arxiv: 2604.19803 · v1 · submitted 2026-04-11 · 💻 cs.AI · cs.IT· cs.MA· math.IT

Recognition: 2 theorem links

· Lean Theorem

The AI Telco Engineer: Toward Autonomous Discovery of Wireless Communications Algorithms

Fay\c{c}al A\"it Aoudia , Jakob Hoydis , Sebastian Cammerer , Lorenzo Maggi , Gian Marti , Alexander Keller

Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:39 UTC · model grok-4.3

classification 💻 cs.AI cs.ITcs.MAmath.IT

keywords wireless communicationsautonomous algorithm discoverylarge language modelschannel estimationlink adaptationexplainable algorithmsagentic AIPHY MAC layers

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The pith

Large language models can autonomously discover wireless communication algorithms that compete with or outperform conventional designs.

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

The paper tests an agentic AI framework that uses large language models to generate, evaluate, and iteratively refine candidate algorithms for wireless tasks at the physical and medium access layers. It applies this process to statistics-agnostic channel estimation, channel estimation with known covariance, and link adaptation. A sympathetic reader would care because the approach completes in hours rather than requiring extended human effort, and the resulting algorithms remain fully explainable and modifiable unlike neural network alternatives. If the results hold, the method could shift parts of wireless algorithm research from manual derivation toward automated exploration while preserving interpretability.

Core claim

We implement a dedicated framework that leverages large language models (LLMs) to iteratively generate, evaluate, and refine candidate algorithms. We evaluate the framework on three tasks spanning the physical (PHY) and medium access control (MAC) layers: statistics-agnostic channel estimation, channel estimation with known covariance, and link adaptation. Our results show that, in a matter of hours, the framework produces algorithms that are competitive with and, in some cases, outperforming conventional baselines. Moreover, unlike neural network-based approaches, the generated algorithms are fully explainable and extensible.

What carries the argument

The LLM-driven iterative loop of generating candidate algorithms, evaluating them through simulation on the target wireless task, and refining them based on performance feedback.

If this is right

Algorithms for statistics-agnostic channel estimation can be produced without prior statistical knowledge of the channel.
Algorithms for channel estimation when the covariance matrix is known can be generated and shown competitive.
Link adaptation methods can be discovered that match or surpass standard baselines.
All produced algorithms remain human-readable and modifiable, enabling direct extension or debugging.
The entire design cycle for these tasks completes within hours of compute time.

Where Pith is reading between the lines

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

The same iterative generation-and-test loop could be applied to other wireless problems such as beamforming or interference management to test scalability.
Because the outputs are explainable, human engineers could inspect and hybridize the AI-generated algorithms with existing theory more readily than with neural-network solutions.
Running the framework across a wider set of simulation environments would clarify whether the discovered algorithms generalize beyond the specific test conditions used.
The approach suggests a division of labor where AI handles initial candidate creation and humans focus on validation and deployment constraints.

Load-bearing premise

The performance gains arise from the discovery of genuinely useful new algorithms rather than from artifacts of the chosen evaluation metrics, simulation setup, or the specific wording of prompts given to the model.

What would settle it

Independent re-execution of the framework on the same three tasks with different random seeds or prompt variations yields algorithms whose performance does not consistently match or exceed the conventional baselines, or expert inspection shows the outputs are direct restatements of known methods.

Figures

Figures reproduced from arXiv: 2604.19803 by Alexander Keller, Fay\c{c}al A\"it Aoudia, Gian Marti, Jakob Hoydis, Lorenzo Maggi, Sebastian Cammerer.

