On optimal parametric field estimation in sensor networks

We develop a framework for field estimation using wireless sensor networks, subject to network power and communication channel constraints. Each field snapshot is described by a real-valued parameter vector and the sensor measurements are assumed independent and identically distributed, conditioned on the parameter values. The nodes communicate appropriate local statistics to a fusion center over a wireless multiple access channel (MAC). If the node statistics satisfy a critical mean condition, a simple uncoded communication strategy yields the optimal (centralized) 1/k squared-error parameter distortion scaling with the number of nodes (k) even with finite total network power. If an additional additive property is satisfied, and the network power grows unbounded (sub-linearly) with the number of nodes, then the uncoded strategy achieves the Cramer-Rao lower bound on distortion. Motivated by these general results, we propose a universal parameter estimation framework based on local type/histogram statistics that satisfies both optimality conditions for arbitrary finite alphabet measurements. It is shown that phase coherent transmission of type statistics achieves the optimal power-distortion scaling even over a fading MAC. When reliable phase synchronization is not possible, a simple coded strategy is proposed that achieves logarithmic distortion reduction with total network power