Nonlinear power harvesting through $$\alpha$$ -fair resource allocation in SWIPT

Ketcham and Moonen J Wireless Com Network (2025) 2025:11 https://doi.org/10.1186/s13638-025-02427-2 EURASIP Journal on Wireless Communications and Networking Open Access RESEARCH Nonlinear power harvesting through α‑fair resource allocation in SWIPT Richard Ketcham1*   and Marc Moonen1 *Correspondence: 1 STADIUS, KU Leuven, Department of Electrical Engineering (ESAT), Kasteelpark Arenberg 10 postbus 2440, Leuven 3001, Belgium Abstract The concurrent nature of multiuser (MU) simultaneous wireless information and power transfer (SWIPT), coupled with the complexity of orthogonal frequency division multiplexing (OFDM) and precoding, poses a challenging non-convex resource allocation problem. While conventional methods like subcarrier assignment or interference suppression can enhance tractability, they are not always optimal. Recent work has proposed leveraging hidden convexity in multicarrier systems to bypass these suboptimal methods, instead utilizing a multiple access channel (MAC)-broadcast channel (BC) duality for a near-optimal linear precoder design. However, this novel strategy relies on a linear power harvesting model, disregarding the nonlinear character of power harvesting in SWIPT networks. This paper addresses this issue by incorporating nonlinear power harvesting effects through a power harvesting model based on sigmoidallike functions. Sigmoidal-like functions, being neither convex nor concave, typically necessitate transformation for tractability, a challenge compounded by the MAC-BC duality. We propose an alternate approach in which a parameterized class of utility functions known as α-fairness is used to generalize the SWIPT resource allocation problem and concavify the nonlinear power harvesting model. This methodology simplifies optimization and facilitates the integration of nonlinear effects across a broad spectrum of fairness values. Keywords: Energy harvesting, Fairness, Multiuser, Multicarrier, Multiantenna, Nonlinear, OFDM, Power harvesting, Resource allocation, Sigmoidal, SWIPT, Timeswitching, Time-sharing 1 Introduction The utility of an energy-constrained wireless network is often limited due to the reliance on finite energy resources. Owing to its potential to assuage this type of constraint, a technology termed simultaneous wireless information and power transfer (SWIPT) has garnered attention. By combining wireless communication and wireless power transfer concepts, SWIPT uses shared resources to deliver power and information simultaneously to remote wireless users thereby alleviating the limitations imposed by the energy constraints. SWIPT related research has covered a wide variety of topics since it was first introduced in [1–3], but primarily seeks to advance © The Author(s) 2025. Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/. Ketcham and Moonen J Wireless Com Network (2025) 2025:11 the utilization of limited system resources. Optimal resource allocation is crucial to improving the feasibility of SWIPT, so designing efficient resource allocation methods while incorporating technologies that improve power utilization, such as orthogonal frequency division multiplexing (OFDM) and precoding [4], is essential. Multiuser (MU) SWIPT’s concurrent nature, coupled with the complexity of OFDM and precoding, poses challenging non-convex resource allocation problems. While mitigating user interference through orthogonal frequency division multiple access (OFDMA) or zero forcing (ZF) precoding is a common way to enhance tractability, they are optimal only under high interference conditions [5, 6]. In contrast, a novel method in [7] exploits hidden convexity in multicarrier systems [8, 9] to solve nonconvex problems via Lagrangian decomposition, bypassing OFDMA and ZF precoding. This approach leverages a multiple access channel (MAC)-broadcast channel (BC) duality to simplify precoder design, linking the problem to the dual MAC symbol power. However, this duality treats user interference as noise linearly related to the precoding vectors, necessitating the use of a linear power harvesting model over nonlinear alternatives. In this paper, we seek to include nonlinear power harvesting effects in the resource allocation method developed in [7]. Unlike traditional wireless communication networks, a SWIPT network must contend with power harvesting where received radio frequency (RF) power is converted to direct current (DC) power via a rectifier. Hence, incorporating an accurate power harvesting model is a critical aspect of resource allocation for SWIPT. It is well known that power harvesting is nonlinear [10]. Yet, many works utilize a linear harvesting model for tractability [11, 12], with some citing an ability to place several power harvesting circuits in parallel to enlarge the linear power conversion region as justification [7]. Two means for considering nonlinear effects include the diode nonlinear model and the saturation nonlinear model [10]. The diode nonlinear model is based on the physics of the specific circuit while the saturation nonlinear model is based on curve fitting to circuit measurements. The diode nonlinear model is useful for setting phases and amplitudes required in waveform design. It is based on the small-signal model around an induced quiescent point, operating in the transition region between the square law region and the linear region [13]. However, as the RF input power increases, the harvesting circuit enters the linear region and eventually saturates causing the small-signal model to no longer hold [14]. In contrast, the saturation nonlinear model is a tractable method for modeling the linear and saturation regions of the harvesting circuitry. While it may have mild discrepancies in the low-power region [10], from a power allocation perspective it is arguably more important to avoid entering saturation. As such, the saturation nonlinear model is more applicable to improving the power allocation method designed in [7]. A practical saturation nonlinear (...truncated)