Information and Energy Transmission with Wavelet-Reconstructed Harvesting Functions

In practical simultaneous information and energy transmission (SIET), the exact energy harvesting function is usually unavailable because a harvesting circuit is nonlinear and nonideal. In this work, we consider a SIET problem where the harvesting function is accessible only at sample points that are experimentally taken in the presence of noise. Assuming that the harvesting function is of bounded variation that may have discontinuities, we propose to design SIET based on the wavelet-reconstructed harvesting function. The main focus is its asymptotic performance of expected energy and information rate. Specifically, we propose to design a SIET system based on the wavelet-reconstructed harvesting function with soft-thresholding estimation. Then, the expected loss in energy transmission asymptotically vanishes as the number of samples grows, which turns out to be optimal up to a logarithmic factor. The expected loss in information transmission also vanishes if the target energy delivery is in the interior of the deliverable energy range.