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arxiv: 2604.04147 · v1 · submitted 2026-04-05 · 📡 eess.SP

Wireless Energy Transfer from Space to Ground via Satellite Constellation Grids

Mohammad Shehab , Osmel M. Rosabal , Onel L. A. Lopez , Mohamed-Slim Alouini This is my paper

Pith reviewed 2026-05-13 16:52 UTC · model grok-4.3

classification 📡 eess.SP
keywords wireless energy transfersatellite constellationmaximum ratio transmissionharvested energyremote chargingspace-to-groundline-of-sight
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The pith

Satellite grids can deliver milli-joule energy to remote devices via wireless transfer during visibility periods.

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

This paper develops a framework for charging wirelessly chargeable devices in hard-to-reach locations using a constellation of multi-antenna satellites. It derives closed-form expressions for the energy harvested at the device under maximum ratio transmission beamforming, ensuring the received power exceeds a circuit threshold. The analysis shows that milli-joule amounts of energy are feasible during the short time the device is in line of sight of the satellite grid. Factors like the number of satellites, their height, operating frequency, and the grid's tilt affect how much energy gets transferred. This approach targets scenarios where traditional power infrastructure is absent, such as disaster zones or isolated areas.

Core claim

A constellation of satellites equipped with multiple antennas can wirelessly transfer energy to a ground device by coherently combining signals through maximum ratio transmission, yielding closed-form expressions for harvested energy that meet the device's charging threshold and deliver milli-joule levels over the visibility window.

What carries the argument

Maximum ratio transmission (MRT) beamforming across a grid of multi-antenna satellites, which aligns phases to maximize power delivery to the line-of-sight device.

If this is right

  • Energy harvesting scales with the number of satellites in the grid.
  • Lower satellite altitudes increase harvested energy due to reduced path loss.
  • Optimal charging frequencies balance propagation and device efficiency.
  • Grid inclination affects the duration of visibility and thus total energy delivered.

Where Pith is reading between the lines

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

  • Such systems could integrate with existing satellite communication networks for dual use in power and data.
  • Extending to moving devices would require dynamic beam tracking.
  • Atmospheric effects at higher frequencies might limit practical ranges beyond the modeled LOS assumption.

Load-bearing premise

The device stays in perfect line-of-sight with all satellites in the grid, allowing ideal beamforming without interference or atmospheric losses.

What would settle it

Measure the actual harvested energy at a ground device when a real satellite constellation passes overhead and compare it to the predicted milli-joule levels under the derived formulas.

Figures

Figures reproduced from arXiv: 2604.04147 by Mohamed-Slim Alouini, Mohammad Shehab, Onel L. A. Lopez, Osmel M. Rosabal.

Figure 1
Figure 1. Figure 1: A satellite grid transferring energy to a WCD. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Harvested energy vs the number of satellites for different WCD [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Harvested energy vs the operating frequency for different number of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: a illustrates how the charging efficiency is affected by the satellite azimuth angle ϕ. The main takeaway here is that, the charging efficiency is very sensitive to ϕ as it decreases rapidly and energy availability is not well exploited when the satellite plane is slightly inclined, specially for higher receiver sensitivity and lower number of satellites. Therefore, when multiple satellite swarms are avail… view at source ↗
read the original abstract

This letter presents a framework for space-to-ground wireless energy transfer (WET) for wirelessly chargeable devices (WCD) located in remote areas or disaster situations. We consider a grid of multi-antenna satellites that charge a WCD within line-of-sight. Closed-form expressions for harvested energy are derived considering maximum ratio transmission (MRT) ensuring that the WCD meets its circuit charging threshold $P_{th}$. Simulations elucidate that milli-joule-level energy can be harvested during satellite grid visibility, with charging efficiency influenced by the number of satellites, their altitude, charging frequency, and grid inclination.

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

2 major / 2 minor

Summary. This paper proposes a framework for space-to-ground wireless energy transfer (WET) using a grid of multi-antenna satellites to charge wirelessly chargeable devices (WCDs) in remote or disaster areas. It derives closed-form expressions for harvested energy at the WCD via maximum ratio transmission (MRT) beamforming that ensures the received power exceeds the circuit threshold P_th. Simulations show that milli-joule levels of energy can be harvested during the satellite grid visibility window, with efficiency depending on the number of satellites, altitude, charging frequency, and grid inclination.

