Least Favorable Distributions for the Design of Randomly Deployed Sensor Detection Systems

The design of a detection system in which sensors are randomly located to detect a low-power signal emitter in a random location tends to be difficult because the measurements are conditionally dependent in general and the alternative hypothesis is composite. It is shown that there are conditions that allow a system designer to deal with these problems by assuming a least favorable distribution for the emitter location that not only makes the alternative hypothesis simple and ensures a detection performance, but also causes the measurements to become conditionally i.i.d., making models more amenable for analysis. Since a design based on a least favorable distribution may be considered too conservative, this paper proposes the use of a most favorable distribution for the emitter location and uses the theory of asymptotic relative efficiency (ARE) to evaluate how conservative the design based on a least favorable distribution is. It is further shown that, if the system designer can place sensors in an enlarged deployment region, then there are situations in which the design based on a least favorable distribution becomes less and less conservative as the dimensions of the region of interest increase.