Distribution-Free Adaptive Modulation and Coding via Online Conformal Inference under Non-Stationary Fading

Machine learning--based adaptive modulation and coding (ML-AMC) has demonstrated strong empirical performance for next-generation wireless systems, yet existing approaches provide no formal guarantees on block error rate (BLER) coverage under the non-stationary fading conditions ubiquitous in 5G-NR and 6G deployments. We propose Conformal-AMC, a principled framework that wraps any pre-trained MCS classifier with online adaptive conformal inference (ACI) to produce prediction sets with finite-sample, distribution-free miscoverage guarantees. The central theoretical contribution is a tight bound on time-averaged miscoverage that decomposes into an adaptation-noise term, a non-stationarity penalty governed by the channel Markov chain's mixing time $\tau_{\text{mix}}$, and a total-variation drift $V_T$; this decomposition yields a closed-form, Doppler-adaptive learning rate $\eta_{\text{Jakes}}^*$ computable entirely from pilot-estimated channel statistics, requiring no labeled data or manual tuning. We further establish a two-sided coverage--throughput tradeoff (Theorem 4.4) and prove that antenna diversity monotonically tightens the guarantee (Theorem 4.5). Experiments under 3GPP TDL channel models at UE speeds of 3--500~km/h show that Conformal-AMC tracks the target miscoverage level $\alpha = 0.10$ to within $\pm 0.012$ across all speed transitions while achieving a singleton rate of 82.4\%---exceeding the 77.1\% of Split CP and 75.3\% of OLLA at the same coverage level---with all pairwise improvements over baselines significant at $p < 0.001$.