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arxiv: 2604.17169 · v2 · submitted 2026-04-18 · 📡 eess.SP

Two-Tier High Altitude Platform Stations (HAPS) for Exploring Wireless Energy Harvesting

Faicel Khennoufa , Khelil Abdellatif , Halim Yanikomeroglu , Safwan Alfattani , Metin Ozturk , Ferdi Kara This is my paper

Pith reviewed 2026-05-10 05:55 UTC · model grok-4.3

classification 📡 eess.SP
keywords High Altitude Platform StationsWireless Energy HarvestingTwo-tier ArchitectureQ-learningData Rate PerformanceIterative Optimization6G Aerial Networks
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The pith

A two-tier HAPS architecture lets regular platforms harvest wireless energy from a mother platform to reach higher data rates than conventional setups.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes a two-tier system for high-altitude platform stations in which a mother HAPS-SMBS coordinates regular HAPS-SMBS nodes that collect energy from transmitted signals. This setup is positioned to support energy-efficient 6G connectivity by reducing reliance on onboard power sources. The authors derive optimal node locations to cut signal loss, then solve a joint problem for positioning and energy-harvesting factor with an iterative algorithm and Q-learning. Results show both methods improve data rate over non-harvesting systems, with Q-learning gaining an edge in linear cases after training and maximum transmit power yielding the largest benefit.

Core claim

In the two-tier HAPS-SMBS architecture, regular nodes harvest energy from the mother node's signals while the mother coordinates with the ground station. Optimal positioning of regular nodes is derived to reduce attenuation and power loss. The joint optimization of positioning and harvesting factor is solved by the iterative distance and EH factor algorithm, whose performance is checked with Q-learning. The EH-enabled system produces higher data rates than conventional approaches, with maximum transmit power delivering the largest improvement.

What carries the argument

The two-tier HAPS-SMBS architecture, where a mother node manages coordination and energy transfer while regular nodes harvest from its signals, together with the iterative distance and EH factor algorithm that jointly tunes node location and harvesting ratio.

If this is right

  • Optimal regular HAPS-SMBS placement reduces signal attenuation and power loss in the two-tier setup.
  • Maximizing transmit power produces larger data-rate gains than operating without energy harvesting.
  • Q-learning approximates optimal values more closely than the iterative algorithm after sufficient training in linear models.
  • EH-enabled HAPS-SMBS nodes deliver measurably higher data rates than conventional systems without harvesting.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Persistent aerial coverage could become feasible in remote regions if energy sharing between platforms proves reliable.
  • The coordination role of the mother HAPS might scale to dynamic UAV swarms that share energy on demand.
  • Ground-station integration could let the system adapt harvesting factors in real time based on traffic load.
  • Atmospheric and mobility effects omitted in the model would need separate validation before deployment.

Load-bearing premise

Wireless energy can be harvested from nearby HAPS signals with enough efficiency to produce real performance gains, without accounting for atmospheric losses or platform motion.

What would settle it

A side-by-side field measurement of harvested energy and achieved data rate on moving HAPS platforms under real atmospheric conditions versus the paper's simulated non-EH baseline.

Figures

Figures reproduced from arXiv: 2604.17169 by Faicel Khennoufa, Ferdi Kara, Halim Yanikomeroglu, Khelil Abdellatif, Metin Ozturk, Safwan Alfattani.

Figure 1
Figure 1. Figure 1: Generic architecture of HAPS-SMBS supported by the EH scheme. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Block diagram of energy harvesting and informa [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: HAPS-SMBS supported by the EH scheme. the wavelength, c is the speed of light in a vacuum, f is the frequency, whereas Gt and Gr are the transmitter and receiver antenna gains, respectively. Likewise, to represent the dynamics of the RF energy conversion efficiency for various input power levels, we employ a realistic and parametric non-linear EH model. The logistic function-based non-linear EH model was i… view at source ↗
Figure 4
Figure 4. Figure 4: Data rate w.r.t. transmit power (Pt): Comparison between EH and without EH. 17 17.5 18 18.5 19 19.5 20 20.5 21 d AP2 (Km) 1.5 2 2.5 3 Data Rate (bps) 1010 Without EH Linear EH Non-linear EH Linear EH (Theorem 1) Non-linear EH (Theorem 2) [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Data rate w.r.t. dAP2 (Km): Comparison between the EH with and without optimization (Theorems 1 and 2) and without EH. A. Performance Evaluation of Proposed Optimization In this subsection, we evaluate the effectiveness of the proposed optimization frameworks, including the optimal positioning of the regular HAPS-SMBS (dA) derived in Theorems 1 and 2, as well as the joint optimization of positioning and th… view at source ↗
Figure 6
Figure 6. Figure 6: Average reward w.r.t. number of episodes: Com [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Data rate comparison between linear and non-linear [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Transmit power comparison between linear and [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Data rate comparison between linear and non-linear [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: Data Rate comparison for linear and non-linear [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 10
Figure 10. Figure 10: Output energy Ev EH under linear and non-linear models: (a) Ev EH w.r.t. transmit power with different frequencies (f); (b) Ev EH w.r.t. receiver antenna gain (Gr) with different distances (d1). at lower transmit power values. This can be explained as follows. Higher frequencies experience more attenuation, which limits the harvested energy. Furthermore, higher frequencies may be more vulnerable to enviro… view at source ↗
Figure 12
Figure 12. Figure 12: Total output energy under linear and non-linear [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗
read the original abstract

