PaperlayerView exact revision on arXiv

Source-linked AI summary

TRACE-CRC: Trajectory-Adaptive Conformal Risk Control for Multi-Step Channel State Information Prediction

Kiarash Rezaei, Mehdi Sattari, Javad Aliakbari, Tommy Svensson, Paolo Monti, Carlos Natalino

arXiv:2608.27124v1cs.LGstat.ML

TL;DR

Multi-step CSI predictors often provide point estimates without calibrated trajectory-level uncertainty, although downstream wireless decisions may depend on the full predicted channel path. TRACE-CRC constructs horizon-adaptive Frobenius-norm uncertainty balls, stratifies trajectory difficulty, and applies LTT-based CRC. It achieves TC = 0.933 ± 0.011 and AFR = 13.64 ± 0.41, exceeding the 0.90 target while remaining more efficient than trajectory-level and simultaneous corrections.

  • Problem

    Deep CSI predictors typically lack calibrated uncertainty for multi-step trajectories, limiting reliability information available to downstream wireless decisions.

  • Method

    TRACE-CRC calibrates per-horizon Frobenius-norm uncertainty balls using horizon-dependent error profiles, trajectory difficulty stratification, and trajectory-level CRC with LTT.

  • Results

    TC = 0.933 ± 0.011 and AFR = 13.64 ± 0.41; TRACE-CRC exceeds the 0.90 target while using smaller radii than trajectory-level and simultaneous representatives.

  • Takeaways & Limitations

    TRACE-CRC shifts uncertainty assessment from marginal horizon coverage to reliability of the complete predicted trajectory for downstream wireless decisions.

  • Takeaways & Limitations

    The certificate and ball tightness depend on calibration and validation data, forecast horizon length, and trajectory-level exchangeability between validation and deployment.

Abstract

from arXiv · show

Reliable prediction of time-varying channel state information (CSI) is essential for efficient wireless communication. Each CSI frame is a matrix-valued representation of the wireless channel response, and a sequence of CSI frames forms a temporal channel trajectory. Modern deep learning-based CSI predictors, however, often provide only point predictions and lack calibrated uncertainty estimates. This limitation is particularly problematic in multi-step CSI prediction, where the target is a sequence of future CSI matrices, and downstream decisions such as beamforming or scheduling may fail if any part of the predicted trajectory is unreliable. We propose trajectory-adaptive calibration and error profiling with conformal risk control (TRACE-CRC), a method for trajectory-aware uncertainty quantification in multi-step CSI prediction. TRACE-CRC constructs Frobenius-norm uncertainty balls around predicted CSI matrices and controls the risk that at least one future frame is uncovered. Instead of calibrating each future step independently, TRACE-CRC combines future-step-dependent error profiling, trajectory difficulty stratification, and learn-then-test (LTT) risk control. Empirically, TRACE-CRC achieves reliable trajectory-level coverage with substantially smaller uncertainty balls than conservative multi-step corrections, while avoiding the trajectory undercoverage of compact stepwise and adaptive conformal baselines.

1. Introduction

Accurate CSI prediction supports wireless communication, but multi-step deep predictors typically lack calibrated uncertainty for complete future trajectories. TRACE-CRC addresses this gap with trajectory-level conformal risk control and adaptive uncertainty balls.

  • CSI is a high-dimensional complex-valued representation of wireless channel responses needed to realize MIMO communication gains.
  • Deep CSI predictors improve point-prediction accuracy but typically lack calibrated uncertainty for downstream decisions such as beamforming, scheduling, and link adaptation.
  • Standard conformal prediction does not directly address trajectory-level reliability when errors grow across horizons and any uncovered future frame can make the trajectory unreliable.
  • TRACE-CRC constructs per-horizon Frobenius-norm uncertainty balls whose radii adapt to horizon-dependent error growth and trajectory difficulty.
  • TRACE-CRC combines trajectory-adaptive calibration with LTT to select an uncertainty rule with finite-sample trajectory-level risk control.
  • TRACE-CRC achieves trajectory coverage 0.933 at target coverage 0.90 while reducing conservatism relative to simultaneous-correction baselines.

2. Related Work

Related work develops conformal methods for classical, adaptive, weighted, sequential, and risk-controlled prediction settings. TRACE-CRC differs by calibrating matrix-valued multi-step CSI trajectories against a full-trajectory failure risk.

  • Classical split conformal prediction provides finite-sample marginal coverage under exchangeability, while CQR adds adaptive regression intervals.
  • Time-series conformal methods address temporal dependence, nonstationarity, distribution shift, online adaptation, and residual structure.
  • CRC calibrates prediction sets for user-specified losses, and LTT provides high-confidence risk control through a multiple-testing formulation.
  • Wireless applications of conformal prediction have included classification, online channel prediction, context-dependent covariate shift, and decision-oriented channel uncertainty.
  • TRACE-CRC targets Frobenius-norm uncertainty balls for matrix-valued multi-step CSI trajectories and certifies trajectory-level failure risk.

