Approximate SER Analysis of LoRa Communication with Timing and Frequency Offset

In high-mobility LoRa communications, carrier frequency offset (CFO) stemming from low-cost crystal oscillators causes signal energy to disperse across frequency bins. To quantify the impact of CFO and sampling time offset (STO) induced by sampling rate conversion on the symbol error rate (SER), this paper derives approximate SER bounds under Additive White Gaussian Noise (AWGN) channels. Simulations verify these bounds, revealing that low spreading factors (SFs) combined with high STO and CFO induce significant energy leakage and performance degradation. Furthermore, Low Rate Optimization (LRO) is employed to enhance signal robustness. The proposed SER bounds are shown to hold for LRO-enhanced systems, with simulations confirming that LRO effectively improves overall performance.