Significance. If the closed-form expressions hold under realistic conditions, the work provides analytical tools for evaluating satellite-based WET systems and demonstrates the potential for milli-joule energy delivery to remote devices without terrestrial infrastructure. The use of standard MRT applied to satellite geometries offers tractable expressions, and the parameter sweeps in simulations give initial design insights. However, the idealized assumptions limit immediate applicability to practical orbital scenarios.

major comments (2)
  1. [Abstract and derivation of harvested energy expressions] The closed-form harvested energy expressions (Abstract) rest on a static perfect-MRT LOS assumption with constant channel vectors throughout the visibility window. Given satellite orbital velocities of ~7 km/s, the geometry, distances, and phases vary continuously; no explicit time integration over the visibility interval is provided to justify replacing the instantaneous MRT gain with a fixed closed-form result. This is load-bearing for the milli-joule energy claim and the assertion that P_th is met.
  2. [Simulations section] The weakest assumption (perfect simultaneous LOS to the entire grid with no atmospheric or interference losses) is not validated against real propagation data or orbital dynamics. The simulations appear to use fixed parameters (altitude, frequency, inclination) without benchmarking against time-varying channel models or existing satellite propagation standards.
minor comments (2)
  1. [Abstract] The abstract would benefit from explicitly stating the assumed visibility duration and orbital period used to obtain the milli-joule figures.
  2. [System model] Notation for the MRT beamforming vector and the definition of P_th should be introduced earlier with a clear reference to the system model equation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive feedback on our manuscript. We address the major comments point by point below, indicating where revisions will be incorporated.

read point-by-point responses

  1. Referee: [Abstract and derivation of harvested energy expressions] The closed-form harvested energy expressions (Abstract) rest on a static perfect-MRT LOS assumption with constant channel vectors throughout the visibility window. Given satellite orbital velocities of ~7 km/s, the geometry, distances, and phases vary continuously; no explicit time integration over the visibility interval is provided to justify replacing the instantaneous MRT gain with a fixed closed-form result. This is load-bearing for the milli-joule energy claim and the assertion that P_th is met.

    Authors: The referee correctly identifies that our derivation assumes a static geometry for deriving the closed-form expressions. This assumption is made to obtain analytically tractable results for the harvested energy under MRT beamforming. We agree that orbital motion introduces time variation. In the revised manuscript, we will add a paragraph in the system model section discussing the approximation, explaining that the visibility window is treated as a snapshot for the purpose of closed-form analysis, and that the milli-joule claim is based on this instantaneous model scaled by the window duration. We will also include a note that full time integration would require numerical methods and is left for future work. This revision clarifies the scope without changing the expressions. revision: partial

  2. Referee: [Simulations section] The weakest assumption (perfect simultaneous LOS to the entire grid with no atmospheric or interference losses) is not validated against real propagation data or orbital dynamics. The simulations appear to use fixed parameters (altitude, frequency, inclination) without benchmarking against time-varying channel models or existing satellite propagation standards.

    Authors: We acknowledge the idealized assumptions in the simulations, which focus on the potential of the proposed framework under perfect LOS conditions. The fixed parameters are representative of typical LEO constellations. To address this, we will revise the simulations section to explicitly state the assumptions and reference standard models such as the 3GPP NTN channel models or ITU-R P.618 for atmospheric effects, noting that losses would reduce the harvested energy but the framework remains applicable. Benchmarking against full orbital dynamics is beyond the scope of this letter but will be mentioned as a limitation. No changes to the simulation results are needed as they illustrate the analytical expressions. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivations apply standard MRT to satellite geometry

full rationale

The paper derives closed-form harvested energy expressions by applying maximum ratio transmission (MRT) beamforming to a static line-of-sight satellite grid model. These steps follow directly from standard wireless channel and beamforming formulas without any reduction to fitted parameters by construction, self-definitional loops, or load-bearing self-citations. Simulation results depend on explicit inputs (altitude, frequency, number of satellites) that are not claimed as predictions but as evaluations under the stated assumptions. The derivation chain remains self-contained and independent of the target results.

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 0 invented entities

The framework rests on standard wireless propagation and beamforming assumptions rather than new postulates. Simulation parameters such as satellite count, altitude, frequency, and inclination function as free variables explored numerically rather than fitted constants. No new physical entities are introduced.

free parameters (4)
  • number of satellites
    Varied in simulations to demonstrate influence on harvested energy levels.
  • satellite altitude
    Parameter that affects path loss and visibility duration in the energy calculations.
  • charging frequency
    Input that influences propagation and efficiency in the closed-form expressions.
  • grid inclination
    Geometric parameter controlling satellite visibility window over the target device.
axioms (2)
  • domain assumption Line-of-sight propagation holds between the satellite grid and the wireless chargeable device throughout the visibility period.
    Invoked to enable wireless energy transfer without blockage or fading models.
  • domain assumption Maximum ratio transmission beamforming can be implemented perfectly across the satellite grid.
    Used to derive the closed-form harvested-energy expressions.

pith-pipeline@v0.9.0 · 5407 in / 1422 out tokens · 33680 ms · 2026-05-13T16:52:07.560612+00:00 · methodology

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Reference graph

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