Status from a Random Field: How Densely Should One Update?

In many applications, status information of a general spatial process, in contrast to a point information source, is of interest. In this paper, we consider a system where status information is drawn from a random field and transmitted to a fusion center through a wireless multiaccess channel. The optimal density of spatial sampling points to minimize the remote status estimation error is investigated. Assuming a one-dimensional Gauss Markov random field and an exponential correlation function, closed-form expressions of remote estimation error are obtained for First-Come First-Served (FCFS) and Last-Come First-Served (LCFS) service disciplines. The optimal spatial sampling density for the LCFS case is given explicitly. Simulation results are presented which agree with our analysis.