On the Different Mathematical Realizations for the Digital Synthesis of LoRa-Based Modulation

LoRa has established itself as one of the leading technologies within evolving Low Power Wide Area Networks. LoRa is primarily pillared on its patented LoRa modulation scheme that features linearly increasing chirp signals that span the LoRa bandwidth. The patented implementation of LoRa signals relies on the accurate generation of stable frequency modulated chirps using a fractional-N phase-locked loop. On the other hand, very limited research have explored alternatives for the DSP realization of LoRa-based modulation. In this paper, we focus on mathematical representations that enable the DSP generation of LoRa signals. Furthermore, we emphasize on the ability to guarantee inter-symbol phase continuity with the perspective of supporting coherent detection of LoRa signals. In conjunction with such coherent realizations, we investigate utilization of the quadrature axis with respect to each nominal LoRa signal in constructing additional orthogonal dimensions for LoRa signaling. Consequently, each transmitted extended LoRa (E-LoRa) symbol may include one extra bit when compared to nominal LoRa symbols. We build on our previous analysis for the non-coherent detection of LoRa signals in order to derive approximation formulas for BER performance of nominal LoRa under coherent detection as well as of E-LoRa. Analytical and simulation results show that coherent detection of LoRa renders approximately 0.7 dB of performance gain. On the other hand, E-LoRa supports a capacity increase that could reach up to 14% with a minimal penalty on BER performance at the scale of only 0.3 dB.