In sixth-generation (6G) cellular networks and beyond, aerial platforms, such as uncrewed aerial vehicles (UAVs) and high-altitude platform stations (HAPS), are anticipated to play a crucial role in enhancing connectivity, expanding network coverage, and supporting advanced communication services. However, the deployment of energy-efficient onboard communication systems is essential for their widespread adoption and effectiveness. The integration of energy harvesting (EH) into aerial platforms is envisioned to be pivotal in promoting both energy and cost efficiency. In this paper, we propose a new paradigm for aerial platforms in which they can collect energy from the transmitted signals of nearby aerial platforms. The paper employs a two-tier architecture with HAPS super-macro base stations (HAPS-SMBS) system: regular HAPS-SMBS nodes serve as base stations, while a "mother" HAPS-SMBS node acts as a manager to coordinate communications between regular HAPS-SMBS and the ground station, thus enabling wireless energy transfer. Specifically, we analyze the characteristics of EH-enabled HAPS-SMBS and compare their performance with those without EH. Additionally, we derive the optimal regular HAPS-SMBS positioning to mitigate signal attenuation and power loss. Subsequently, we formulate a joint optimization problem for regular HAPS-SMBS positioning and the EH factor. We solve the problem using the iterative distance and EH factor algorithm (IDFA); however, we employ $Q$-learning to verify its effectiveness. Our findings indicate that, compared to conventional EH systems, IDFA and $Q$-learning exhibit higher data rate performance. In contrast, $Q$-learning outperforms IDFA systems in linear modelswith intensive training in approximating optimal values. Furthermore, maximizing transmit power achieves higher gains than systems without EH.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes a two-tier HAPS architecture for 6G networks in which a coordinating 'mother' HAPS-SMBS node enables wireless energy transfer to regular HAPS-SMBS nodes that serve as base stations. It analyzes EH-enabled HAPS-SMBS performance versus non-EH systems, derives optimal regular HAPS-SMBS positioning to reduce attenuation, formulates a joint optimization of positioning and EH factor, solves it via the proposed Iterative Distance and EH Factor Algorithm (IDFA), and employs Q-learning for verification. The central claims are that IDFA and Q-learning yield higher data rates than conventional EH baselines, that Q-learning outperforms IDFA under intensive training in linear models, and that maximizing transmit power produces higher gains than non-EH systems.

Significance. If the optimization procedure and reported gains can be placed on a rigorous footing with convergence guarantees and reproducible simulations, the work would offer a concrete contribution to energy-efficient aerial platform design by showing how inter-platform wireless power transfer and positioning can be jointly managed. The two-tier coordination idea and the explicit comparison of an iterative heuristic against reinforcement learning are potentially useful for the community, but the absence of supporting analysis currently prevents the claims from being actionable.

major comments (3)
  1. [Abstract / IDFA section] Abstract and IDFA description: the paper asserts that IDFA solves the joint positioning-plus-EH-factor problem and delivers higher data rates than conventional EH, yet supplies neither a convergence analysis, iteration bound, nor optimality gap for IDFA. Because the headline performance superiority rests on IDFA reaching the claimed operating points, the lack of these guarantees is load-bearing.
  2. [Abstract] Abstract: the statement that 'Q-learning outperforms IDFA systems in linear models with intensive training' directly indicates that IDFA returns only locally good solutions. Without a quantitative comparison of the IDFA–Q-learning gap or a benchmark against global search / convex relaxation, the claim that IDFA itself improves upon conventional EH cannot be secured.
  3. [EH analysis and positioning section] EH modeling and positioning derivation: the feasibility of meaningful energy harvesting from nearby HAPS signals is asserted without accounting for atmospheric attenuation, Doppler due to platform motion, or realistic EH circuit efficiency curves. These factors directly affect whether the derived optimal positioning and EH factor produce the claimed rate gains.
minor comments (2)
  1. [Abstract] Abstract contains a typographical error: 'linear modelswith' should be 'linear models with'.
  2. [System model] Notation for the EH factor and the 'mother HAPS-SMBS' entity is introduced without a clear symbol table or consistent definition across the optimization formulation.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which help improve the rigor of our work. We address each major comment point by point below, outlining the specific revisions planned for the next manuscript version.

