Hardware Complexity of Binary Distributed Detection Systems with Isolated Local Bayesian Detectors

Two multisensor multiobservation detection schemes are analyzed and compared, and their hardware complexity (= number of sensors) is discussed. The studied schemes are: a Bayesian optimal parallel-sensor centralized architecture and a suboptimal binary distributed-detection system. Both systems are to have the same performance, as measured in terms of a Bayesian risk. In the optimal system sensors transmit their raw measurements to a decision maker that minimizes a global Bayesian risk. In the suboptimal architecture each sensor acts as a local detector: it minimizes its own Bayesian risk locally, and submits a binary decision to a data fusion center that minimizes the same global risk (for the given fixed architectures of the local detectors). Two specific cases are studied: 1) discrimination between two Gaussian populations that differ in their means; and 2) discrimination between two Poisson populations that differ in their parameters. The tradeoff between performance and hardware complexity is demonstrated, and the cost (in terms of hardware units) of the design simplicity that characterizes the suboptimal system is calculated. Results are useful for comparing different distributed-sensor detection schemes. It is shown that in the Gaussian case, a high signal-to-noise ratio (SNR) decentralized system with 2N sensor/ detectors performs at least as well as the centralized system with N sensors and a single detector.