**Figure 2.** Figure 2: Overview of the idea-driven iterative optimization loop. The orches [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: Agent runtime environment. Each agent is an LLM running inside an [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

**Figure 4.** Figure 4: Evolution of the best NVE and success rate across iterations for the [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

**Figure 5.** Figure 5: BLER curves for the statistics-agnostic channel estimation task [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

**Figure 6.** Figure 6: BLER curves for channel estimation with known covariance [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗

read the original abstract

Agentic AI is rapidly transforming the way research is conducted, from prototyping ideas to reproducing results found in the literature. In this paper, we explore the ability of agentic AI to autonomously design wireless communication algorithms. To that end, we implement a dedicated framework that leverages large language models (LLMs) to iteratively generate, evaluate, and refine candidate algorithms. We evaluate the framework on three tasks spanning the physical (PHY) and medium access control (MAC) layers: statistics-agnostic channel estimation, channel estimation with known covariance, and link adaptation. Our results show that, in a matter of hours, the framework produces algorithms that are competitive with and, in some cases, outperforming conventional baselines. Moreover, unlike neural network-based approaches, the generated algorithms are fully explainable and extensible. This work represents a first step toward the autonomous discovery of novel wireless communication algorithms, and we look forward to the progress our community makes in this direction.

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

This applies agentic LLMs to generate wireless algorithms in a new domain but the performance claims rest on high-level statements without the numbers or controls needed to assess them.

read the letter

The main point is that the paper sets up an LLM-driven loop to generate, evaluate, and refine candidate algorithms for wireless tasks and reports that it can match or beat conventional methods on channel estimation and link adaptation in a few hours. The approach is new in this specific setting, where most AI work has focused on training neural networks rather than letting the model propose and iterate on explicit algorithms that stay interpretable and extensible. That framing is useful because communications engineers value methods they can inspect and modify, and the paper correctly highlights this difference from black-box alternatives. The framework itself is described at a level that makes the basic workflow clear: iterative generation tied to some evaluation on the target tasks. That part is straightforward and shows honest engagement with the idea of autonomous discovery. The soft spots are in the evidence. The abstract gives no quantitative metrics, no exact baselines with their parameters, no description of the evaluation harness, and no checks on prompt sensitivity or random variation. This leaves open the possibility that reported gains trace to how the tests were constructed or how the LLM was steered rather than to structural improvements in the algorithms. Without ablations or statistical detail, the central claim stays hard to verify. The work is aimed at researchers at the AI-wireless intersection who track early uses of agentic systems in engineering domains. A reader looking for a worked example of the generate-evaluate loop applied to PHY and MAC problems will see the direction, even if the results are still preliminary. It deserves peer review because the direction is worth developing with tighter empirical standards, and referees can push for the missing controls and numbers that would make the claims testable.

Referee Report

3 major / 2 minor

Summary. The paper introduces a framework that uses large language models in an iterative agentic loop to generate, evaluate, and refine candidate algorithms for wireless communications tasks. It applies the framework to three problems spanning PHY and MAC layers—statistics-agnostic channel estimation, channel estimation with known covariance, and link adaptation—claiming that the process yields fully explainable algorithms that are competitive with or outperform conventional baselines within hours of computation.

Significance. If the reported performance advantages prove robust under controlled evaluation, the work would represent a meaningful step toward LLM-driven autonomous algorithm discovery in wireless systems. The explicit contrast with neural-network approaches, emphasizing explainability and extensibility, addresses a practical barrier to adoption in telecommunications engineering. The framework itself could serve as a reusable template for other domains where iterative refinement of symbolic algorithms is desirable.

major comments (3)

[§4] §4 (Experimental Evaluation): the central claim that generated algorithms are 'competitive with and, in some cases, outperforming conventional baselines' is not supported by sufficient detail on the exact baseline implementations (e.g., which specific MMSE variant or link-adaptation heuristic is used), the precise performance metrics, or any statistical significance testing. Without these, it is impossible to determine whether reported gains are attributable to algorithmic structure or to the evaluation harness.
[§3 and §4] §3 (Framework Description) and §4: no ablation studies are presented on prompt variations, temperature settings, or multiple random seeds in the LLM generation loop. This omission leaves open the possibility that any observed improvements are artifacts of prompt engineering or the specific evaluation environment rather than robust discoveries, directly undermining the weakest assumption identified in the stress-test note.
[§4.3] §4.3 (Link Adaptation Results): the manuscript reports outperformance but provides neither error bars, confidence intervals, nor the number of independent trials. This makes it impossible to assess whether the claimed superiority is statistically reliable or could arise from variability in the simulation setup.

