Error probability performance of chirp modulation in uncoded and coded LoRa systems

This paper focuses on the error probability performance of LoRa, a long-range low-power wireless communication technology suited for the Internet of Things (IoT). We propose accurate approximations for the bit error probability of the uncoded LoRa chirp modulation in additive white Gaussian noise (AWGN) channel. Our approach, which is based on a smart modification of a union bound on the error probability, is applied to both coherent and noncoherent detection. Simulation results show that the proposed theoretical bit error rate (BER) expressions are more accurate than the existing BER approximations that use similar complexity. We show that the proposed BER expressions are valid for both orthogonal and quasi-orthogonal LoRa, and are easier to compute than the exact BER for orthogonal signaling. Moreover, we extend the theoretical performance analysis to coded LoRa systems and we propose analytical BER expressions for Hamming-coded LoRa signals with hard-decision decoding. In addition, we analyze by simulation the error probability of coded LoRa systems with soft-decision decoding in multipath channels. The obtained results (both theoretical and simulated) quantify the performance gains of channel coding with respect to uncoded transmissions, in both AWGN and multipath channels, for coded LoRa systems that use the same bandwidth (with lower bit rate) of the uncoded LoRa system.