Fairness in Distributed Sensor Systems to Detect Emitters

When designing a distributed sensor system to detect the occurrence of an emitter in multiple communities, the designer may face questions related to fairness. To assist designers answer such questions, we adopt a fairness definition based on envy-free fairness: we define a design to be envy-free fair when all communities have the same probability of detecting the emitter. Using an optimization framework considering a constraint in the total rate of false alarms, we show that, when communities are isolated, the optimum envy-free fair system exists; and, for a given sensor allocation, we propose an algorithm to find such a system. We also propose an algorithm to allocate sensors to communities and, through examples, we illustrate that it can produce allocations close to the optimum allocation most of the times.