Measurement Matrix Design for Compressed Detection with Secrecy Guarantees

We consider the problem of designing the measurement matrix for high dimensional signal detection based on compressed measurements while ensuring physical layer secrecy. We assume that the network operates in the presence of an eavesdropper who intends to discover the state of the nature being monitored. To keep the data secret from the eavesdropper, we propose to use cooperating trustworthy nodes that assist the fusion center by injecting artificial noise to deceive the eavesdropper. We design measurement matrices to obtain compressed data at distributed nodes so that the detection performance of the network is maximized while guaranteeing a certain level of secrecy. The design of optimal measurement matrices depends on the signal being detected, and we provide solution considering three different scenarios: 1) the signal is known; 2) the signal lies in a low dimensional subspace; and 3) the signal is sparse. We show that the detection performance of the system can be improved while guaranteeing a certain level of secrecy by using optimized measurements along with noise injection based techniques.