Optimized Power Control for Multi-User Integrated Sensing and Edge AI

Biao Dong; Bin Cao

arxiv: 2510.21378 · v4 · pith:IX6VIIGUnew · submitted 2025-10-24 · 📡 eess.SP

Optimized Power Control for Multi-User Integrated Sensing and Edge AI

Biao Dong , Bin Cao This is my paper

Pith reviewed 2026-05-21 21:09 UTC · model grok-4.3

classification 📡 eess.SP

keywords integrated sensing and edge AIAirComppower allocationtransceiver optimizationTDMFDMcollaborative inferenceover-the-air computation

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The pith

Closed-form power allocation optimizes transceiver designs in integrated sensing and edge AI systems for TDM and FDM.

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

The paper aims to show that optimal power allocation for devices in a multi-user system combining target sensing and collaborative edge inference can be derived in closed form. It does this by introducing two proxies that link the errors in over-the-air feature aggregation to the final inference performance. A sympathetic reader would care because these designs could lead to more efficient use of wireless resources in applications where sensing and AI inference happen together at the network edge. The work covers both time-division and frequency-division approaches, highlighting different optimization structures.

Core claim

Optimal transceiver designs in terms of closed-form power allocation are derived for both time-division multiplexing (TDM) and frequency-division multiplexing (FDM) settings, revealing threshold-based and dual-decomposition structures, respectively, using computation-optimal and decision-optimal proxies to characterize AirComp error and inference performance.

What carries the argument

The computation-optimal proxy minimizing aggregation distortion and the decision-optimal proxy maximizing inter-class separability, which connect AirComp errors to inference quality and enable closed-form power control derivations.

Load-bearing premise

The two proposed proxies sufficiently capture the relationship between AirComp error and actual inference performance for the purpose of transceiver optimization.

What would settle it

An experiment showing that inference performance does not align with the predictions from the computation-optimal or decision-optimal proxies under the derived power allocations would falsify the utility of these proxies for optimization.

Figures

Figures reproduced from arXiv: 2510.21378 by Biao Dong, Bin Cao.

**Figure 1.** Figure 1: III. METRICS To quantify the classification performance, we introduce two proxies, namely the computation-optimal and decision-optimal proxies. A theoretical justification for both proxies is provided by analyzing their relationship with the correct classification probability. A. Computation-Optimal Proxy The computation-optimal proxy is built upon the concept of the classification margin γ [11], [16], whi… view at source ↗

**Figure 2.** Figure 2: Inference performance comparison under different system parameters: (a) varying [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

read the original abstract

This work investigates an integrated sensing and edge artificial intelligence (ISEA) system, where multiple devices first transmit probing signals for target sensing and then offload locally extracted features to the access point (AP) via analog over-the-air computation (AirComp) for collaborative inference. To characterize the relationship between AirComp error and inference performance, two proxies are established: the \emph{computation-optimal} proxy that minimizes the aggregation distortion, and the \emph{decision-optimal} proxy that maximizes the inter-class separability, respectively. Optimal transceiver designs in terms of closed-form power allocation are derived for both time-division multiplexing (TDM) and frequency-division multiplexing (FDM) settings, revealing threshold-based and dual-decomposition structures, respectively. Experimental results validate the theoretical findings.

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 gives closed-form power allocations for a sensing-plus-AirComp edge inference system using two proxies, but the real test is whether those proxies reliably improve actual classification accuracy.

read the letter

The main point is that this paper finds closed-form power allocation strategies for a multi-user system that combines target sensing with over-the-air computation for collaborative edge inference. They split the problem into TDM and FDM cases and get explicit solutions based on two proxies for the AirComp error impact. What the work does is bring together the sensing phase and the feature aggregation phase under one optimization framework. The threshold-based structure for TDM and the dual-decomposition for FDM are the concrete outputs, and they claim these come from standard convex methods applied to the proxies. If the derivations are correct, that gives practitioners some ready-to-use rules without needing heavy numerical solvers each time. The abstract also mentions experimental validation, which is good to see for this kind of optimization paper. The weaker part is the choice of proxies. One minimizes aggregation distortion and the other maximizes inter-class separability. These are sensible stand-ins, but the real test is whether optimizing them leads to better end-to-end classification accuracy compared to just minimizing MSE or using other heuristics. The stress test note flags this, and without seeing the full experiments I can't tell if they ran ablations against direct accuracy optimization or included proper baselines with error bars. If the validation is only on the proxy values themselves, the optimality claim for the ISEA system stays conditional. This paper is aimed at people working on integrated sensing and communication for 6G edge AI applications. A reader who needs specific power control designs for similar setups could pull the formulas and adapt them. It is not a broad theoretical advance but a solid applied optimization result. I would recommend sending it for peer review. The math appears grounded in standard models, the topic is relevant, and the closed-forms are a plus even if the proxy-to-accuracy mapping needs more scrutiny in revision.

Referee Report

2 major / 1 minor

Summary. The manuscript investigates an integrated sensing and edge AI (ISEA) system in which multiple devices perform target sensing via probing signals and then offload locally extracted features to an access point using analog over-the-air computation (AirComp) for collaborative inference. Two proxies are introduced to relate AirComp error to inference performance: a computation-optimal proxy that minimizes aggregation distortion and a decision-optimal proxy that maximizes inter-class separability. Closed-form optimal power allocations are derived for both time-division multiplexing (TDM) and frequency-division multiplexing (FDM) settings, exhibiting threshold-based and dual-decomposition structures, respectively, with experimental results claimed to validate the derivations.

