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In this paper, we analyze the ergodic capacity performance of channel state information (CSI)-assisted amplify-and-forward (AF) cooperative networks with partial relay selection under outdated CSI. Assuming that channels suffer from independent but not necessarily identical Rayleigh fading, we derive an exact and closed-form expression for the ergodic capacity of this system. Furthermore, the effects of the correlation coefficient, number of relays, and path-loss exponent on the ergodic capacity are investigated.