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

cs.LGAug 27, 2026

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

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

Organizations: Department of Electrical Engineering, Chalmers University of Technology, Gothenburg, Sweden

Abstract

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.

Figures & tables

Panel of Figure 1 — Figure 1: Snapshots of the real part of a CSI frame at different time steps.

Method	$w_{j}$	$q_{g}$	$\lambda^{\star}$
Global-CRC	$\times$	$\times$	✓
Horizon-Profile CRC	✓	$\times$	✓
Trajectory-Stratified CRC	$\times$	✓	✓
TRACE-CRC	✓	✓	✓

Table 1: Ablation structure for TRACE-CRC components.

Category	Method	MHC	WHC	TC	AFR
Standard split-conformal	Horizon-wise	$0.872\pm 0.002$	$0.855\pm 0.006$	$0.710\pm 0.009$	$10.73\pm 0.06$
Standard split-conformal	Residual Quantile	$0.965\pm 0.002$	$0.939\pm 0.003$	$0.903\pm 0.007$	$14.30\pm 0.21$
Time-series adaptive	AgACI-Horizon	$0.896\pm 0.001$	$0.891\pm 0.001$	$0.744\pm 0.006$	$11.49\pm 0.06$
Time-series adaptive	EnbPI-Trajectory	$0.984\pm 0.001$	$0.937\pm 0.007$	$0.919\pm 0.008$	$21.80\pm 0.24$
Structured multi-step	Bonferroni-CRC	$0.993\pm 0.001$	$0.985\pm 0.003$	$0.968\pm 0.004$	$20.00\pm 0.29$
Structured multi-step	CopulaCPTS	$0.969\pm 0.004$	$0.945\pm 0.004$	$0.892\pm 0.012$	$14.87\pm 0.29$

Table 2: Representative conformal methods for CSI uncertainty under the fixed random trajectory-level split. The target trajectory coverage is

0.90

. Results are reported as mean

\pm

standard deviation across five diffusion inference seeds. For each seed, MHC is the mean coverage across forecast horizons, WHC is the worst-horizon coverage, TC is full-trajectory coverage, and AFR is the mean Frobenius radius across forecast horizons and test trajectories.

Panel of Figure 2 — Figure 2: Horizon-wise coverage $\mathrm{HC}_{j}$ (left) and average Frobenius radius $\mathrm{AFR}_{j}$ (right) for standard split-conformal baselines and TRACE-CRC. Curves show means over five diffusion inference seeds, and shaded regions indicate $\pm 1$ standard deviation across seeds. The dashed line marks the target coverage $1-\alpha=0.90$ ; legend entries report trajectory coverage (TC).

Panel of Figure 3 — Figure 3: Horizon-wise coverage and average Frobenius radius for time-series adaptive conformal baselines and TRACE-CRC. Dashed curves denote trajectory-level variants, solid curves denote horizon-wise variants, and the diamond-marked curve denotes TRACE-CRC.

Panel of Figure 4 — Figure 4: Horizon-wise coverage and average Frobenius radius for structured multi-step baselines and TRACE-CRC.

Panel of Figure 5 — Figure 5: Horizon-wise coverage and average Frobenius radius for TRACE-CRC and its risk-control ablations.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Category	Method	MHC	WHC	TC	AFR
Standard split-conformal	Global Residual	$0.880\pm 0.003$	$0.658\pm 0.006$	$0.642\pm 0.006$	$12.98\pm 0.13$
	Horizon-wise	$0.872\pm 0.002$	$0.855\pm 0.006$	$0.710\pm 0.009$	$10.73\pm 0.06$
	Max-score Split	$0.973\pm 0.001$	$0.901\pm 0.005$	$0.882\pm 0.005$	$19.52\pm 0.26$
	Residual Quantile	$0.965\pm 0.002$	$0.939\pm 0.003$	$0.903\pm 0.007$	$14.30\pm 0.21$
Time-series adaptive	EW-Horizon	$0.893\pm 0.001$	$0.885\pm 0.001$	$0.735\pm 0.005$	$11.40\pm 0.03$
	EW-Trajectory	$0.976\pm 0.001$	$0.908\pm 0.001$	$0.891\pm 0.002$	$20.25\pm 0.11$

Appendix

Table 3: Validity and efficiency of all conformal methods under the fixed

300/700

calibration–test split. Results are reported as mean

\pm

standard deviation over five random diffusion inference seeds; the target trajectory coverage is

0.90

Method	Parameters used
Global Residual	Pooled split-conformal residual quantile, $\alpha=0.10$ .
Horizon-wise	Per-horizon split-conformal residual quantiles, $\alpha=0.10$ .
Max-score Split	Split conformal on $S_{i}=\max_{1\leq j\leq T}E_{i,j}$ , $\alpha=0.10$ .
Residual Quantile	$50/50$ training/calibration split; QuantileRegressor with quantile $=0.90$ , regularization $=10^{-4}$ , and solver = highs.
EW-Horizon $\,{}^{\dagger}$	$\beta=0.02$ ; horizon-wise exponentially weighted quantiles with online residual-history updates.
EW-Trajectory $\,{}^{\dagger}$	$\beta=0.02$ ; exponentially weighted trajectory-max quantiles with online residual-history updates.

