Information-Energy Capacity Region for SLIPT Systems over Lognormal Fading Channels: A Theoretical and Learning-Based Analysis

TL;DR

This work analyzes the information-energy capacity region for SLIPT over lognormal fading channels, incorporating peak and average power as well as nonlinear energy harvesting constraints. By extending Smith's framework and employing a Hermite-polynomial basis, it proves that the capacity-achieving input distribution is discrete with a finite number of mass points and derives a high-SNR achievable distribution on a discrete alphabet. It then introduces the Cooperative Information-Energy Capacity Learning (CIECL) framework, a GAN-based method that learns capacity-achieving distributions without input-space discretization while enforcing PP, AP, and EH constraints for SLIPT with a dual receiver setup. Numerical results show that lognormal fading tightens the information-energy region relative to AWGN and demonstrate the framework's ability to recover and extend known discreteness properties under practical SLIPT constraints, offering design insights for challenging optical wireless environments.

Abstract

This paper presents a comprehensive analysis of the information-energy capacity region for simultaneous lightwave information and power transfer (SLIPT) systems over lognormal fading channels. Unlike conventional studies that primarily focus on additive white Gaussian noise channels, we study the complex impact of lognormal fading, which is prevalent in optical wireless communication systems such as underwater and atmospheric channels. By applying the Smith's framework for these channels, we demonstrate that the optimal input distribution is discrete, characterized by a finite number of mass points. We further investigate the properties of these mass points, especially at the transition points, to reveal critical insights into the rate-power trade-off inherent in SLIPT systems. Additionally, we introduce a novel cooperative information-energy capacity learning framework, leveraging generative adversarial networks, to effectively estimate and optimize the information-energy capacity region under practical constraints. Numerical results validate our theoretical findings, illustrating the significant influence of channel fading on system performance. The insights and methodologies presented in this work provide a solid foundation for the design and optimization of future SLIPT systems operating in challenging environments.

Figures (8)

• Figure 1: A SLIPT system over a lognormal-fading channel with an LED/LD transmitter, a PD-based information decoder, and a PV cell EH receiver.
• Figure 2: Proposed information-energy capacity learning framework inspired by GAN.
• Figure 3: Neural networks used in CIECL. (a) Generator. (b) Discriminator.
• Figure 4: Optimal input distribution learned by CORTICAL at different training steps under lognormal channels with $A = 1$, $\varepsilon =1$, $E_{th} = 1$ mJ.
• Figure 5: Optimal input distribution learned by CORTICAL at different $E_{th}$ values. $A= 5$, $\varepsilon = 2.5$, and the training epoch is $100000$ in all cases.

Theorems & Definitions (11)

• Theorem 1
• proof
• Corollary 1
• proof
• Theorem 2
• proof
• Corollary 2
• proof
• Theorem 3
• proof