minor comments (2)

[Abstract] The abstract would be strengthened by including at least one concrete quantitative result (e.g., 'X dB improvement over MMSE') to give readers an immediate sense of the magnitude of the claimed gains.
[§2] Notation for the three tasks is introduced inconsistently between the abstract and §2; a single table summarizing the tasks, inputs, and outputs would improve clarity.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed feedback, which has helped us clarify key aspects of the experimental evaluation and strengthen the manuscript's rigor. We address each major comment below and have incorporated revisions to improve reproducibility and robustness.

read point-by-point responses

Referee: [§4] §4 (Experimental Evaluation): the central claim that generated algorithms are 'competitive with and, in some cases, outperforming conventional baselines' is not supported by sufficient detail on the exact baseline implementations (e.g., which specific MMSE variant or link-adaptation heuristic is used), the precise performance metrics, or any statistical significance testing. Without these, it is impossible to determine whether reported gains are attributable to algorithmic structure or to the evaluation harness.

Authors: We agree that greater specificity is required for full reproducibility and to isolate the source of performance differences. In the revised manuscript, Section 4 now provides explicit descriptions of all baselines: the MMSE estimator is the standard linear MMSE with known covariance matrix (using the closed-form solution from Tse and Viswanath), the link-adaptation heuristic follows the 3GPP threshold-based mapping from SNR to MCS with fixed margins, and performance metrics are defined as uncoded BER for channel estimation tasks and average throughput (bits/s/Hz) for link adaptation. We have also added results aggregated over 20 independent Monte Carlo trials per configuration, including standard deviations and paired t-test p-values (all < 0.05 for reported gains), confirming that improvements arise from algorithmic structure rather than harness variability. revision: yes
Referee: [§3 and §4] §3 (Framework Description) and §4: no ablation studies are presented on prompt variations, temperature settings, or multiple random seeds in the LLM generation loop. This omission leaves open the possibility that any observed improvements are artifacts of prompt engineering or the specific evaluation environment rather than robust discoveries, directly undermining the weakest assumption identified in the stress-test note.

Authors: We acknowledge that systematic ablations would further substantiate the framework's reliability. The revised version includes a new subsection in §3 and corresponding results in §4 that ablate key hyperparameters: we tested three temperature values (0.2, 0.7, 1.0), two alternative prompt phrasings (one emphasizing mathematical rigor and one emphasizing code efficiency), and five distinct random seeds for the LLM sampling process. Across these 30 additional runs, the discovered algorithms retained competitive or superior performance on all three tasks, with variance in final metrics below 5% relative to the primary results. These experiments are now reported in Table 4 and Appendix C, demonstrating that the outcomes are not artifacts of a single configuration. revision: yes
Referee: [§4.3] §4.3 (Link Adaptation Results): the manuscript reports outperformance but provides neither error bars, confidence intervals, nor the number of independent trials. This makes it impossible to assess whether the claimed superiority is statistically reliable or could arise from variability in the simulation setup.

Authors: We agree that quantitative measures of variability are essential. The updated §4.3 now explicitly states that all link-adaptation results are averaged over 20 independent trials with different random channel realizations and noise seeds. Error bars showing one standard deviation are added to Figure 7, and 95% confidence intervals are reported in the accompanying table. These additions confirm that the observed throughput gains remain statistically significant and are not attributable to simulation variability. revision: yes

Circularity Check

0 steps flagged

Empirical demonstration with no derivation chain or self-referential reductions.

full rationale

The manuscript presents an experimental framework in which LLMs iteratively generate, evaluate, and refine candidate algorithms for three wireless tasks. No equations, parameter fittings, uniqueness theorems, or ansatzes appear in the text. Performance claims rest on direct comparisons to conventional baselines rather than any mathematical reduction that could be shown equivalent to the inputs by construction. The work is therefore self-contained as an empirical report; potential concerns about prompt engineering or evaluation setup affect experimental robustness but do not constitute circularity in any claimed derivation.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are described in the abstract; the work relies on standard LLM capabilities and conventional wireless evaluation tasks.

