Robustness of the Counting Rule for Distributed Detection in Wireless Sensor Networks

We consider the problem of energy-efficient distributed detection to infer the presence of a target in a wireless sensor network and analyze its robustness to modeling uncertainties. The sensors make noisy observations of the target's signal power, which follows the isotropic power-attenuation model. Binary local decisions of the sensors are transmitted to a fusion center, where a global inference regarding the target's presence is made, based on the counting rule. We consider uncertain knowledge of: 1) the signal decay exponent of the wireless medium; 2) the power attenuation constant; and 3) the distance between the target and the sensors. For a given degree of uncertainty, we show that there exists a limit on the target's signal power below which the distributed detector fails to achieve the desired performance regardless of the number of sensors deployed. Simulation results are presented to determine the level of sensitivity of the detector to uncertainty in these parameters. The results throw light on the limits of robustness for distributed detection, akin to 'SNR walls' for classical detection.