Spreading Factor-Dependent Carrier Frequency Offset Tolerance in LoRa: Empirical Characterisation and Oscillator Selection for Adaptive Data Rate Networks

Abstract

Carrier frequency offset (CFO) tolerance in Long-Range (LoRa) modulation decreases with increasing spreading factor because longer symbol durations accumulate greater phase rotation per unit frequency error. This paper presents a systematic empirical characterization of CFO tolerance across the LoRa spreading factor range under controlled high-margin indoor conditions using a software-defined radio receiver. Five spreading factors (SF7–SF10 and SF12) are directly measured; SF11 is estimated by log-linear interpolation owing to a software decoder limitation. Measured tolerance ranges from more than 20 kHz at SF7 to 0.5 kHz at SF12—a 40-fold variation—and exhibits two distinct behavioral regimes: a tracking-limited plateau at SF7–SF8 and a coherence-failure regime at SF9–SF12 described by an exponential decay model. Measured tolerances exceed Semtech theoretical predictions by factors of 66–189, attributed to receiver-side implementation techniques including fractional frequency estimation and soft-decision decoding. These measured margins are then compared with the frequency drift of standard ±10 ppm crystal oscillators (8.68 kHz at 868 MHz) to identify a graduated vulnerability threshold: SF7–SF9 operates with adequate margin, SF10 lies in a marginal zone where forward error correction compensated for physical-layer errors under the controlled conditions of this study, and SF11–SF12 operates below the commodity oscillator drift limit. Because Adaptive Data Rate (ADR) algorithms may increase the spreading factor dynamically, oscillator adequacy at low spreading factors does not guarantee adequacy across the full ADR range. An evidence-based oscillator selection framework is derived from these results. SF11 CFO tolerance is reported as an estimate obtained by log-linear interpolation, clearly labelled throughout, owing to a decoder limitation of the software demodulator used.