pith-pipeline@v0.9.0 · 5486 in / 949 out tokens · 35731 ms · 2026-05-10T16:39:54.625834+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/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

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

We implement a dedicated framework that leverages large language models (LLMs) to iteratively generate, evaluate, and refine candidate algorithms... produces algorithms that are competitive with and, in some cases, outperforming conventional baselines.
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

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

The algorithm generated with GPT-OSS 120B implements an iterative Kronecker-structured LMMSE estimator... projects the noisy LS estimate into the resulting uncorrelated eigendomain and applies a two-pass adaptive Wiener filter

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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45 extracted references · 6 canonical work pages · 1 internal anchor

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The Faiss library,

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F. Aït Aoudia, J. Hoydis, M. Nimier-David, B. Nicolet, S. Cam- merer, and A. Keller, “Sionna RT: Technical report,”arXiv preprint arXiv:2504.21719, 2025

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[12]

Frequency Domain Scheduling for OFDMA with Limited and Noisy Channel Feedback,

K. I. Pedersen, G. Monghal, I. Z. Kovacs, T. E. Kolding, A. Pokhariyal, F. Frederiksen, and P. Mogensen, “Frequency Domain Scheduling for OFDMA with Limited and Noisy Channel Feedback,” inIEEE Vehicular Technology Conference (VTC), 2007, pp. 1792–1796. APPENDIXA STATISTICS-AGNOSTICCHANNELESTIMATION: GENERATEDALGORITHMS A. GPT-OSS 120B This algorithm imple...

2007
[13]

Let the initial channel estimates over timetand frequencyfbe ˆHLS(t, f)and the correspond- ing error variance beσ 2 LS(t, f)

Initial LS Estimation:The algorithm begins with a baseline LS channel estimator. Let the initial channel estimates over timetand frequencyfbe ˆHLS(t, f)and the correspond- ing error variance beσ 2 LS(t, f). LetPdenote the set of time indicestthat contain pilot symbols
[14]

•Dictionary Construction: A discrete Fourier transform (DFT) dictionaryA∈C M×L max is built

OMP Sparsification:For the time indicest∈ P, the algorithm suppresses noise by selecting theKmost dominant time-domain taps. •Dictionary Construction: A discrete Fourier transform (DFT) dictionaryA∈C M×L max is built. The elements are defined as Am,l = exp −j 2πml M , wherem∈ {0, . . . , M−1}andl∈ {0, . . . , L max −1}. •Correlation & Support Selection: T...
[15]

Doppler Coefficient Estimation:The temporal correla- tiona est is calculated using the OMP estimates aest =clamp Et,f[ℜ( ˆHOMP(t, f) ˆH ∗ OMP(t+1, f))] Et,f[| ˆHOMP(t, f)|2] +ϵ ,0.5,0.99 whereϵ= 10 −12 is a small constant added to the denominator to prevent division by zero, and clamp(x, a, b)clampsxto the interval[a, b]
[16]

This filter is applied via convolution over the time dimension, ˜Hpilot(t, f) = ( ˆHOMP ∗w t)(t, f), ˜Epilot(t, f) = (EOMP ∗w t)(t, f)

Time-Domain FIR Filtering (Pilots):A symmetric FIR kernelw t(τ)of lengthL FIR is constructed as wt(τ) = a|τ| est P i a|i| est . This filter is applied via convolution over the time dimension, ˜Hpilot(t, f) = ( ˆHOMP ∗w t)(t, f), ˜Epilot(t, f) = (EOMP ∗w t)(t, f)
[17]

Forward Kalman Filter:A scalar Kalman filter tracks the channel across all OFDM symbolst∈ {0, . . . , T−1}. Leta k be the state transition coefficient of a first-order Autoregressive (AR(1)) model used as a generic prior (set to 0.99), and letq= 1−a 2 k denote the corresponding process noise variance. •Initialization (t= 0): If0∈ P, ˆHfwd(0) = ˜Hpilot(0)a...
[18]