Significance. If the proxies prove faithful surrogates for end-to-end inference accuracy, the closed-form transceiver designs would provide efficient, low-complexity power control solutions for multi-user ISEA systems that integrate sensing, AirComp, and edge inference. The explicit structures (threshold for TDM, dual decomposition for FDM) and the use of standard convex optimization tools constitute a concrete contribution to resource allocation in integrated sensing-communication-AI scenarios.

major comments (2)

[Abstract and proxy-definition section] The central optimality claim for the derived power allocations rests on the unverified assumption that the two proxies (computation-optimal and decision-optimal) are sufficiently faithful surrogates for actual inference accuracy. The manuscript defines these proxies and states that experiments validate the findings, yet no ablation is described that directly compares inference accuracy under the proxy-optimized designs against either direct accuracy optimization or standard baselines (e.g., digital offloading or uniform power allocation). Without such evidence, the mapping from proxy optimum to classification performance remains conditional.
[Experimental results section] Experimental validation is asserted but lacks reported details on whether actual inference metrics (accuracy, F1-score) are measured, whether error bars or statistical significance are provided, and whether the simulations employ realistic classifiers or only linear proxies. If only proxy values are plotted, the load-bearing link between the closed-form solutions and end-to-end performance is not demonstrated.

minor comments (1)

[Abstract] The abstract ends with an extraneous 'respectively' that should be removed for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We appreciate the referee's constructive comments on our manuscript. We address each major comment below, clarifying the role of the proxies and the experimental validation, and indicate where revisions will be made.

read point-by-point responses

Referee: [Abstract and proxy-definition section] The central optimality claim for the derived power allocations rests on the unverified assumption that the two proxies (computation-optimal and decision-optimal) are sufficiently faithful surrogates for actual inference accuracy. The manuscript defines these proxies and states that experiments validate the findings, yet no ablation is described that directly compares inference accuracy under the proxy-optimized designs against either direct accuracy optimization or standard baselines (e.g., digital offloading or uniform power allocation). Without such evidence, the mapping from proxy optimum to classification performance remains conditional.

Authors: We agree that a direct ablation comparing proxy-optimized designs to explicit accuracy optimization would provide stronger support. The manuscript already compares the proposed threshold-based (TDM) and dual-decomposition (FDM) allocations against uniform power and other baselines, demonstrating improved end-to-end classification accuracy when the proxies are optimized. The computation-optimal proxy minimizes aggregation distortion, which directly impacts feature quality for inference, while the decision-optimal proxy targets inter-class separability; both are analytically linked to inference quality. To further address the concern, we will add a limited ablation (for small-scale cases) against numerically optimized accuracy in the revision. revision: partial
Referee: [Experimental results section] Experimental validation is asserted but lacks reported details on whether actual inference metrics (accuracy, F1-score) are measured, whether error bars or statistical significance are provided, and whether the simulations employ realistic classifiers or only linear proxies. If only proxy values are plotted, the load-bearing link between the closed-form solutions and end-to-end performance is not demonstrated.

Authors: The experimental section evaluates end-to-end inference accuracy using a realistic multi-layer perceptron classifier applied to the AirComp-aggregated features. Classification accuracy is the reported metric (not proxy values alone), with results averaged over multiple Monte Carlo trials and error bars shown for variability. We will revise the text to explicitly describe the classifier architecture, training procedure, and confirm that accuracy (rather than proxy values) is plotted, thereby strengthening the demonstrated link to end-to-end performance. revision: yes

Circularity Check

0 steps flagged

No circularity: derivations optimize explicitly introduced proxies via standard convex methods on channel models

full rationale

The paper defines the computation-optimal and decision-optimal proxies as modeling choices to link AirComp error to inference performance, then derives closed-form power allocations for TDM (threshold-based) and FDM (dual-decomposition) by optimizing those proxies under standard wireless channel assumptions. No equation reduces by construction to a fitted parameter or self-citation; the optimality claims are conditional on the proxies but the derivation chain itself remains independent and self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions from wireless communications and convex optimization plus the modeling choice that the two proxies adequately represent inference quality.

axioms (2)

domain assumption Wireless channels follow standard fading models that allow closed-form power allocation solutions.
Invoked implicitly when deriving threshold-based and dual-decomposition structures for TDM and FDM.
ad hoc to paper The computation-optimal and decision-optimal proxies are valid surrogates for the true impact of AirComp distortion on collaborative inference accuracy.
Introduced in the abstract as the link between AirComp error and inference performance; no independent justification supplied in the provided text.

pith-pipeline@v0.9.0 · 5651 in / 1455 out tokens · 36432 ms · 2026-05-21T21:09:55.118819+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Optimal transceiver designs in terms of closed-form power allocation are derived for both time-division multiplexing (TDM) and frequency-division multiplexing (FDM) settings, revealing threshold-based and dual-decomposition structures, respectively.
IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

two proxies are established: the computation-optimal proxy that minimizes the aggregation distortion, and the decision-optimal proxy that maximizes the inter-class separability

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extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
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