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In this letter, we consider decentralized estimation of unknown random vectors by using wireless sensors and a fusion center (FC). We adopt a linear model for decentralized estimation of vector sources where both observation models and sensor operations are linear and the multiple access channel (MAC) is coherent. Each sensor observes a different vector source, where vector sources can be correlated. Sensors are designed to minimize the total mean square error (MSE) at the fusion center subject to transmit power constraints at the sensors. While a closed form solution cannot be found, an iterative algorithm is proposed. Simulations are provided to verify the analysis and present the performance of the proposed scheme.