  This paper considers the problem of simultaneous information and energy
transmission (SIET), 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 harvesting functions are a
subclass 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 worst loss in
information rate vanishes in the interior of the energy domain, however, does
not always vanish at maximal energy. We further show 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 distortion and
harvesting functions both are known only at samples.
