Resilience Characterization of AI-Native Wireless Receivers via Persistent Homology

2026-05-20

AI Summary

Conventional metrics such as bit error rate struggle to effectively evaluate the robustness of deep learning-based wireless receivers under channel distribution shifts. This work proposes the first real-time resilience indicator, TRI, grounded in persistent homology and Ollivier–Ricci curvature, which quantifies the structural stability of receivers adapting online to non-stationary channels through three complementary perspectives: loss landscape topology, drift in channel impulse response distributions, and geometry of the channel manifold. TRI enjoys theoretical guarantees including boundedness, monotonicity, and Lipschitz stability. Evaluated across ten ITU-R cross-environment channel transfer scenarios, TRI provides early warnings of performance degradation on average one OFDM symbol ahead of failure and enables a burst re-adaptation strategy that achieves an 80% relative reduction in bit error rate within 200 symbols.

Abstract

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.

Problem

• AI-native wireless receivers
• distributional shifts
• resilience characterization
• non-stationary channels
• bit error rate

Innovation

• Topological Resilience Index
• Persistent Homology
• AI-Native Wireless Receivers
• Non-stationary Channels
• Wasserstein Stability