Information and Energy Transmission with Experimentally-Sampled Harvesting Functions

This paper considers the problem of simultaneous information and energy transmission (SIET), where the energy harvesting function is only known experimentally at sample points. We investigate the performance loss due to this partial knowledge of the harvesting function in terms of transmitted energy and information. In particular, we assume harvesting functions are a class of Sobolev space and consider two cases, where experimental samples are either taken noiselessly or in the presence of noise. Using constructive function approximation and regression methods for noiseless and noisy samples respectively, we show that the worst loss in energy transmission vanishes asymptotically as the number of samples increases. Similarly, the loss in information rate vanishes in the interior of the energy domain, however, does not always vanish at maximal energy.