Distributed Detection with False Alarm Rate Constraints

Abstract

In this chapter, we consider the distributed detection problem for situations where the probability of false alarm is to remain less than an acceptable value. This formulation is especially suitable for radar applications. First, we consider the Neyman—Pearson formulation of the problem. This formulation does not require the knowledge of a priori probabilities associated with different hypotheses or an assignment of costs to different courses of action. System probability of detection is maximized under a probability of false alarm constraint. Under this formulation, the parallel fusion network topology without a fusion center is not appropriate because systemwide probabilities of detection and false alarm can not be defined. Therefore, a fusion center is always assumed to be present. We consider only the parallel fusion network topology here. Other network topologies can be treated similarly. In Section 5.2, the distributed Neyman—Pearson detection problem is formulated and decision rules are derived. A number of interesting issues, such as randomization, arise. These and other related aspects are discussed. In practical radar signal detection scenarios, noise and clutter background are often nonstationary. In this case, the optimum Neyman—Pearson detector with a fixed threshold fails to maintain a constant false alarm rate (CFAR), and adaptive thresholding based on observations from the neighboring region is required. Distributed CFAR processing is discussed in Section 5.3. Issues, such as robustness in the presence of homogeneous and nonhomogeneous backgrounds, are also examined. In Section 5.4, distributed detection of weak signals is considered, and locally optimum decision rules are derived.