Sensor networks: towards a theory of computation and communication of functions of measurements to a fusion center

Sensor networks consist of nodes with sensing as well as limited wireless and computation capabilities. In many applications, some statistic, or more generally function of the various sensor measurements, is required to be communicated to a fusion center. Computing and communicating such a function efficiently is an important, and perhaps a primary, task to be performed by a sensor network. We are interested in the rate at which such functions can be computed and communicated in sensor networks. It would be expected that there are more efficient approaches, in terms of the communication required, than to communicate all the raw data to the fusion center and have it compute the desired function. As may be expected, the maximum rate depends jointly on the particular structural properties of the function as well as the spatial configuration of the sensor network. In this paper, we study how this rate scales with network size for various functions and spatial configurations of interest. Our approach has two important aspects. First, we consider a simplified multihop model of wireless communication rather than the more general information theoretic one. Secondly, our approach is deterministic in that we do not model input probability distributions, but rather allow arbitrary measurement values within a fixed finite set.