Coupling Effect of Single-Threshold Sensor Rules in Two-Sensor Tandem Network

We consider a distributed detection network that has two sensors in tandem and in collaboration to detect the presence of a deterministic signal in correlated Gaussian noise. It is known that the optimum decision rules of both sensors are coupled in nature. By partitioning the two-dimensional signal space into three regions, we establish in each region the availability and properties of coupled single-threshold sensor rules. Results are also validated with numerical results. The detection performance of coupled single-threshold sensor rules is further compared with sensor rules generated using the genetic algorithm. The effect of placement of two sensors in the tandem network is also discussed. In addition, we prove that the optimal fusion rule in tandem configuration converges to Exclusive-OR rule, the same fusion rule obtained in the parallel configuration, as the correlation coefficient approaches 1.