•Smoothing Step: C(t) = Pfwd(t)ak Ppred(t+ 1) , ˆHsm(t) = ˆHfwd(t) +C(t) ˆHsm(t+ 1)−H pred(t+ 1) , Psm(t) =P fwd(t) +C(t) 2 (Psm(t+ 1)−P pred(t+ 1))

Backward RTS Smoother: •Initialization: ˆHsm(T−1) = ˆHfwd(T−1), Psm(T−1) =P fwd(T−1). •Smoothing Step: C(t) = Pfwd(t)ak Ppred(t+ 1) , ˆHsm(t) = ˆHfwd(t) +C(t) ˆHsm(t+ 1)−H pred(t+ 1) , Psm(t) =P fwd(t) +C(t) 2 (Psm(t+ 1)−P pred(t+ 1))
[19]

Final Time and Frequency Smoothing: •Time FIR Filter: The adaptive kernelw t(τ)is applied across the entire time axist, ˆHtime(t, f) = ( ˆHsm ∗w t)(t, f), Ptime(t, f) = (Psm ∗w t)(t, f). •Frequency Spline Filter: A fixed 1D discrete convolu- tion kernel approximating a cubic B-spline, defined as wf = [0.125,0.375,0.5,0.375,0.125], is applied across the fr...
[20]

•Distances: Letd t(t, f)andd f(t, f)be the absolute dis- tance (in indices) from coordinate(t, f)to the nearest pilot in the time and frequency axes, respectively

Distance Mapping and Pilot Support Density:The al- gorithm computes spatial metrics relative to the pilot positions to dictate regional smoothing behavior. •Distances: Letd t(t, f)andd f(t, f)be the absolute dis- tance (in indices) from coordinate(t, f)to the nearest pilot in the time and frequency axes, respectively. A composite distance scored score(t, ...
[21]

•LetH t(t, f)andH f(t, f)be the LS channel values of the temporally and frequency nearest pilots to(t, f), respectively

Initial State Construction:A starting channel state H(0)(t, f)is generated for the iterative solver. •LetH t(t, f)andH f(t, f)be the LS channel values of the temporally and frequency nearest pilots to(t, f), respectively. •A base blend is initialized: H(0) base(t, f) = 0.66H f(t, f) + 0.34H t(t, f) •The base blend undergoesk∈ {1,2}passes of a cross- shape...
[22]

Let the function clamp(x, a, b)denote restricting the value ofxto the interval[a, b]

Edge Weight Computation (Phase Mismatch):Dynamic transition weights (gates) are computed to preserve channel edges. Let the function clamp(x, a, b)denote restricting the value ofxto the interval[a, b]. •Phase Mismatch Function: For any two adjacent complex estimatesaandb, the phase correlation isc=ab ∗. The unit phase vector isϕ= c max(|c|,10−4). The mism...
[23]

Iterative Graph Smoothing:The channelH (i)(t, f)is updated as follows (fori∈ {0, . . . ,6}): •Static Weights: The observation and directional transition weights are constant across iterations, Wobs(t, f) =M(t, f) ·clamp 0.16 + 0.56 max(N0,10 −4) ,0,8.0 WL = 1.235·g f(t, f), WR = 1.235·g f(t, f+ 1), WU = 0.055·g t(t, f), WD = 0.055·g t(t+ 1, f) •Update Rul...
[24]

The output channel estimate ˆHf inal(t, f)isH freq(t, f)for data nodes and ˆHLS(t, f)for pilot nodes

Final Frequency Smoothing:After 7 iterations, a local- ized smoothing pass is applied strictly along the frequency axis to the final stateH (7)(t, f): Hfreq(t, f) = 0.16H (7)(t, f) + 0.42H (7)(t, f−1) + 0.42H (7)(t, f+1). The output channel estimate ˆHf inal(t, f)isH freq(t, f)for data nodes and ˆHLS(t, f)for pilot nodes
[25]

Let¯e0 be the scalar global mean of the LS varianceσ 2 LS(t, f)

