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arxiv: 2604.10196 · v1 · submitted 2026-04-11 · 📡 eess.SP · cs.IT· math.IT

Energy-Efficient Hybrid Data Computation via Coordinated AirComp and Edge Offloading

Yudan Jiang , Xiao Tang , Jinxin Liu , Qinghe Du , Dusit Niyato , Zhu Han This is my paper

Pith reviewed 2026-05-10 16:03 UTC · model grok-4.3

classification 📡 eess.SP cs.ITmath.IT
keywords hybrid computationAirCompedge offloadingenergy efficiencyblock coordinate descentpower controluser scheduling6G networks
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The pith

Coordinating AirComp with edge offloading minimizes total energy use under capacity and accuracy limits.

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

The paper sets out to show that jointly optimizing user scheduling, power control, and transceiver scaling in a hybrid AirComp and edge-offloading system yields lower overall energy consumption than treating the two modes separately. The authors minimize the combined costs of data transmission and computation while enforcing limits on offloading capacity and aggregation accuracy. They apply a block coordinate descent procedure that alternates among the subproblems until the solution stabilizes. Simulations indicate that the resulting coordinated operating points consume noticeably less energy than baseline strategies.

Core claim

The central claim is that a block coordinate descent framework decomposes the energy-minimization task for hybrid AirComp and edge offloading into alternating subproblems of user scheduling, power control, and transceiver scaling; iterating these subproblems produces a feasible solution that satisfies the offloading-capacity and aggregation-accuracy constraints and delivers lower total energy than uncoordinated baselines.

What carries the argument

The block coordinate descent procedure that alternates among user scheduling, power control, and transceiver scaling subproblems to solve the joint energy-minimization problem.

Load-bearing premise

The formulation assumes that interference and resource competition between AirComp and edge offloading are fully captured by the stated capacity and accuracy constraints and that the iterative procedure converges to a useful point under realistic channel conditions.

What would settle it

Deploy the algorithm on a real wireless testbed with measured interference and check whether measured total energy remains below the baselines or whether the iterations fail to converge to a feasible point.

Figures

Figures reproduced from arXiv: 2604.10196 by Dusit Niyato, Jinxin Liu, Qinghe Du, Xiao Tang, Yudan Jiang, Zhu Han.

Figure 1
Figure 1. Figure 1: System model. computing offloading activity is indicated by a binary variable αk(i),    αk (i) ∈ {0, 1} , ∀k ∈ K, ∀i ∈ I, X k∈K αk (i) = 1, ∀i ∈ I, (2) where αk(i) = 1, if edge UE k is selected in time slot-i, and αk(i) = 0, otherwise. Thus, the aggregated signal received at the BS is y (i) = P j∈J hj (i)bj (i)sj + P k∈K αk(i)hk(i) p pk(i)xk + n(i), ∀i ∈ I, where hj (i), j ∈ J , is the channel between B… view at source ↗
Figure 2
Figure 2. Figure 2: Energy consumption versus the MSE threshold. 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Power budget of the edge UEs (w) 15 25 35 45 55 Energy consumption (J) Proposed scheme Equal offloading Channel inversion [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: Energy consumption versus the time length. [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Energy consumption under different offloaded data amount. [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
read the original abstract

The development of 6G networks brings an increasing variety of data services, which motivates the hybrid computation paradigm that coordinates the over-the-air computation (AirComp) and edge computing for diverse and effective data processing. In this paper, we address this emerging issue of hybrid data computation from an energy-efficiency perspective, where the coexistence of both types induces resource competition and interference, and thus complicates the network management. Accordingly, we formulate the problem to minimize the overall energy consumption including the data transmission and computation, subject to the offloading capacity and aggregation accuracy. We then propose a block coordinate descent framework that decomposes and solves the subproblems including the user scheduling, power control, and transceiver scaling, which are then iterated towards a coordinated hybrid computation solution. Simulation results confirm that our coordinated approach achieves significant energy savings compared to baseline strategies, demonstrating its effectiveness in creating a well-coordinated and sustainable hybrid computing environment.

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. The paper proposes coordinating over-the-air computation (AirComp) and edge offloading in 6G networks to minimize total energy consumption (transmission plus computation) subject to offloading capacity and aggregation accuracy constraints. A block coordinate descent (BCD) algorithm is developed that alternates over user scheduling, power control, and transceiver scaling subproblems; simulation results are presented to claim significant energy savings relative to baseline strategies.

