A time-reversal spatial hardening effect for indoor speed estimation
Time-reversal (TR) transmission scheme has attracted more and more attention from both academia and industry due to its ability to focus the energy of a transmitted signal at an intended focal spot, both in the time and spatial domains. Based on the extensive data collected in the real world, we observe that the energy distribution around the focal spot is highly stationary and location-independent, which we call as the “TR spatial hardening effect”. This is because TR scheme adds up numerous copies of the transmitted signal bouncing off different scatterers coherently and the randomness from the environment is averaged out. We characterize the statistical behaviors of the energy distribution around the focal spot using a statistical model. By exploiting the hardening effect, the moving speed of transceivers can be estimated in indoor environments and extensive experiments show the superiority of the proposed method compared with previous works using RF signals.