Distributed adaptive quantization for wireless sensor networks: A maximum likelihood approach

We consider the problem of distributed parameter estimation in wireless sensor networks (WSNs), where due to bandwidth/power constraints, each sensor quantizes its local observation into one bit of information that is sent to a fusion center (FC) to form a global estimate. Conventional fixed quantization (FQ) approaches, which utilize a fixed threshold for all sensors, incurs an estimation error growing exponentially with the difference between the threshold and the unknown parameter to be estimated. To overcome this difficulty, we propose a distributed adaptive quantization (AQ) approach, where, under the condition that sensors successively broadcast their quantized data, each sensor adaptively adjusts its quantization threshold using prior transmissions from other sensors. Specifically, our strategy here is to let each sensor choose its quantization threshold as the maximum likelihood (ML) estimate of the unknown parameter based on the quantized data sent from other sensors. The Cramér-Rao bound (CRB) analysis shows that our proposed one-bit AQ approach asymptotically attains an estimation variance that is only π/2 times that of the clairvoyant sample-mean estimator using unquantized observations.