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In wireless networks that experience channel fading, multiuser diversity can be exploited by scheduling users so that they transmit when their channel conditions are favorable. Cooperative relaying provides another form of diversity due to the spatial separation of the users. In this work we study the simultaneous application of these two sources of diversity, in a decentralized manner, and show the significant throughput improvement in wireless networks. To exploit this synergy, in  we have proposed a family of protocols termed Channel Aware Aloha with Cooperation (CAAC). In this work we study the effect of short-term power constraints on the aggregate throughput using CAAC protocol. We derive the scaling behavior of the achievable rate, and show that the overall system performance is significantly improved in comparison with direct transmission.