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In this paper we investigate probability density function (pdf) of the received SNR in cooperative multi-user cellular-based communication system. We show that the pdf of the SNR follows, approximately, Weibull distribution. The resultant approximate pdf of the received SNR simplifies the analysis of the ergodic capacity of a relay-based wireless communication system. We assumed a single amplify-and-forward relay that assist users to receive a second version of the packet beside the directly received one. Maximal ratio combiner is assumed at the receiver end. We also assumed that relay amplification is based on semi-blind mechanism under Nakagami-m fading environment. In this paper, closed form expression of the ergodic capacity of this system is derived. Computer simulation is used to validate the derived closed-form expression. The simulation results almost agree with the analytical one with an error no more than 5%.