Walsh-OFDM Breakdown Analysis Breaking the SNR Floor: An Analytical Study of Walsh-Coded OFDM Performance and Breakdown Mechanisms in Low-SNR Rician Fading

Abstract

This paper analyses the performance limits and breakdown mechanisms of a Walsh-coded OFDM Integrated Sensing and Communication (ISAC) waveform operating in severe Rician fading. The waveform, previously introduced as a robust low-rate design for wearable links, is here used as a testbed to study how sensing and communication capabilities diverge in ultra-low Signal-to-Noise Ratio (SNR) regimes. We specifically quantify the “breaking points” of the system, demonstrating that while the Walsh-coded communication link becomes unreliable around −18 dB, the direction finding (DF) capability persists with sub-degree accuracy (Root Mean Square Error RMSE $\lt ~1^{\circ }$ ) down to −33 dB. This reveals a distinct $\approx {\mathrm {15~dB}}$ “Sensing-Only” operational gap under quasi-static Rician fading assumptions. Notably, reducing the integration window shifts the sensing threshold upward by $\approx {\mathrm {10~dB}}$ per decade reduction in snapshots, while the required hundreds-of-milliseconds observation latency is suitable for quasi-static wearables but may limit real-time tracking applications. Furthermore, we provide analytical approximations for the effective SNR and Angle-of-Arrival (AoA) Cramér-Rao Lower Bound (CRLB) under massive time-frequency averaging, and present a new comparative benchmark against standard estimators (Schmidl-Cox, Moose, MUSIC). Results confirm that the pilot-aided framework extends the synchronisation lock range by $\approx {\mathrm {19~dB}}$ compared to classical baselines, establishing it as a reference for analysing breakdown physics in next-generation body-centric networks.