Asymptotic optimal quantizer design for distributed Bayesian estimation

We address the optimal quantizer design problem for distributed Bayesian parameter estimation with one-bit quantization at local sensors. A performance limit obtained for any distributed parameter estimator with a known prior is adopted as a guidance for quantizer design. Aided by the performance limit, the optimal quantizer and a set of noisy observation models that achieve the performance limit are derived. Further, when the performance limit may not be achievable for some applications, we develop a near-optimal estimator which consists of a dithered noise and a single threshold quantizer. In the scenario where the parameter is Gaussian and signal-to-noise ratio is greater than −1.138 dB, we show that one can construct such an estimator that achieves approximately 99.65% of the performance limit.