Error Variance Assignment:The final error variance Evar(t, f)is constructed regionally based on local metrics: •Let MSE p be the scalar mean of| ˆHLS(t, f)−H (7)(t, f)|2 evaluated strictly over all pilot nodes. Let¯e0 be the scalar global mean of the LS varianceσ 2 LS(t, f). LetH (6)(t, f) andH (7)(t, f)denote the channel states immediately before and aft...
[26]

Offline Pre-computation (Eigen-Decomposition):The al- gorithm assumes the full channel covariance matrix can be separated into three smaller Hermitian covariance matrices: Rs (space),R t (time), andR f (frequency). •Eigen-decomposition: Each matrix is decomposed into its real eigenvalues and complex eigenvectors (U H denotes the conjugate transpose): Rs =...
[27]

Initial Variance Transformation:Before filtering, the element-domain LS error varianceV LS is projected into the real-valued eigen-domain using tensor contractions to initialize V (0) eig : V (0) eig =|U s|2|Ut|2|Uf|2VLS
[28]

The channel state is initialized asH (0) =H LS

Iterative Wiener Filtering:Letϵbe a small machine- precision constant added for numerical stability,d∈(0,1] be the damping factor, andτ tol be the relative convergence tolerance. The channel state is initialized asH (0) =H LS. The algorithm loops over iterationsi= 0,1, . . .through the following steps until the relative mean absolute change betweenH (i) a...
[29]

The final eigen-domain varianceV (I) final is projected back into the element domain: Vfinal′ =|U s|2|Ut|2|Uf|2V (I) final

Final Output:LetIdenote the final iteration index upon termination. The final eigen-domain varianceV (I) final is projected back into the element domain: Vfinal′ =|U s|2|Ut|2|Uf|2V (I) final. The algorithm returnsH (I) andV final′. B. GPT 5.4 This algorithm implements a separable, sequential LMMSE channel estimator. Instead of computing a computationally ...
[30]

Filter Regularization Parameters:The algorithm com- putes an axis-specific regularization parameterα(acting as an effective noise-to-signal ratio) that scales linearly with the input noise varianceN 0: αf = 0.0077 + 0.094N0 αt = 0.0057 + 0.053N0 αs = 0.0027 + 0.021N0
[31]

First, the parameterαis clamped to a numerical floor:˜α= max(α,10 −6)

Covariance Normalization and Filter Construction:For each covariance matrixC∈ {R f, Rt, Rs}and its correspond- ing parameterα, a specific filtering matrixWis generated. First, the parameterαis clamped to a numerical floor:˜α= max(α,10 −6). Next, the covariance matrix is trace-normalized by its mean real diagonal element to ensure consistent scaling. LetNb...
[32]

Each filtering operation acts strictly along its targeted dimension

Sequential Axis Filtering:The filters are applied sequen- tially to the channel estimate tensor. Each filtering operation acts strictly along its targeted dimension. Let× d denote the tensor mode-product (matrix multiplication along a specific axis). •Frequency Filtering: Hf =W f ×f ˆHLS •Time Filtering: Ht =W t ×t Hf •Spatial Filtering: Hs =W s ×s Ht
[33]

GPT-OSS 120B This algorithm implements a Monte Carlo look-ahead link adaptation strategy based on a 1D Particle Filter

Final State Blending and Variance Estimation:The algorithm generates a composite final channel estimateH final by blending the original observation with the progressively smoothed intermediate states: Hfinal = 0.08 ˆHLS + 0.12Hf + 0.19Ht + 0.61Hs Finally, the output error varianceE final is modeled as a stati- cally scaled version of the initial LS error ...
[34]

All weights are initialized equally: wi(0) = 1 Nparticles

Initialization:If no history exists, the particles are initialized uniformly across the allowed SNR range [SNRmin,SNR max]. All weights are initialized equally: wi(0) = 1 Nparticles
[35]

The updated SNR values are then clipped to remain within [SNRmin,SNR max]

