Multi-bit Quantizer Design for Distributed Parameter Estimation

We consider sensors deployed in diverse locations measuring a common parameter through noisy observations. These observations are quantized to be sent to a fusion center doing the estimation of the common parameter. We design these quantizers to minimize the worst-case mean square error for common parameter estimation. Relying on an asymptotic regime in terms of sensors’ number and on random multi-bit quantizer per sensor, we provide a relevant continuous distribution for the thresholds of these quantizers via signomial programming. Through numerical simulations, we show that the proposed quantizers outperform the uniformly-distributed one and some deterministic ones even when the number of sensors is limited.