Information and Energy Transmission with Experimentally Sampled Harvesting Functions

This paper considers the problem of simultaneous information and energy transmission, where the energy harvesting function is only known experimentally at sample points, e.g., due to nonlinearities and parameter uncertainties in harvesting circuits. 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 that the harvesting function is a subclass of the Sobolev space and consider two cases, where the 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 increase. Similarly, the loss in information rate vanishes in the interior of the energy domain; however, it does not always vanish at maximal energy. We further show that the same principle applies in multicast settings, such as medium access in the Wi-Fi protocol. We also consider the end-to-end source-channel communication problem under source distortion constraint and channel energy requirement, where both distortion and harvesting functions are known only at samples.