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Decentralized and dynamic behavior of peer to peer networks along with drawbacks of wireless environment necessitates the development of techniques achieving high reception rates and thus short reception times for the requestor peers. In this paper we discuss, through capacity optimization, the effects of user cooperation on the performance of a generalized wireless peer-to-peer network with Rayleigh fading additive white Gaussian noise (AWGN) channels. At the transmitter side, we utilize either parallel downloading, where transmitters send independent file portions, or user cooperation diversity, where transmitters simultaneously send same portions of the file. At the receiver side, we first analyze no cooperation case and then consider two cooperation strategies; decode-and-forward (DF) and amplify-and-forward (AF). We compare the performances of these transmitter and receiver cooperation schemes based on the time elapsed for the worst receiver to receive the whole file. Results show that user cooperation dramatically decreases reception times of the requestor peers.