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Bit assignment for local sensor data quantization in the decentralized best-linear-unbiased-estimation (BLUE) scenario is widely addressed in the signal processing research for wireless sensor networks. When the timely knowledge of the instantaneous sensor noise variance (for implementing the BLUE fusion rule) is too costly to obtain, one plausible alternative is to exploit the associated statistical characterization. Related such proposals, however, do not explicitly take into account the communication link impairments such as channel fading. In this paper we extend the current results to the more realistic case when signal transmission is subject to the fading effect. We show that the optimal bit allocation problem can be reformulated in the form of convex optimization, and then derive an analytical solution. Through numerical simulation the proposed solution is seen to outperform the uniform energy allocation scheme.