On Quantizer Design for Distributed Estimation in Bandwidth Constrained Networks

We consider the problem of distributed estimation of an unknown zero-mean Gaussian random variable in a bandwidth constrained network, when only partial information of observation model is available. Sensors employ uniform quantizers with variable rates and transmit their quantized observations to a fusion center (FC). Assuming the FC employs the linear minimum mean-square error (LMMSE) estimator, we provide a closed-form expression for the corresponding MSE, and propose a rate allocation scheme that minimizes the MSE, subject to a total bandwidth constraint (measured in quantization bits). Simulation results show the superiority of the proposed scheme over uniform bit allocation scheme.