Optimal Nonuniform Deployment of Sensors for Distributed Detection in Wireless Sensor Networks

We determine the optimal nonuniform spatial density of nodes in a single-hop Wireless Sensor Network (WSN) whose task is the distributed detection of a target within its sensing field. The optimization approach accounts for such factors as the Medium Access Control (MAC) protocol being used, the wireless channel's propagation characteristics, a randomized sleep/wake-up scheduling protocol, network coverage constraints, the energy consumed, the time to reach a decision, and the number of nodes in the network. The node density that minimizes the average Decision Error Probability (DEP) when a node at the center of the network serves as the Cluster Head (CH) is shown to be a function of the distance from this CH. The solution of this optimization problem and simulations demonstrate both the significant performance improvement provided by nonuniform spatial densities and the trade-offs that are possible amongst energy, network lifetime, detection performance, and time to reach a decision.