Emerging applications such as connected farms, wildness monitoring, smart cities, and Factory of the Future leverage emerging Low Power Wide Area Networks (LPWAN), allowing a good trade-off between radio range, data rate, and energy consumption. However, only few theoretical studies of these recent technologies are available to help network designers to optimize real field deployments or even achieve real-time adaptation of transmission parameters. A new approach based on Marcum function is proposed in this paper to estimate -in a fast and accurate manner -the performance in terms of Bit Error Rate of LoRa, one of the most used LPWAN technologies. The method is proposed for Gaussian channels, over challenging propagation environments, i.e., Ricean and Nakagami fadings. Simulation results show that our proposed approximation reduces the approximation error about one order of magnitude compared to existing ones and can be computed by classical software.

In the last decade Internet of Things (IoT) grew up in an exponential behavior with applications requiring long range and low power wireless transmissions. Factory of the Future (FoF), also called Industry 4.0, aims to use IoT technologies to enhance productivity, therefore adding high reliability constraints. Several IoT standards were proposed and LoRa has emerged as a high potential candidate for a variety of applications. LoRa modulation is based on a chirp spread-spectrum technique and offers efficient transmission up to 50 kbps over several kilometers. The performance of LoRa in terms of symbol or bit error probability has been theoretically analyzed in few recent papers for a Gaussian channel. However, the industrial environment is often corrupted with impulsive non Gaussian noise generated by high-power equipment. In this paper, the impact of impulsive noise, modeled by the Middleton Class-A noise, is introduced and the robustness of a LoRa communication is studied. Compared to the Gaussian case, simulations show that impulsive noise may severely degrade system performance. This Signal-to-Noise Ratio loss can reach up to 10 dB, but increasing the spreading factor can reduce the noise impact.

In the last years, LoRa has emerged as a high potential candidate among several standards for the Internet of Things (IoT) subject to an exponential development. LoRa modulation is based on a classical chirp spread-spectrum technique and permits wireless data transmission up to 50 kbps over several kilometers with a high energy efficiency. Although a well-known principle, its performance in terms of symbol or bit error probability has been theoretically analyzed in few recent papers only. Recently, closedform approximations of Bit Error Probability (BEP) for additive white Gaussian noise channels and Rayleigh fading channels were proposed. In this paper, we introduce a new approach using Marcum function for approximating the LoRa BEP. The latter is available for both Additive White Gaussian Noise channels and Rayleigh fading channels and the approach should deal with a variety of fadings. Simulations and comparisons with the state of the art show that the proposed approximation is almost ten times more accurate and may be considered as a numerical reference.