read point-by-point responses

  1. Referee: [Abstract / IDFA section] Abstract and IDFA description: the paper asserts that IDFA solves the joint positioning-plus-EH-factor problem and delivers higher data rates than conventional EH, yet supplies neither a convergence analysis, iteration bound, nor optimality gap for IDFA. Because the headline performance superiority rests on IDFA reaching the claimed operating points, the lack of these guarantees is load-bearing.

    Authors: We agree that the absence of a formal convergence analysis for IDFA weakens the claims. IDFA is an alternating iterative procedure that successively optimizes positioning and the EH factor. In the revised manuscript we will add a dedicated subsection proving convergence to a stationary point (under the Lipschitz continuity of the rate function and bounded step sizes) and reporting empirical iteration counts from the simulations. We will also quantify the optimality gap by comparing IDFA solutions against exhaustive search on reduced-scale instances. revision: yes

  2. Referee: [Abstract] Abstract: the statement that 'Q-learning outperforms IDFA systems in linear models with intensive training' directly indicates that IDFA returns only locally good solutions. Without a quantitative comparison of the IDFA–Q-learning gap or a benchmark against global search / convex relaxation, the claim that IDFA itself improves upon conventional EH cannot be secured.

    Authors: The referee is correct that the statement implies IDFA may reach only local solutions. To secure the improvement claim, we will revise the abstract and add a new results subsection that reports the numerical gap (in bps/Hz) between IDFA and Q-learning across all simulated scenarios. We will further benchmark IDFA against a convex relaxation obtained by successive convex approximation and, where tractable, against global search, thereby placing the gains over non-EH baselines on firmer ground. revision: yes

  3. Referee: [EH analysis and positioning section] EH modeling and positioning derivation: the feasibility of meaningful energy harvesting from nearby HAPS signals is asserted without accounting for atmospheric attenuation, Doppler due to platform motion, or realistic EH circuit efficiency curves. These factors directly affect whether the derived optimal positioning and EH factor produce the claimed rate gains.

    Authors: We acknowledge that the present model uses ideal free-space propagation. In the revision we will replace the EH link model with one that includes atmospheric attenuation (via ITU-R recommendations for HAPS altitudes), Doppler shift arising from platform velocity, and a realistic RF-to-DC efficiency curve drawn from measured rectenna data. The optimal positioning derivation and all rate comparisons will be recomputed under the updated model, with the changes clearly highlighted. revision: yes

Circularity Check

0 steps flagged

No significant circularity; optimization and verification steps remain independent of fitted inputs

full rationale

The paper derives optimal HAPS-SMBS positioning from path-loss considerations, formulates a joint optimization over positioning and EH factor, introduces IDFA as an iterative solver, and invokes Q-learning solely for verification against conventional EH baselines. No equations or steps reduce by construction to the same data or parameters used for evaluation; IDFA is presented as a new algorithm without self-referential fitting, and performance claims rest on explicit comparisons rather than tautological renaming or self-citation chains. The derivation chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The proposal rests on standard wireless EH assumptions and introduces a new coordination entity; no independent evidence for practical EH gains between HAPS is provided.

free parameters (2)
  • EH factor
    Jointly optimized with HAPS positioning to balance energy harvesting and communication performance.
  • regular HAPS positioning
    Optimized to mitigate signal attenuation and power loss.
axioms (1)
  • domain assumption Wireless energy can be harvested from RF signals transmitted by nearby HAPS platforms
    Central premise enabling the EH capability in the two-tier system.
invented entities (1)
  • mother HAPS-SMBS node no independent evidence
    purpose: Acts as manager to coordinate communications and enable wireless energy transfer between regular HAPS-SMBS and ground station
    New entity introduced to facilitate the two-tier architecture and EH coordination.

pith-pipeline@v0.9.0 · 5655 in / 1325 out tokens · 46428 ms · 2026-05-10T05:55:19.279212+00:00 · methodology

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