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The problem of distributed estimation in wireless sensor networks (WSNs) has attracted much attention. As bandwidth and power are severely limited in WSNs, one of the main objectives in current WSN research is to design bandwidth and power efficient algorithms. A multitude of studies along this line have appeared. Among them, some previous works (e.g., (A. Ribeiro and G.B. Giannakis, 2006), (Z. Luo, 2005), (J.-J. Xiao, 2006), (J. Li and G. AlRegib, 2007), (H. Li and J. Fang, 2007)) consider distributed estimation using aggressively quantized versions of the original observations. In this setup, quantization becomes an integral part of the estimation process and is critical to the estimation performance. Another category of methods (e.g., (K. Zhang et al., 2003), (Z-Q Luo et al., 2005), (Y. Zhu et al., 2005), (E. Song et al., 2005), (I.D. Schizas et al., 2007), (J. Fang and H. Li)), not relying on the above low-rate quantization strategy, follow an optimal decentralized compression-estimation approach to reduce the transmission requirement. In these methods, the data dimensionality is reduced before each sensor sends its data to a fusion center (FC). Upon receiving the compressed data, the FC combines them according to some fusion criterion to obtain a final estimate. The crux of these techniques is to design the compression matrix so as to minimize the estimation mean-square error (MSE), which has been extensively investigated by (K. Zhang et al., 2003), (Z-Q Luo et al., 2005), (Y. Zhu et al., 2005), (E. Song et al., 2005), (I.D. Schizas et al., 2007), (J. Fang and H. Li) under different fusion criterions and observation correlation scenarios. These works (K. Zhang et al., 2003), (Z-Q Luo et al., 2005), (Y. Zhu et al., 2005), (E. Song et al., 2005), (I.D. Schizas et al., 2007), (J. Fang and H. Li), however, mostly assume perfect wireless channels through which the signals can be sent from the sensors to the fusion center (FC) without any distortion. This assumption,- - clearly, is unrealistic in practice because the wireless links inevitably suffer from the channel noise and adverse channel effects such as fading and attenuation. In this paper, we study the problem of decentralized compression-estimation in the presence of channel noise and fading. By utilizing a series of matrix transformations and established properties, we present a scheme to design the compression matrices. Specifically, for the single sensor case, an analytic solution of the optimal compression is derived.