This paper presents both cooperative and noncooperative amplify-and-forward (AF) relay networks consisting of a one-source-one-destination pair and N-relays under receiver power constraint (RPC) at the destination. The optimal AF relay amplifying matrices for the relays by minimizing the mean square error are analytically derived. This paper also shows that the performance of the optimum cooperative relay network is identical to that of the optimum noncooperative network, as long as the same receiver power constraint is applied. The purpose of the RPC is to reduce the interference level for users located in neighboring cells. Finally, using the derived optimal relay amplifying matrices, the achievable rate, the pairwise error probability, and the outage probability are investigated.