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arxiv: 2606.22534 · v1 · pith:M5Z25JFAnew · submitted 2026-06-21 · 📡 eess.SY · cs.SY

LAWNs Meet SWIPT: Beamforming and Power Splitting Optimization for Predictive Control

Jun Wu , Wenchao Liu , Weijie Yuan , Nanchi Su This is my paper

Pith reviewed 2026-06-26 09:43 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords SWIPTLAWNbeamformingpower splittingmodel predictive controltrajectory optimizationUASsemidefinite relaxation
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The pith

A two-stage MPC and SDR-SCA framework jointly optimizes control inputs, beamforming vectors, and power splitting ratios for SWIPT-enabled LAWNs.

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

The paper develops a SWIPT system in which a multi-antenna base station delivers both control commands and wireless energy to a fleet of UASs. Reference trajectories are first built with stream-function theory to guarantee collision avoidance around mobile no-fly zones. A real-time joint optimization then minimizes wireless control cost while maximizing harvested energy by tuning predictive control inputs, beamforming, and power-splitting ratios. The non-convex problem is solved in two stages: MPC generates the control sequence, after which an iterative SDR-SCA algorithm optimizes the wireless variables and the SDR relaxation is shown to be tight. Numerical results indicate that the resulting design improves both trajectory tracking accuracy and harvested energy relative to benchmark schemes.

Core claim

By constructing collision-free reference trajectories via stream functions and then solving a joint non-convex optimization of MPC control inputs, transmit beamforming vectors, and power-splitting ratios with a two-stage framework that applies SDR (proven tight) followed by SCA, the system enables a multi-antenna base station to guide multiple UASs along safe paths while simultaneously transferring information and energy.

What carries the argument

Two-stage optimization framework: MPC generates predictive control inputs; SDR-SCA iteration then optimizes beamforming vectors and power-splitting ratios, with a proof that the SDR relaxation is tight.

If this is right

  • UAS fleets can maintain accurate trajectory tracking while harvesting sufficient energy to extend flight time.
  • The same base station can simultaneously serve multiple UASs without separate power or control channels.
  • Real-time implementation becomes feasible because the SDR tightness removes the need for randomization or further approximation.
  • The approach directly supports battery-limited operation in low-altitude networks that must avoid dynamic no-fly zones.

Where Pith is reading between the lines

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

  • The same joint-control-plus-energy formulation could be applied to other wireless-controlled mobile platforms such as ground robots or surface vehicles.
  • Because the SDR step is proven tight, the computational cost scales mainly with the number of antennas and power-splitting variables rather than with combinatorial search.
  • Extending the stream-function construction to three-dimensional NFZs would be a direct next step for urban air-mobility scenarios.

Load-bearing premise

The non-convex joint optimization admits a tight SDR solution and the stream-function trajectories stay collision-free under the real-time wireless constraints and mobile NFZs.

What would settle it

A simulation or hardware test in which the SDR relaxation gap is nonzero or in which tracking error and harvested energy fail to exceed the benchmark schemes when mobile NFZs are present.

Figures

Figures reproduced from arXiv: 2606.22534 by Jun Wu, Nanchi Su, Weijie Yuan, Wenchao Liu.

Figure 1
Figure 1. Figure 1: The considered SWIPT-LAWN scenario, where the BS [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Static NFZ avoidance via stream functions (30), where [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Reference trajectory generation and the corresponding [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The CDF of trajectory tracking performance in terms [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: The average harvested energy versus the maximum [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The average harvested energy vs. transmit antenna [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The average harvested energy versus the required SE [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
read the original abstract

Simultaneous wireless information and power transfer (SWIPT) has emerged as a promising paradigm for enabling sustainable connectivity in battery-limited low-altitude wireless networks (LAWNs). This paper investigates a SWIPT-enabled LAWN system in which a multi-antenna base station (BS) simultaneously delivers control information and wireless energy to a fleet of uncrewed aircraft systems (UASs) via power splitting. In particular, the BS remotely guides the UASs to accurately track predefined reference trajectories toward their destinations while avoiding multiple mobile no-fly zones (NFZs). To guarantee collision-free path planning, we first construct smooth and safe reference trajectories using stream function theory. Then, a real-time optimization problem is formulated, which jointly takes into account the wireless control cost and energy sustainability by optimizing control inputs, transmit beamforming vectors, and the power splitting ratios. To address the resultant non-convex problem, a two-stage optimization framework is proposed. First, we develop a model predictive control (MPC)-based method to generate predictive control inputs. Subsequently, we derive a computationally efficient iterative algorithm to optimize the beamforming vectors and power splitting ratios by applying semidefinite relaxation (SDR) and successive convex approximation (SCA) techniques. We further prove that the SDR is tight for our formulation. Extensive numerical results demonstrate that our proposed design significantly outperforms benchmark schemes in terms of tracking accuracy and harvested energy, thereby validating its effectiveness for sustainable implementation in LAWN systems.

