On the use of ambient noise sources for passive communication

Motivated by applications to wireless communication, we consider the propagation of waves transmitted by ambient noise sources and interacting with metamaterials. We discuss a generalized Helmholtz-Kirchhoff identity that is valid in dissipative and dispersive media and we characterize the statistical properties of the empirical cross spectral density of the wave field. We can then introduce and analyze an original communication scheme between two passive arrays that uses only ambient noise illumination. The passive transmitter array does not transmit anything but it is a tunable metamaterial surface that can modulate its dispersive properties and encode a message in the modulation. The passive receiver array made of two receivers that are half-a-wavelength apart from each other can decode the message from the empirical cross spectral density of the wave field.