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We consider the distributed estimation of an unknown vector signal in a resource constrained sensor network with a fusion center. Due to power and bandwidth limitations, each sensor compresses its data in order to minimize the amount of information that needs to be communicated to the fusion center. In this context, we study the linear decentralized estimation of the source vector, where each sensor linearly encodes its observations and the fusion center also applies a linear mapping to estimate the unknown vector signal based on the received messages. We adopt the mean squared error (MSE) as the performance criterion. When the channels between sensors and the fusion center are orthogonal, it has been shown previously that the complexity of designing the optimal encoding matrices is NP-hard in general. In this paper, we study the optimal linear decentralized estimation when the multiple access channel …