Fusion in sensor networks with communication constraints

We address the problem of optimizing the detection performance of sensor networks under communication constraints on the common access channel. Our work helps understanding tradeoffs between sensor network parameters like number of sensors, degree of quantization at each local sensor, and SNR. Traditionally, this problem is tackled using asymptotic assumptions on the number of sensors, an approach that leads to the abstraction of important details such as the structure of the fusion center. We adopt a non-asymptotic approach and optimize both, the sensing and the fusion sides with respect to the probability of detection error. We show that the optimal fusion rule has an interesting structure similar to the majority-voting rule. In addition, we study the convergence with respect to the number of sensors of the performance of the fusion rule. We show that convergence is SNR dependent and that, in low-SNR environments, asymptotics may require a large number of sensors.