Distributed detection with unknown SNR: Separating function and GLRT approaches

In this paper we address distributed detection wherein the instantaneous signal-to-noise ratios (SNRs) at the individual sensors are unknown. A motivating example is a distributed radar receiver when the target radar cross section and/or the noise variance are unknown at each receiver. Recently it has been shown that detection problems can be converted into the estimation of a separating function (SF) followed by comparison to a threshold. Importantly, using an SF eliminates unknown parameters. Here, since the optimal detector depends on the unknown parameters, we propose a Separating Function Estimation Test (SFET) and a Generalized Likelihood Ratio Test (GLRT) at each receiver. Since the likelihood ratio test in the fusion center depends on the detection probability of local receivers, which are unknown, the optimal fusion rule is not applicable. We therefore employ an Asymptotically Optimal SFET (AOSFET) and a GLRT to find a suboptimal fusion rule. We assume that the local SNR at each sensor has a known probability density function. Simulation results show that the SFET outperforms the GLRT in the local detectors and under some conditions, the AOSFET provides better performance as compared to the majority fusion rule.