Optimal quantised bits for estimation over a capacity and power limited, lossy channel

Abstract

This letter considers the problem of estimating the state of a scalar dynamical system over a wireless channel that is lossy, capacity, and power limited. The limited power assumption, which is valid for most real problems, links the number of quantisation bits and packet error rate. As the number of quantisation bits increases, the quantisation noise decreases but the packet loss rate increases. It is shown that the estimation error variance (EEV) is minimised for a range of quantisation bits. Further, it is shown that operating beyond the optimal range sharply increases the EEV. Simulation results corroborating the analytical results are also presented.