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 / 1 minor

Summary. The paper proposes a SWIPT-enabled LAWN system in which a multi-antenna BS delivers both control signals and energy to a fleet of UASs via power splitting. Safe reference trajectories are constructed via stream function theory to avoid mobile NFZs. A joint optimization problem is formulated over control inputs, beamforming vectors, and power splitting ratios to balance tracking performance and harvested energy. The non-convex problem is solved via a two-stage framework: MPC generates predictive control inputs, after which SDR combined with SCA optimizes the wireless variables; SDR tightness is proved for the formulation. Numerical results are claimed to show substantial gains over benchmarks in tracking accuracy and energy harvesting.

Significance. If the two-stage procedure can be shown to produce feasible and near-optimal solutions to the original joint problem, the work would provide a practical route to sustainable wireless control of mobile UAS fleets. The combination of stream-function trajectory planning with SDR-tight beamforming/PS optimization is technically interesting and directly relevant to energy-constrained aerial networks. The explicit proof of SDR tightness is a positive feature that strengthens the algorithmic contribution.

major comments (2)
  1. [Abstract] Abstract (paragraph on the real-time optimization problem and two-stage framework): The manuscript states that the problem 'jointly' optimizes control inputs, beamforming vectors, and power splitting ratios, yet the proposed method first fixes control inputs via MPC (under ideal delivery) and only then optimizes the wireless variables. This separation means the chosen inputs may violate the original joint constraints once actual received control signals (affected by the realized PS ratios and beamforming) are considered, especially under mobile NFZs; the claimed performance therefore rests on an unverified assumption that the decoupled solution remains feasible.
  2. [Abstract] Abstract (SDR tightness claim): The statement that 'we further prove that the SDR is tight for our formulation' applies only to the second-stage problem with fixed control inputs. No argument is given that the overall two-stage procedure solves (or approximates) the original joint non-convex program, nor that the fixed MPC inputs remain admissible after the wireless stage; this gap directly undermines the central claim of joint optimization.
minor comments (1)
  1. The abstract refers to 'extensive numerical results' without indicating the number of Monte-Carlo runs, the range of NFZ velocities, or whether confidence intervals are reported; adding these details would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and valuable comments. We provide point-by-point responses to the major comments and indicate the revisions we will make to address the concerns.

read point-by-point responses

  1. Referee: [Abstract] Abstract (paragraph on the real-time optimization problem and two-stage framework): The manuscript states that the problem 'jointly' optimizes control inputs, beamforming vectors, and power splitting ratios, yet the proposed method first fixes control inputs via MPC (under ideal delivery) and only then optimizes the wireless variables. This separation means the chosen inputs may violate the original joint constraints once actual received control signals (affected by the realized PS ratios and beamforming) are considered, especially under mobile NFZs; the claimed performance therefore rests on an unverified assumption that the decoupled solution remains feasible.

    Authors: We agree with the referee that the two-stage framework decouples the optimization, with MPC generating control inputs under the assumption of ideal signal delivery. This approach does not inherently guarantee that the resulting solution satisfies the original joint constraints when accounting for the actual received signals influenced by beamforming and power splitting, especially in the presence of mobile NFZs. The performance claims are based on the proposed decoupled method rather than a verified joint solution. To address this, we will revise the abstract to more accurately describe the sequential nature of the optimization without implying a fully joint solution. We will also add a discussion section on the feasibility considerations of the two-stage approach. revision: yes

  2. Referee: [Abstract] Abstract (SDR tightness claim): The statement that 'we further prove that the SDR is tight for our formulation' applies only to the second-stage problem with fixed control inputs. No argument is given that the overall two-stage procedure solves (or approximates) the original joint non-convex program, nor that the fixed MPC inputs remain admissible after the wireless stage; this gap directly undermines the central claim of joint optimization.

    Authors: The SDR tightness is proved specifically for the second-stage wireless optimization problem with fixed control inputs. We do not claim or prove that the two-stage procedure solves the original joint non-convex program or that the MPC inputs remain admissible post-optimization. This is a limitation of the current approach. We will revise the abstract to clarify that the SDR tightness applies to the beamforming and power splitting optimization subproblem. Furthermore, we will update the text to avoid overstating the joint optimization aspect and include remarks on the approximation nature of the method. revision: yes

Circularity Check

0 steps flagged

Derivation chain is self-contained with independent optimization stages

full rationale

The paper formulates a joint optimization over control inputs, beamforming vectors and power splitting ratios, addressed by a two-stage framework consisting of MPC to generate predictive control inputs followed by SDR+SCA for the wireless variables, plus an explicit proof that SDR is tight. No load-bearing step reduces by construction to a fitted input, self-definition, or self-citation chain; stream-function trajectory construction and the MPC stage rely on external methods, while the numerical validation compares against independent benchmarks. The derivation therefore remains non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no extractable free parameters, axioms or invented entities; the central claim rests on unstated modeling assumptions about channel conditions, trajectory safety and solver tightness.

pith-pipeline@v0.9.1-grok · 5799 in / 986 out tokens · 13812 ms · 2026-06-26T09:43:10.956997+00:00 · methodology

discussion (0)

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Reference graph

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