False Discovery Rate Based Sensor Decision Rules for the Network-Wide Distributed Detection Problem

This paper presents a new framework for distributed target detection in wireless sensor networks (WSNs). In distributed detection, quantized decisions from local sensors are transmitted to a sink (also known as the fusion center) which combines these decisions to come up with a global decision. Traditionally, while collaboratively detecting the presence or absence of a target in a sensor field, multiple networked sensors use identical decision rules for decision making. This decision rule is obtained by imposing a strict control on the probability of one or more local false alarms from the entire sensor network. This error rate is known as the family-wise error rate (FWER) in the statistical literature. In this paper, we propose the control of the false discovery rate (FDR), defined as the ratio of the number of local false alarms to the total number of local detections, instead of the FWER, to determine possible nonidentical local sensor decision rules. Under the assumption that the fusion center uses a test statistic which is linear in "count" (i.e., the total number of local detections) to reach the global decision regarding the presence or absence of a target, we demonstrate that the control of the FDR to determine the local sensor decision rules, instead of employing identical decision rules, can substantially improve the global detection performance.