Doppler Shift and SFO Robust Synchronization for LoRa-Like Acoustic Underwater Communication

Frequency shift chirp modulation (FSCM) is the modulation technique utilized by the LoRa physical layer, a widely used and relatively new communication technique for radio low-power wide area networks (LPWANs). In this paper, we adapt and implement FSCM for low-power acoustic underwater communication. Opposed to over-water communication based on the electromagnetic wave, the acoustic wave in water travels much slower. Consequently, acoustic underwater communication is more sensitive to motion-based Doppler shifts. For resilient acoustic underwater communication, Doppler tracking and removal is mandatory. In this paper, we mathematically derive the effect of Doppler shifts to FSCM symbols. Afterwards, we describe a novel algorithm for a low-power receiver to track Doppler shifts without modification of the transmitted packet. Finally, we evaluate and compare our algorithm to another Doppler estimation algorithm from literature and study the effect on the bit error rate (BER). We show, that our algorithm can improve with little additional computational overhead the BER by a factor of more than 104 in some cases.