3. Dataset and Problem Formulation

The paper models CSI as matrix-valued temporal trajectories, uses an autoregressive predictor, and formulates conformal uncertainty through Frobenius residual balls. Calibration targets the event that any future horizon is uncovered under trajectory-level exchangeability.

  • 3.1. Dataset: CSI trajectories are sampled from a channel process with mobility, scattering, and multipath propagation, and each frame is a high-dimensional complex-valued matrix.
  • 3.1. Dataset: The dataset contains 1,000 independent samples with Nt = 16 antennas, Nc = 16 subcarriers, 28 GHz carrier frequency, velocities from 30 to 120 km/h, and 100 frames per sample.
  • 3.1. Dataset: Exchangeability is assumed across complete CSI trajectories rather than frames within trajectories, allowing temporal dependence within each trajectory.
  • 3.2. CSI Prediction: CSI prediction maps past CSI frames to a future trajectory over multiple forecast horizons, using a pretrained temporal-encoder and diffusion-generator predictor autoregressively.
  • 3.2. CSI Prediction: Autoregressive feedback can propagate and accumulate prediction errors, motivating uncertainty calibration that accounts for increasing forecast-horizon difficulty.
  • 3.3. Conformal Problem Formulation: Trajectory coverage requires every horizon event to hold, so failure occurs when at least one residual exceeds its assigned radius rather than when only a marginal horizon event fails.
  • 3.3. Conformal Problem Formulation: The method defines Frobenius residuals between true and predicted CSI matrices and uses radii that may depend on horizon and observed inputs or predictions, but not the unobserved future frame.
  • 3.3. Conformal Problem Formulation: CRC selects a data-dependent uncertainty rule under trajectory-level exchangeability, with α controlling target failure and δ controlling the probability of certifying excessive risk.

4. TRACE-CRC: Trajectory-Adaptive Conformal Risk Control

TRACE-CRC calibrates complete multi-step CSI trajectories by combining horizon-dependent error profiles, difficulty stratification, and LTT risk control. It constructs horizon-wise Frobenius uncertainty balls whose global scale is selected for trajectory-level reliability.

  • TRACE-CRC targets the full-trajectory failure event, requiring every future CSI frame to lie within its corresponding uncertainty ball.
  • Calibration stages: Disjoint profile, conformal-calibration, and validation subsets estimate horizon profiles, group-wise quantiles, and the final risk-control multiplier.The validation subset is reserved for selecting the multiplier after the other components are fixed.
  • Horizon difficulty profile: The method distributes uncertainty across horizons using a learned difficulty profile wj and scales it with group-specific conformal quantiles qg.Horizon profiles reflect relative forecast difficulty, with wj > 1 indicating harder-than-average horizons.
  • Trajectory difficulty stratification: TRACE-CRC stratifies trajectories into lower- and higher-difficulty groups using predicted-trajectory features and a ridge regression difficulty model.The features summarize trajectory magnitude, variability, trend, and local smoothness; the median predicted difficulty score separates the two groups.
  • LTT risk control: LTT evaluates candidate multipliers by trajectory-level failure loss and selects the smallest accepted multiplier λ⋆.A trajectory fails when at least one future frame exceeds its scaled horizon-specific radius; if no candidate is certified, the grid must be enlarged.
  • Deployment: For new contexts, TRACE-CRC predicts trajectory difficulty, assigns a group, and applies the final horizon-wise radii to form the trajectory-level prediction band.The resulting band is the collection of Frobenius balls across forecast horizons.

5. Experimental Setup

The experiments apply TRACE-CRC post hoc to a pretrained diffusion CSI predictor and compare it with standard, adaptive, structured multi-step, and risk-control baselines. All methods use shared held-out trajectories and reliability–efficiency metrics.

  • Prediction model: TRACE-CRC is evaluated with a pretrained diffusion-based CSI predictor trained on 10,000 trajectory-level samples.Inference uses 20 dB SNR and 20 reverse-diffusion sampling steps; calibration is offline and deployment adds only the calibrated scaling rule.
  • Data split: The evaluation uses 1,000 trajectories split into 300 calibration and 700 independent test trajectories.No CSI frames from the same trajectory are assigned to both calibration and test sets.
  • TRACE-CRC calibration: TRACE-CRC further divides calibration data into profile, conformal-calibration, and validation subsets of sizes 30, 40, and 230.The largest split is reserved for LTT validation.
  • Baselines: Comparisons include standard split-conformal, time-series adaptive, structured multi-step, and risk-control ablation methods.All methods are evaluated on the same held-out test trajectories using reliability and efficiency metrics.
  • Structured and ablation baselines: Structured baselines include Bonferroni-CRC, Sidak-CRC, and CopulaCPTS, while ablations isolate LTT, horizon profiling, and trajectory stratification.

