Heterogeneous Sensor Networks with Convex Constraints

A wireless sensor network design is always subject to constraints. There are constraints on bandwidth, cost, detection robustness, and even false alarm rates to name but a few. This paper studies the design of Heterogeneous Sensor Networks (HSN) performing distributed binary hypothesis testing subject to convex constraints on the total number and types of sensors available. The relationship between real world engineering constraints and a resultant convex set or solution space will be highlighted. Under these convex sets, a theorem will be presented that defines when a homogenous sensor network will have better performance than a HSN. This theorem depends on stationary statistics, which is not the case for most problems of interest. These challenges are explored in detail for a parallel distributed HSN using the Kullback-Leibler (K-L) information number (K-L Divergence) in conjunction with the Chernoff-Stein Lemma. This method allows sensor counts to be optimized across a finite set of hypothesis or events, enabling a robust hypothesis testing solution similar to problems in traditional multiple hypothesis testing or classification problem. This paper also compares and contrast the detection performance of the standard parallel distributed HSN topology and a modified binary relay tree topology that is similar to clustering methods, where the final fusion is done using a logical OR rule. Finally, the asymptotic performance between these two topologies is studied, including the performance relative to optimal bounds. Ultimately providing a methodology to broadly analyze and optimize HSN design.