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

• CSI is a high-dimensional complex-valued representation of wireless channel responses needed to realize MIMO communication gains.Source: §1 · pp. 1–2
• Deep CSI predictors improve point-prediction accuracy but typically lack calibrated uncertainty for downstream decisions such as beamforming, scheduling, and link adaptation.Source: §1 · p. 2
• 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.Source: §1 · p. 2
• TRACE-CRC constructs per-horizon Frobenius-norm uncertainty balls whose radii adapt to horizon-dependent error growth and trajectory difficulty.Source: §1 · pp. 2–3
• TRACE-CRC combines trajectory-adaptive calibration with LTT to select an uncertainty rule with finite-sample trajectory-level risk control.Source: §1 · p. 3
• TRACE-CRC achieves trajectory coverage 0.933 at target coverage 0.90 while reducing conservatism relative to simultaneous-correction baselines.Source: §1 · p. 3

• Classical split conformal prediction provides finite-sample marginal coverage under exchangeability, while CQR adds adaptive regression intervals.Source: §2.1 · p. 3
• Time-series conformal methods address temporal dependence, nonstationarity, distribution shift, online adaptation, and residual structure.Source: §2.2 · pp. 3–4
• CRC calibrates prediction sets for user-specified losses, and LTT provides high-confidence risk control through a multiple-testing formulation.Source: §2.3 · p. 4
• Wireless applications of conformal prediction have included classification, online channel prediction, context-dependent covariate shift, and decision-oriented channel uncertainty.Source: §2.4 · pp. 4–5
• TRACE-CRC targets Frobenius-norm uncertainty balls for matrix-valued multi-step CSI trajectories and certifies trajectory-level failure risk.Source: §2.4 · p. 5

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.Source: §3.1 · p. 5
• 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.Source: §3.1 · pp. 5–6
• Exchangeability is assumed across complete CSI trajectories rather than frames within trajectories, allowing temporal dependence within each trajectory.Source: §3.1 · p. 6

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.Source: §3.2 · pp. 6–7
• Autoregressive feedback can propagate and accumulate prediction errors, motivating uncertainty calibration that accounts for increasing forecast-horizon difficulty.Source: §3.2 · p. 7

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.Source: §3.3 · pp. 7–8
• 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.Source: §3.3 · p. 7
• 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.Source: §3.3 · p. 8

• TRACE-CRC targets the full-trajectory failure event, requiring every future CSI frame to lie within its corresponding uncertainty ball.Source: §4.1 · pp. 8–9

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.Source: §4.2 · p. 9

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.Source: §4.3 · pp. 9–10, §4.5 · p. 11

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.Source: §4.4 · pp. 10–11

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.Source: §4.6 · pp. 11–12

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.Source: §4.6 · p. 12, §4.7 · p. 12

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.Source: §5 · pp. 12–13

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.Source: §5 · p. 13

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.Source: §5 · p. 13

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.Source: §5.1 · pp. 13–14

Structured and ablation baselines

• Structured baselines include Bonferroni-CRC, Sidak-CRC, and CopulaCPTS, while ablations isolate LTT, horizon profiling, and trajectory stratification.Source: §5.1 · p. 14

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.Source: §6 · p. 15

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.Source: §6 · p. 17

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.Source: §6 · p. 17

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.Source: §6 · p. 18

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.Source: §6 · p. 19

• TRACE-CRC calibrates per-horizon Frobenius-norm uncertainty balls using a trajectory-level failure criterion, horizon profiling, and trajectory stratification.Source: §7 · p. 19
• TRACE-CRC combines horizon profiling with trajectory stratification to reduce conservatism while maintaining trajectory-level reliability.Source: §7 · p. 19
• The method’s risk-control certificate and uncertainty-ball tightness depend on calibration and validation data, forecast horizon length, and trajectory-level exchangeability.Source: §7 · p. 19

• Table 3 covers standard split-conformal, adaptive time-series, structured multi-step, and risk-control ablation methods.Source: Appendix A · p. 24
• The evaluation uses a fixed 300/700 calibration–test split, with results reported as mean ± standard deviation over five diffusion inference seeds.Source: Table 3 · p. 24
• The target trajectory coverage for the complete conformal-method comparison is 0.90.Source: Table 3 · p. 24

• Baseline selection required MHC ≥0.90 for horizon-wise methods and TC ≥0.90 for trajectory-level methods for every inference seed.Source: Appendix B · p. 24
• When no candidate met the all-seed criterion, selection minimized worst-seed coverage shortfall, then mean shortfall, then mean AFR.Source: Appendix B · p. 24
• 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.Source: Appendix B · pp. 24–25, Table 6 · p. 26

• The outer 300/700 trajectory-level calibration/test split was fixed while the 300 calibration trajectories were reallocated into Dprof, Dcp, and Dval.Source: Appendix C · p. 26
• The robustness study used 10 random internal calibration reallocations and five diffusion inference seeds, yielding 50 runs in total.Source: Appendix C · p. 26
• Table 7 summarizes variability using marginal internal-split and inference-seed standard deviations across the corresponding averaged levels.Source: Table 7 · p. 26