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In wireless relay networks, noise at the relays can be correlated possibly due to common interference or noise propagation from preceding hops. A parallel relay network with noise correlation is considered in this network. For the relay strategy of amplify and forward (AF), the optimal rate maximizing relay gains when correlation knowledge is available at the relays are determined. Interestingly, it is shown that, on average, noise correlation is beneficial regardless of whether the relays know the noise covariance matrix. However, the knowledge of correlation can greatly improve the performance. Typically, the performance improvement from correlation knowledge increases with the relay power and the number of relays. With perfect correlation knowledge the system is capable of canceling interference if the number of interferers is less than the number of relays. For a two-hop multiple-access parallel network, closed-form expressions for the maximum sum rate and the optimal relay strategy are determined. Relay optimization for networks with three hops is also considered. Based on the result of two-hop network with noise correlation, an iterative algorithm is proposed for solving the relay optimization problem for three-hop networks.