  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.
