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The performance of amplify-and-forward (AF) cooperative code-division multiple-access (CDMA) systems is analyzed over independent nonidentical (i.n.i.) Nakagami-m fading channels. In the underlying AF relaying scheme, each relay applies interference suppression to the received signal to mitigate the effect of multiple-access interference (MAI) where a soft estimate is obtained before signal amplification takes place. The outage probability of the system is analyzed using the cumulative distribution function (cdf) of the total signal-to-noise ratio (SNR) at the base station. In that, we derive a simplified yet tight lower bound for the AF relaying system. We also define an approximation for the probability density function (pdf) of the total SNR, which enables us to derive an asymptotic outage probability of the system. The derived asymptotic outage probability is used to evaluate the achievable diversity order for various system parameters. Simulations are presented to verify the accuracy of our analytical results.