Significance. If the BCD procedure can be shown to produce reliable operating points and the simulations accurately reflect realistic interference, the coordinated hybrid framework would offer a practical energy-efficient solution for mixed AirComp/MEC workloads. The decomposition into alternating subproblems is a standard, defensible approach for the non-convex joint problem and provides a concrete algorithmic template.

major comments (2)
  1. [Section IV] Section IV (BCD Algorithm): No convergence analysis, monotonicity argument, or stationary-point guarantee is supplied for the alternating optimization, even though the joint problem is non-convex due to the coupling of scheduling, power, and scaling variables through both the AirComp MSE constraint and the shared-spectrum offloading rate constraint. This directly affects the trustworthiness of the energy-savings numbers reported in the simulations.
  2. [Section V] Section V (Numerical Results): The claimed energy savings are presented without Monte-Carlo error bars, without the exact mathematical definitions of the three baseline strategies, and without any sensitivity study to channel estimation error or frequency-selective fading parameters. Because the central claim rests on these simulation outcomes, the lack of such details makes it impossible to judge whether the reported gains are robust.
minor comments (2)
  1. [Section II] Notation for the transceiver scaling factors and the AirComp MSE expression could be introduced earlier and used consistently; a small table summarizing all optimization variables would improve readability.
  2. [Abstract] The abstract states that simulations 'confirm significant energy savings' but does not quantify the savings or list the key simulation parameters; adding one sentence with these details would strengthen the summary.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We agree that additional analysis and details will strengthen the paper and plan to revise accordingly. Below we address each major comment point by point.

read point-by-point responses

  1. Referee: [Section IV] Section IV (BCD Algorithm): No convergence analysis, monotonicity argument, or stationary-point guarantee is supplied for the alternating optimization, even though the joint problem is non-convex due to the coupling of scheduling, power, and scaling variables through both the AirComp MSE constraint and the shared-spectrum offloading rate constraint. This directly affects the trustworthiness of the energy-savings numbers reported in the simulations.

    Authors: We acknowledge that the current manuscript lacks a formal convergence analysis for the BCD algorithm. In the revised version, we will add a dedicated subsection to Section IV that provides a monotonicity argument: each iteration of the alternating optimization yields a non-increasing value of the total energy objective when the subproblems are solved to optimality. We will also discuss conditions (e.g., when the subproblems admit unique solutions) under which the sequence converges to a stationary point of the original non-convex problem. While the joint formulation is indeed non-convex due to the indicated couplings, the decomposition into tractable subproblems remains valid, and our numerical results already show rapid practical convergence; the added analysis will further support the reliability of the reported energy savings. revision: yes

  2. Referee: [Section V] Section V (Numerical Results): The claimed energy savings are presented without Monte-Carlo error bars, without the exact mathematical definitions of the three baseline strategies, and without any sensitivity study to channel estimation error or frequency-selective fading parameters. Because the central claim rests on these simulation outcomes, the lack of such details makes it impossible to judge whether the reported gains are robust.

    Authors: We agree that the simulation section requires more rigorous supporting details. In the revised manuscript we will: (i) add Monte-Carlo error bars (standard deviation across independent channel realizations) to all performance figures; (ii) explicitly state the mathematical formulations of the three baseline strategies in Section V; and (iii) include a new sensitivity study examining the impact of channel estimation error variance and frequency-selective fading parameters on the achieved energy savings. These additions will allow readers to assess the robustness of the claimed gains under realistic conditions. revision: yes

Circularity Check

0 steps flagged

No circularity: optimization posed directly from energy terms; savings shown via external simulation comparison

full rationale

The paper formulates the energy-minimization objective and the offloading-capacity plus aggregation-accuracy constraints directly from the system model without embedding the target savings or any fitted parameter. Block coordinate descent is applied as a standard decomposition technique to the resulting non-convex program; the reported energy savings are obtained by running the algorithm on simulated channels and comparing the numerical outcomes against independent baseline strategies. No equation, subproblem solution, or convergence claim reduces the final performance numbers to a tautological restatement of the inputs, and no self-citation is invoked as the sole justification for the central result.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The abstract relies on standard wireless-network modeling assumptions without introducing new free parameters or postulated entities.

axioms (1)
  • domain assumption Wireless channels, interference, and computation energy costs can be expressed as deterministic functions of power, scheduling, and scaling variables.
    Implicit in the energy-minimization formulation and constraint set.

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