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This paper investigates the problem of distributed best linear unbiasedestimation (BLUE) of a random parameter at the fusion center (FC) of a wirelesssensor network (WSN). In particular, the application of limited-feedbackstrategies for the optimal power allocation in distributed estimation isstudied. In order to find the BLUE estimator of the unknown parameter, the FCcombines spatially distributed, linearly processed, noisy observations of localsensors received through orthogonal channels corrupted by fading and additiveGaussian noise. Most optimal power-allocation schemes proposed in theliterature require the feedback of the exact instantaneous channel stateinformation from the FC to local sensors. This paper proposes alimited-feedback strategy in which the FC designs an optimal codebookcontaining the optimal power-allocation vectors, in an iterative offlineprocess, based on the generalized Lloyd algorithm with modified distortionfunctions. Upon observing a realization of the channel vector, the FC finds theclosest codeword to its corresponding optimal power-allocation vector andbroadcasts the index of the codeword. Each sensor will then transmit its analogobservations using its optimal quantized amplification gain. This approacheliminates the requirement for infinite-rate digital feedback links and isscalable, especially in large WSNs.

Limited-Feedback-Based Channel-Aware Power Allocation for Linear Distributed Estimation