Energy scaling laws for distributed inference in random fusion networks

The energy scaling laws of multihop data fusion networks for distributed inference are considered. The fusion network consists of randomly located sensors distributed i.i.d. according to a general spatial distribution in an expanding region. Under Markov random field (MRF) hypotheses, among the class of data-fusion policies which enable optimal statistical inference at the fusion center using all the sensor measurements, the policy with the minimum average energy consumption is bounded below by the average energy of fusion along the minimum spanning tree, and above by a suboptimal policy, referred to as Data Fusion for Markov Random Fields (DFMRF). Scaling laws are derived for the energy consumption of the optimal and suboptimal fusion policies. It is shown that the average asymptotic energy of the DFMRF scheme is strictly finite for a class of MRF models with Euclidean stabilizing dependency graphs.