Characterizing Failures of Deep-Learning Models Under Data Paucity for Wireless Time-Varying Channel Estimation

Fast time-varying propagation environments in 5G/6G wireless systems require channel estimators that can rapidly adapt to unseen channel conditions with very limited labeled data. Conventional pilot-based estimators such as least squares (LS) are robust but inaccurate in low-SNR regimes. Deep learning-based approaches improve reconstruction accuracy but often require retraining across heterogeneous channel statistics, Signal-to-Noise Ratio (SNR) levels, often with a large training data volume. However, most wireless environments incur a high cost during training data collection and hence channel estimation in such scenarios requires models that are effective training under data paucity. Despite its importance, this question has not been investigated thoroughly in wireless channel estimation. To this end, this work presents a rigorous investigation of the performance of deep learning-based channel estimation models, compared to traditional channel estimators, under time-varying channels also suffering from data paucity. We undertake this investigation across multiple line-of-sight (LOS) and non line-of-sight (NLOS) channel models under varying noise conditions. Our findings reveal that deep learning models exhibit significant degradation under data paucity, particularly in noisy, high-dimensional, and distribution-shifted environments, while classical estimators remain robust. These results highlight fundamental limitations of current data-driven approaches for wireless channel estimation under limited data.