Distributed Detection of Sparse Signals with Physical Layer Secrecy Constraints: A Falsified Censoring Strategy

In this paper, we investigate the problem of distributed detection of sparse signals in wireless sensor networks (WSNs) with censoring sensors in the presence of an Eavesdropper (Eve). The Eve, which is able to perfectly monitor the 'idle' and 'busy' states of the communication channels between the local sensors and the fusion center (FC), also wants to detect the sparse signals. For the classical problem of distributed detection with censoring sensors, applying appropriate censoring thresholds to attain the same transmission probability under either hypothesis to ensure perfect secrecy has previously been studied. We refer to it as the clairvoyant censoring method since it requires full knowledge of the distributions of the observations. However, the clairvoyant censoring method is not practical to implement for the detection of sparse signals with an unknown sparsity level. In this paper, a falsified censoring (FACE) strategy is proposed, in which a group of cooperating deceitful nodes censor their local observations in a way that is opposite to what would be done at the regular nodes. Based on this setup, the optimization problem to maximize the detection performance at the FC under communication and secrecy constraints is formulated and numerical methods are provided to find the near optimal system parameters. Simulation results exhibit excellent performance of our proposed strategy.