arxiv: 2604.26741 · v1 · submitted 2026-04-29 · 💻 cs.IT · eess.SP· math.IT· math.OC

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Analytically Characterized Optimal Power Control for Signal-Level-Integrated Sensing, Computing and Communication in Federated Learning

Paul Zheng , Yao Zhu , Xiaopeng Yuan , Yulin Hu , Anke Schmeink

Authors on Pith no claims yet

Pith reviewed 2026-05-07 10:40 UTC · model grok-4.3

classification 💻 cs.IT eess.SPmath.ITmath.OC

keywords power controlintegrated sensing and communicationfederated learningover-the-air computationconvex optimizationAirComptarget detection

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The pith

A variable transformation turns the non-convex joint power and scaling problem for sensing-integrated AirComp federated learning into an equivalent convex form solvable optimally in polynomial time.

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

The paper shows how to allocate transmit powers and a receive scaling factor so that the same waveform from edge devices can simultaneously sense a target and perform over-the-air model aggregation for federated learning. The objective is to minimize the distortion in the aggregated model while keeping the sensing detection performance above a required threshold. Although the original formulation is non-convex, the authors prove that a change of variables produces an equivalent convex problem whose solution yields the globally optimal powers and scaling factor. An algorithm that exploits the resulting analytical optimality conditions computes this solution with polynomial complexity. This matters because it removes the need for slow iterative searches in resource-constrained IoT networks where sensing, computation, and communication must share the same signal.

Core claim

The joint power and receive-scaling control problem for uplink signal-level integrated sensing, computing and communication in AirComp-based federated learning is non-convex in the original variables yet admits an equivalent convex reformulation after a suitable variable transformation. Exploiting analytical optimality properties, the authors derive a robust optimal algorithm of polynomial-time complexity that computes the transmit powers and receive scaling factor minimizing AirComp aggregation distortion subject to the joint target-detection requirement.

What carries the argument

The variable transformation that produces an equivalent convex problem, together with the closed-form optimality properties derived from it, which together enable direct computation of the optimal transmit powers and receive scaling factor.

If this is right

The minimal AirComp aggregation distortion is attained while the target detection constraint is satisfied.
Transmit powers and the receive scaling factor are obtained directly without numerical search over the original non-convex surface.
Federated learning convergence improves relative to heuristic or separate-design baselines.
The procedure remains numerically stable across varying channel and noise conditions.

Where Pith is reading between the lines

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

Similar variable changes may convexify power-allocation problems in other integrated sensing and computing scenarios that use over-the-air aggregation.
The polynomial-time property makes real-time re-optimization feasible when device channels or detection thresholds change between learning rounds.
Energy consumed per learning iteration could be reduced by reusing the same waveform for sensing, potentially lengthening battery life in large-scale IoT deployments.

Load-bearing premise

The joint target-detection requirement stays feasible for some choice of powers that also keeps the AirComp distortion finite.

What would settle it

A channel realization and detection threshold for which the algorithm outputs powers that violate the required detection probability, or for which a feasible point in the original variables achieves strictly lower distortion than the algorithm's output.

Figures

Figures reproduced from arXiv: 2604.26741 by Anke Schmeink, Paul Zheng, Xiaopeng Yuan, Yao Zhu, Yulin Hu.

**Figure 1.** Figure 1: Run time comparison between off-the-shelf NLP solver and proposed view at source ↗

**Figure 2.** Figure 2: Illustration of the two-user-group scenario. view at source ↗

**Figure 3.** Figure 3: Evaluation of MSE vs. second ED group location with different target view at source ↗

**Figure 6.** Figure 6: Test accuracy (top) and aggregation MSE (bottom) on CIFAR-10, view at source ↗

**Figure 5.** Figure 5: Test accuracy (top) and aggregation MSE (bottom) on MNIST, with view at source ↗

read the original abstract

In the Internet-of-Things (IoT) era, efficient functionality integration is essential to address the growing demands of communication, computation, and sensing. Signal-level integrated sensing, computing, and communication (Sig-ISCC) is envisioned, where a single waveform simultaneously supports sensing, computing and communication via over-the-air computation (AirComp). Meanwhile, federated learning (FL) is widely regarded as a promising distributed machine learning framework that enables network intelligence in a privacy-preserving and secure manner, and exhibits strong synergy with AirComp, which alleviates the communication bottleneck of FL. In this paper, we study uplink Sig-ISCC design for AirComp-FL with joint target detection. We formulate the joint power and receive-scaling control problem, where edge devices' transmitted signals should serve both sensing and AirComp purposes. The goal is to minimize the AirComp aggregation distortion subject to a joint target-detection requirement. Although the resulting problem is non-convex in the original variables, we show that it admits an equivalent convex reformulation after a suitable variable transformation. By exploiting analytical optimality properties, we develop a robust, optimal, and polynomial-time-complexity algorithm that efficiently achieves the optimal transmit powers and receive scaling factor. Simulation results validate the optimality and numerical robustness of the proposed algorithm and show its superior FL performance compared to baseline methods.

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.

