In practical simultaneous information and energy transmission (SIET), the exact energy harvesting function is usually unavailable because an energy harvesting circuit is nonlinear and nonideal. In this work, we consider a SIET problem where the harvesting function is accessible only at experimentally-taken sample points and study how close we can design SIET to the optimal system with such sampled knowledge. Assuming that the harvesting function is of bounded variation that may have discontinuities, we separately consider two settings where samples are taken without and with additive noise. For these settings, we propose to design a SIET system as if a wavelet-reconstructed harvesting function is the true one and study its asymptotic performance loss of energy and information delivery from the true optimal one. Specifically, for noiseless samples, it is shown that designing SIET as if the wavelet-reconstructed harvesting function is the truth incurs asymptotically vanishing energy and information delivery loss with the number of samples. For noisy samples, we propose to reconstruct wavelet coefficients via soft-thresholding estimation. Then, we not only obtain similar asymptotic losses to the noiseless case but also show that the energy loss by wavelets is asymptotically optimal up to a logarithmic factor.

翻译：在实际的同步信息与能量传输（SIET）系统中，由于能量采集电路的非线性和非理想特性，精确的能量采集函数通常难以获取。本文研究了一种SIET问题，其中能量采集函数仅通过实验采样点获得，并探讨在仅有采样知识的情况下，如何使设计的SIET系统逼近最优系统。假设能量采集函数为可能包含不连续点的有界变差函数，我们分别考虑了无噪声采样和有加性噪声采样两种情况。针对这些场景，我们提出将小波重构的能量采集函数视为真实函数来设计SIET系统，并研究其与真实最优系统在能量和信息传输方面的渐近性能损失。具体而言，对于无噪声采样情况，研究表明：将小波重构的能量采集函数视为真实函数来设计SIET，其能量和信息传输损失随采样数量增加而渐近消失。对于有噪声采样情况，我们提出通过软阈值估计重构小波系数，不仅获得了与无噪声情况相似的渐近损失结果，还证明了基于小波方法的能量损失在对数因子意义下渐近最优。