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In this paper, a binary hypothesis distributed detection problem in correlated wireless sensor networks with cooperative relays deployment is considered. In particular, the effect of correlation between sensor nodes is modeled and analyzed in Rayleigh flat fading channels in order to explore the natural tradeoffs between the number of sensor/relay nodes and the detection error performance in the network. Specifically, two communication protocols are utilized; in protocol I, each sensor node communicates its observation directly to the fusion center while in protocol II, amplify-and-forward (AF) cooperative relays are deployed and a fewer number of sensors is used. Based on the theoretical analysis and simulations, it is revealed that employing less sensor nodes and instead deploying relay nodes results in significant performance gains under strict network power constraint It is concluded that with cooperative distributed detection and exploitation of spatial diversity, better detection error performance is achieved as well as reduction in the required number of sensor nodes.