6. Results and Discussion

TRACE-CRC maintains trajectory coverage above the 0.90 target while using smaller uncertainty radii than conservative trajectory-level and simultaneous-correction baselines. Across adaptive, structured, and ablation comparisons, horizon profiling and trajectory stratification improve the reliability–efficiency trade-off.

  • Overall comparison: TRACE-CRC achieves TC = 0.933 ± 0.011 and AFR = 13.64 ± 0.41, exceeding the 0.90 target with smaller radii than trajectory-level and simultaneous representatives.It also uses smaller radii than Residual Quantile and CopulaCPTS while achieving higher trajectory coverage.
  • Time-series adaptive baselines: Adaptive horizon-level methods have TC values from 0.733 to 0.790, while trajectory-level variants reach 0.891–0.919 at AFR values of 20.25–21.80.TRACE-CRC provides higher trajectory coverage than all adaptive baselines while remaining more efficient than their trajectory-level variants.
  • Structured multi-step baselines: Bonferroni-CRC and Sidak-CRC reach TC = 0.968 but yield AFR = 20.00, whereas CopulaCPTS has AFR = 14.87 and TC = 0.892.TRACE-CRC attains TC = 0.933 with the smallest average radius in this group, AFR = 13.64.
  • Risk-control ablations: TRACE-CRC reduces AFR from 24.37 for Global-CRC to 13.64 while TC decreases from 0.957 to 0.933; horizon profiling provides most of the efficiency gain.Trajectory stratification further reduces uncertainty radii when combined with horizon-aware calibration.
  • Robustness: Across 50 calibration-partition runs, TRACE-CRC achieved average TC = 0.940±0.015 and exceeded the target in every run.Variability was small and driven primarily by the internal calibration partition rather than diffusion inference.

7. Conclusion

TRACE-CRC targets uncertainty quantification for complete multi-step CSI trajectories rather than only marginal or horizon-wise coverage. The study reports a reliability–efficiency trade-off, while recognizing dependence on calibration data, horizon length, and trajectory-level exchangeability.

  • TRACE-CRC calibrates per-horizon Frobenius-norm uncertainty balls using a trajectory-level failure criterion, horizon profiling, and trajectory stratification.
  • TRACE-CRC combines horizon profiling with trajectory stratification to reduce conservatism while maintaining trajectory-level reliability.
  • The method’s risk-control certificate and uncertainty-ball tightness depend on calibration and validation data, forecast horizon length, and trajectory-level exchangeability.

Appendix A. Complete Results

The complete-results appendix documents the evaluated conformal-method set and the fixed calibration–test evaluation protocol. Results target trajectory coverage of 0.90 and are summarized across five diffusion inference seeds.

  • Table 3 covers standard split-conformal, adaptive time-series, structured multi-step, and risk-control ablation methods.
  • The evaluation uses a fixed 300/700 calibration–test split, with results reported as mean ± standard deviation over five diffusion inference seeds.
  • The target trajectory coverage for the complete conformal-method comparison is 0.90.

Appendix B. Method Parameters

The method-parameters appendix specifies fixed selection procedures, baseline search spaces, and CRC certification details. It also records the parameter and LTT outcomes used for final evaluation.

  • Baseline selection required MHC ≥0.90 for horizon-wise methods and TC ≥0.90 for trajectory-level methods for every inference seed.
  • When no candidate met the all-seed criterion, selection minimized worst-seed coverage shortfall, then mean shortfall, then mean AFR.
  • CRC variants used 27 prespecified multipliers in a single Holm correction with one-sided Hoeffding–Bentkus p-values, and Table 6 reports calibrated quantities and selected LTT multipliers.

Appendix C. Robustness to the Internal Calibration Partition

TRACE-CRC was evaluated across 10 internal calibration reallocations and five diffusion inference seeds, producing 50 runs. Coverage remained stable across these internal partitions.

  • The outer 300/700 trajectory-level calibration/test split was fixed while the 300 calibration trajectories were reallocated into Dprof, Dcp, and Dval.
  • The robustness study used 10 random internal calibration reallocations and five diffusion inference seeds, yielding 50 runs in total.
  • Table 7 summarizes variability using marginal internal-split and inference-seed standard deviations across the corresponding averaged levels.
Loading 2608.27124v1…