AI-native wireless receivers based on deep learning exhibit remarkable performance under stationary channel conditions, yet their resilience to distributional shifts remains poorly characterized by conventional metrics such as bit error rate (BER). To overcome these limitations, this paper proposes a novel real-time metric, the Topological Resilience Index (TRI), grounded in persistent homology and persistence exponents. TRI quantifies the structural stability of a neural network receiver's parameter space during online adaptation to non-stationary channels. Specifically, TRI captures resilience through three complementary dimensions: (i) validation-loss resilience measuring model-channel mismatch, grounded in the topological persistence of loss-landscape sublevel sets; (ii) channel impulse response (CIR) distribution shift, tracking geometric drift of CIR vectors from the calibration reference distribution; and (iii) channel manifold topology, quantified by the spectral gap of the Gaussian kernel matrix normalized by the Olivier-Ricci curvature norm. We establish theoretical guarantees showing that TRI is bounded, monotonic under performance degradation, and Lipschitz-stable with respect to perturbations in channel distributions measured in Wasserstein distance. Simulation results for an OFDM deep-learning receiver adapting across ten ITU-R inter-environment transitions at three shift rates demonstrate that TRI provides a consistent mean warning lead of more than one OFDM symbol over gradient-norm and validation-loss baselines, whereas the gradient-norm baseline achieves zero lead in every scenario. Furthermore, the proposed TRI-guided burst re-adaptation reduces post-shift BER by 80% relative to no adaptation within 200 OFDM symbols.

翻译：基于深度学习的AI原生无线接收机在静态信道条件下表现出卓越性能，然而其对抗分布偏移的鲁棒性仍难以通过误码率（BER）等传统指标有效表征。为突破这一局限，本文提出一种基于持久同调与持久指数的实时新型度量——拓扑鲁棒性指数（TRI）。该指标量化了神经网络接收机在非平稳信道在线自适应过程中参数空间的结构稳定性。具体而言，TRI通过三个互补维度刻画鲁棒性：（i）泛化损失鲁棒性，基于损失景观子水平集的拓扑持久性度量模型-信道失配程度；（ii）信道冲激响应（CIR）分布偏移，追踪CIR向量相对于标定参考分布的几何漂移；（iii）信道流形拓扑，通过经奥利维耶-里奇曲率范数归一化的高斯核矩阵谱间隙进行量化。我们建立了理论保证，证明TRI具有有界性、性能退化下的单调性，以及关于Wasserstein距离度量的信道分布扰动的Lipschitz稳定性。针对在三种偏移速率下跨越十组ITU-R跨环境转换场景进行自适应的OFDM深度学习接收机仿真结果表明：相较于梯度范数与泛化损失基线，TRI可实现超过一个OFDM符号的持续平均预警提前量，而梯度范数基线在所有场景下的提前量为零。此外，本文提出的TRI引导的突发重自适应策略在200个OFDM符号内，相较于无自适应方案可将偏移后BER降低80%。