Abstract

Securing signals from unintended eavesdroppers has become an increasingly important problem with the emergence of the Internet-of-Things. Herein, we examine learning problems in signal processing that are inherently hard without key side information. In particular, we exploit necessary resolution limits for classical compressed sensing problems. To limit an eavesdropper’s capabilities, we create an environment for the eavesdropper wherein the appropriate compressed sensing algorithm would provably fail. The intended receiver overcomes this ill-posed problem by leveraging secret side information shared between the intended transmitter and receiver. Two scenarios are considered: one for communication over a wireless channel where a novel block-sparsity based signaling strategy is employed and one for localization where novel structured noise is introduced to degrade the form of the eavesdropper’s channel. In the latter scenario, the transmitter designs a beamformer that introduces spurious paths, or alternatively spoofs the line-of-sight path, in the channel without having access to the channel state information. Both far-field and near-field cases are considered for the private localization. In both private communication and private localization, the amount of secret information that must be shared is very modest. Theoretical guarantees can be provided for both cases. Preliminary results on the information theoretic limits of this form of private communication are provided. Proposed algorithms are validated via numerical results and it is seen that the eavesdropper’s capabilities are severely degraded.