Distributed Detection of a Non-cooperative Target with Multiplicative Fading

We tackle distributed detection of a non-cooperative target with a Wireless Sensor Network (WSN) made of tiny and inexpensive sensor nodes. When the target is present, sensors observe an (unknown) deterministic signal with attenuation depending on the distance between the sensor and the (unknown) target positions, multiplicative fading (accounting for both line-of-sight and non-line-of-sight components), and additive Gaussian noise. To model energy-constrained operations usually encountered in an Internet of Things (IoT) scenario, local one-bit quantization of the raw measurement is performed at each sensor. The Fusion Center (FC) receives quantized sensor observations through error-prone binary symmetric channels and is in charge of performing a more-accurate global decision. Such model leads to a two-sided test with nuisance parameters (i.e. the target position xxT) observable solely in the case of H1 hypothesis. After introducing the Generalized Likelihood Ratio Test (GLRT) for the problem, the appealing Davies’ framework is exploited to design a generalized form of the Rao test which obviates GLRT high complexity requirements. Equally important, a rationale for threshold-optimization (resorting to a heuristic principle) is proposed and confirmed via simulations. Finally, the aforementioned rules are compared in terms of detection rate in practical scenarios.