Appendix

Table 4: Parameters used for the standard, adaptive, and structured conformal baselines.

Method	Val. MHC	Val. TC	Val. fail	Val. AFR
EW-Horizon $\,{}^{\dagger}$	$0.8977\pm 0.0044$	$0.7511\pm 0.0151$	$0.2489\pm 0.0151$	$10.9397\pm 0.0901$
EW-Trajectory $\,{}^{\dagger}$	$0.9760\pm 0.0010$	$0.8956\pm 0.0054$	$0.1044\pm 0.0054$	$19.9327\pm 0.1515$
EnbPI-Horizon	$0.9099\pm 0.0071$	$0.8200\pm 0.0227$	$0.1800\pm 0.0227$	$11.0966\pm 0.0835$
EnbPI-Trajectory	$0.9778\pm 0.0009$	$0.9044\pm 0.0054$	$0.0956\pm 0.0054$	$20.2111\pm 0.1577$
ACI-Horizon $\,{}^{\dagger}$	$0.8996\pm 0.0014$	$0.7600\pm 0.0249$	$0.2400\pm 0.0249$	$11.0983\pm 0.2292$
ACI-Trajectory $\,{}^{\dagger}$	$0.9771\pm 0.0013$	$0.8956\pm 0.0054$	$0.1044\pm 0.0054$	$20.1203\pm 0.2402$

Appendix

Table 5: Validation performance of the selected baseline configurations, reported as mean

\pm

standard deviation across five diffusion inference seeds.

Method	Fixed parameters	Calibrated quantities	LTT outcome
Global-CRC	No method-specific hyperparameters	$q_{\mathrm{global}}=11.607\pm 0.170$	$\lambda^{\star}=2.100\pm 0.071$ $[2.000,2.200]$
Horizon-Profile CRC	Smoothing window $K=3$ ; stabilization ratio $\rho=0.15$	$q_{\mathrm{global}}=11.607\pm 0.170$	$\lambda^{\star}=1.360\pm 0.055$ $[1.300,1.400]$
Trajectory-Stratified CRC	Number of groups $=2$ ; Ridge penalty $\eta=1.0$	$q_{0}^{\mathrm{raw}}=13.877\pm 2.521$ ; $q_{1}^{\mathrm{raw}}=23.850\pm 1.907$	$\lambda^{\star}=1.253\pm 0.099$ $[1.167,1.400]$
TRACE-CRC	Number of groups $=2$ ; smoothing window $K=3$ ; stabilization ratio $\rho=0.15$ ; Ridge penalty $\eta=1.0$	$q_{0}=10.857\pm 0.386$ ; $q_{1}=15.052\pm 0.326$	$\lambda^{\star}=1.073\pm 0.037$ $[1.033,1.100]$

Appendix

Table 6: Method-specific parameters, calibrated quantities, and LTT outcomes for the conformal risk-control variants. Reported values are mean

\pm

standard deviation across five diffusion inference seeds; brackets show the observed range of

\lambda^{\star}

Metric	Overall SD	Internal split SD	Inference-seed SD
MHC	0.0062	0.0051	0.0021
WHC	0.0081	0.0063	0.0025
TC	0.0155	0.0109	0.0058
AFR	0.9753	0.6691	0.3114

Appendix

Table 7: Variability of TRACE-CRC over

50

runs using

10

internal calibration partitions and five diffusion inference seeds. Internal-split and inference-seed SDs are marginal standard deviations across the corresponding averaged levels.

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This paper considers channel state information (CSI) prediction using neural networks for time-varying multi-antenna channels from noisy historical observations. The main challenge is to exploit temporal correlation while distinguishing channel evolution from observation noise. We propose JEPA-kMMVAE, which combines a joint-embedding predictive architecture with a k-memory Markov variational autoencoder to predict future CSI through temporally structured latent representations. The framework supports direct prediction and residual corrections relative to the latest latent state and noisy CSI observation. Simulation results show that the residual configuration outperforms the evaluated baselines at moderate and high input CSI signal-to-noise ratios, while sequence baselines remain more accurate under stronger noise.

Abstract

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