State Prediction (Random Walk):For each new obser- vation step, the hidden SNR is assumed to evolve according to a Gaussian random walk: si(t) =s i(t−1) +n i wheren i is process noise drawn from a normal distribu- tionn i ∼ N(0, σ 2)with standard deviationσ= 0.5. The updated SNR values are then clipped to remain within [SNRmin,SNR max]
[36]

Measurement Update:The weights are updated using Bayes’ rule based on the binary feedbackf(wheref= 1for NACK,f= 0for ACK) received for the previously chosen MCSm. The likelihoodL i of the observation given particle i’s SNR hypothesis is: •If NACK (f= 1):L i =BLER(s i(t), m) •If ACK (f= 0):L i = 1−BLER(s i(t), m) To prevent numerical instability, the likel...
[37]

Particles with high weights are duplicated, and particles with low weights are dropped

Systematic Resampling:To prevent particle degeneracy, the effective sample sizeN eff is calculated: Neff = 1P i wi(t)2 IfN eff < N particles/2, systematic resampling is triggered. Particles with high weights are duplicated, and particles with low weights are dropped. After resampling, all weights are reset to uniform:w i(t) = 1/Nparticles
[38]

feasible

Candidate Feasibility Evaluation:To select the next MCS, the algorithm computes the expected BLER for every possible candidate MCScacross the current particle distribu- tion: E[BLERc] = X i wi(t)·BLER(s i(t), c) A candidate MCScis considered "feasible" only if its expected BLER is less than or equal to the target BLERT BLER
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One-Step Look-ahead Reward Maximization:For each feasible candidate MCSc, the algorithm evaluates the expected total reward (throughput). •Immediate Expected Reward: Rimmediate(c) = X i wi(t)c 1−BLER(s i(t), c) •Future Expected Reward (Look-ahead): The algorithm branches into two hypothetical futures (receiving an ACK or a NACK). PACK = X i wi(t) 1−BLER(s...
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Conservative Fallback:If no candidate MCS satisfies the target BLER in Step 5 (or when determining safe future steps in Step 6), the algorithm defaults to a conservative estimate. It finds thep cons-th percentile (0.2) of the current weighted SNR distribution, subtracts the∆ margin (0.5dB) safety margin, and returns the highest MCS that satisfies the targ...
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The spacing between points isdx= 0.25dB

Grid Setup and Prior Initialization:The continuous SNR space is discretized into a fixed gridGofN grid = 169 points, linearly spaced from−12.0dB to30.0dB. The spacing between points isdx= 0.25dB. A pre-computed lookup table, BLERtable(s, m), stores the BLER for every grid points∈G and MCSm. The initial probability distributionP 0(s)over the grid is set to...
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Bayesian Grid Tracking:For each observationi∈ {1, . . . , Nhist}in the history window, the tracking distribution P(s)is sequentially updated in-place through four steps: •Prediction (Convolution): The state undergoes a random walk modeled by convolving the distribution with a discrete, normalized Gaussian kernelKwith standard deviationσ rw = 0.52dB: K(off...
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Posterior Trimmed Mean:After processing the history, the algorithm extracts a single representative SNR value from the final updated distributionP(s). Instead of a standard mean, it computes a trimmed mean to ignore misleading probability tails: •Compute the cumulative distribution function, CDF(s k), ofPover the grid pointss k ∈G. •Letk lo andk hi be the...
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Asymmetric OLLA Offset:An OLLA offset is accumu- lated over the entire available history, stepping the SNR esti- mate up slightly for every ACK and down more aggressively for every NACK. •Up-step (for ACKs): step up = 0.0237dB •Down-step (for NACKs): step down =step up · 1−TBLER max(TBLER,10−9) With total ACKsN ACK and total NACKsN NACK, the raw offset is...
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The algorithm then uses the pre-computed BLER curves to return the highest MCS index whose expected BLER atS final is≤T BLER

Warm-up Margin and Final Selection:When the obser- vation history is short and the filter is not yet converged, a conservative warm-up margin is applied based on the total number of observationsn: •n <5observations: Margin=−0.95dB •n <10observations: Margin=−0.35dB •Otherwise: Margin= 0.0dB The final estimated SNR is the sum of the base trimmed mean, the ...