Desk Editor's Note private letter to a colleague

The paper delivers a clean variable transformation that convexifies the joint power and scaling problem for Sig-ISCC AirComp-FL, yielding a polynomial-time optimal algorithm.

read the letter

The central result is that the non-convex uplink power control problem for AirComp aggregation distortion under a joint target-detection constraint admits an equivalent convex form after a suitable change of variables, which then supports an efficient optimal algorithm. This is the main new piece: prior work treated AirComp and ISAC separately, while this integrates them at signal level for FL with explicit detection requirements. The authors use analytical optimality properties to avoid iterative search, and the simulations confirm both optimality and improved FL accuracy over baselines. That part is useful and directly addresses a practical resource bottleneck in wireless edge learning. The formulation avoids circularity by tying the objective to measurable distortion and detection metrics rather than fitted parameters. The stress-test finds no internal inconsistency in the claimed equivalence, which is reassuring. A minor soft spot is that feasibility of the detection constraint under the power budget depends on channel and sensing models that need explicit verification in the full derivations; if those hold only in limited regimes, the practical scope narrows. The paper is aimed at researchers working on integrated sensing-communication-computation for distributed learning. Anyone optimizing wireless FL or ISAC systems will get concrete algorithmic value from the reformulation and the closed-form insights. It is worth sending to peer review because the core claim is falsifiable, the application is timely, and the analytical route is reproducible if the transformation steps check out.

Referee Report

1 major / 2 minor

Summary. The paper studies uplink signal-level integrated sensing, computing, and communication (Sig-ISCC) design for AirComp-based federated learning with joint target detection. It formulates a joint power and receive-scaling control problem to minimize AirComp aggregation distortion subject to a joint target-detection requirement. The central claim is that although the problem is non-convex in the original variables, it admits an equivalent convex reformulation after a suitable variable transformation; exploiting analytical optimality properties then yields a robust, optimal, polynomial-time algorithm for the transmit powers and receive scaling factor.

Significance. If the reformulation and algorithm hold, the work supplies an analytically characterized, computationally efficient solution for integrating sensing, computing, and communication in FL systems. The polynomial-time complexity and explicit optimality properties are strengths that could support practical deployment in resource-limited IoT settings; simulation validation of optimality and improved FL performance over baselines adds concrete evidence of utility.

major comments (1)

[Optimization Problem and Reformulation] The equivalence of the convex reformulation after variable transformation is load-bearing for the central claim. The manuscript should explicitly verify that the transformation preserves optimality and feasibility for the full range of channel realizations and detection thresholds stated in the problem setup (typically around the optimization-problem section), including any implicit assumptions on noise and sensing models.

minor comments (2)

[Abstract and Introduction] The abstract and introduction would benefit from a brief, explicit statement of the channel and detection models (e.g., Rayleigh fading parameters, detection probability thresholds) used to ensure the joint requirement remains feasible.
[Notation and Algorithm] Notation for the transformed variables and the receive scaling factor should be cross-checked for consistency between the problem statement, the reformulation, and the algorithm pseudocode.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation and the constructive comment on the optimization reformulation. We address the major comment below and will incorporate the requested clarification to strengthen the manuscript.

read point-by-point responses

Referee: [Optimization Problem and Reformulation] The equivalence of the convex reformulation after variable transformation is load-bearing for the central claim. The manuscript should explicitly verify that the transformation preserves optimality and feasibility for the full range of channel realizations and detection thresholds stated in the problem setup (typically around the optimization-problem section), including any implicit assumptions on noise and sensing models.

Authors: We agree that an explicit verification of the transformation's properties across the full problem domain will reinforce the central claim. In the current manuscript, the equivalence is established analytically in the proof of Theorem 1 (Section III-B), where the substitution p_k = exp(x_k) (with x_k real-valued) is shown to be bijective, the objective becomes convex, and the detection constraint is equivalently reformulated while preserving the feasible set and optimal value. To make this fully explicit as requested, we will add a dedicated verification paragraph (or short appendix) that (i) confirms bijectivity and optimality preservation for all channel realizations with |h_k| > 0 (as implicitly assumed in the uplink model), (ii) covers the complete range of detection thresholds 0 ≤ γ ≤ 1, and (iii) states the modeling assumptions (AWGN noise for both AirComp and sensing links, and a standard linear matched-filter sensing model for target detection). Boundary cases (e.g., γ = 0 or γ approaching the maximum feasible value) will be briefly discussed. This addition will be included in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on standard convex reformulation

full rationale

The paper poses a joint power and receive-scaling optimization problem whose objective (AirComp distortion) and constraints (target detection) are defined externally via channel and sensing models. It then applies a variable transformation to obtain an equivalent convex form and exploits analytical optimality conditions to derive a polynomial-time algorithm. No step reduces by construction to a fitted parameter, self-defined quantity, or load-bearing self-citation; the equivalence is a standard mathematical change-of-variables argument whose validity can be verified independently of the paper's results. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard wireless channel models and AirComp aggregation assumptions typical in the field, plus the feasibility of the joint sensing constraint; no new invented entities are introduced.

axioms (2)

domain assumption Standard additive white Gaussian noise and fading channel models for uplink transmission
Implicit in the power control and AirComp formulation for wireless IoT systems.
domain assumption Over-the-air computation accurately aggregates model updates via signal superposition
Core to the AirComp-FL setup described.

pith-pipeline@v0.9.0 · 5558 in / 1291 out tokens · 31450 ms · 2026-05-07T10:40:53.377172+00:00 · methodology

discussion (0)

Reference graph

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