained SINR expression is then computed based entirely on the available local information and without any knowledge about the interfering users. The results obtained above are then used to optimally design the cooperative system. In particular, it is shown how the amount of cooperation between each collaborating pair can be adjusted to simultaneously achieve a preassigned target SINR for both users. Based on the local information, the globally optimal amount of the relay power is obtained that maximizes the achieved SINR at the access point. It is shown that increasing the relay power does not necessarily result in improving the quality of reception at the access point and, to maximize each user's SINR, its relay power should be carefully adjusted based on the environmental parameters such as the interpartner channel link and the powers of MAI and the relay noise. The connection between the cooperative and the conventional multiuser systems is also studied and simulations are used to demonstrate the validity of the analytical results.