Frame Error Rate Approximations in Coded LoRa Systems

Abstract

In this study, we consider the approximations for calculating the frame error rate (FER) of a communication system using the coded low power long range (LoRa) modulation for the additive white Gaussian noise (AWGN) channel. The discrete-time baseband model of the LoRa communication system encompasses the (7,4) Hamming encoder, a diagonal interleaver, a Gray encoder, and the LoRa baseband modulator. Two FER approximations using a tighter uncoded symbol error rate (SER) bound are derived. The derived approximations are compared against the numerical evaluation of the FER in Monte Carlo trials and the state-of-art FER approximations. Numerical results show that the proposed FER approximations are tighter.

Keywords

• Frame Error Rate
• Hamming Coding
• LoRa
• Internet of Things (IoT)

References

1. [1] G. Durisi, T. Koch and P. Popovski, “Toward Massive, Ultrareliable, and Low-Latency Wireless Communication With Short Packets,” in Proceedings of the IEEE, vol. 104, no. 9, pp. 1711-1726, Sept. 2016.
2. [2] M. C. Coşkun et al., “Efficient error-correcting codes in the short blocklength regime,” Phys. Comm., vol. 34, pp. 66-79, Jun. 2019.
3. [3] O. Afisiadis, A. Burg and A. Balatsoukas-Stimming, “Coded LoRa Frame Error Rate Analysis”, IEEE ICC, Dublin, Ireland, 2020, pp. 1-6.
4. [4] G. Baruffa, L. Rugini, L. Germani, F. Frescura, “Error probability performance of chirp modulation in uncoded and coded LoRa systems,” Digit. Signal Process., vol. 106, Nov. 2020.
5. [5] J. Tapparel, M. Xhonneux, D. Bol, J. Louveaux and A. Burg, "Enhancing the reliability of dense LoRaWAN networks with multiuser receivers", IEEE Open J. Commun. Soc., vol. 2, pp. 2725-2738, 2021.
6. [6] T. Elshabrawy and J. Robert, “Closed-Form Approximation of LoRa Modulation BER Performance,” in IEEE Comm. Letters, vol. 22, no. 9, pp. 1778-1781, Sept. 2018.
7. [7] R. V. Şenyuva, “Union bounds on the symbol error probability of LoRa modulation for flat Rician block fading channels”, Phys. Comm., vol. 58, 2023.
8. [8] Z. L. OO, T. W. Lai, and A. Moe, “IoT Based Home Automation System using a REST API Architecture”, EJT, vol. 12, no. 2, pp. 123-128, 2022.

9. [9] R. Daş, and T. Ababaker, “Design and Application of a Smart Home System based on Internet of Things”, EJT, vol. 11, no. 1, pp. 34-42, 2021.
10. [10] F. Abdulkafi, S. Kurnaz, and F. A. Abdulkafi, “Security Improvements of Internet of Things Systems.” EJT, vol. 10, no. 2, pp. 476 - 488, 2020.
11. [11] U. Raza, P. Kulkarni and M. Sooriyabandara, “Low Power Wide Area Networks: An Overview,” in IEEE Comm. Surveys & Tutorials, vol. 19, no. 2, pp. 855-873, Secondquarter 2017.
12. [12] M. Centenaro, L. Vangelista, A. Zanella and M. Zorzi, “Long-range communications in unlicensed bands: the rising stars in the IoT and smart city scenarios,” in IEEE Wireless Comm., vol. 23, no. 5, pp. 60-67, Oct. 2016.
13. [13] M. Chiani and A. Elzanaty, “On the LoRa Modulation for IoT: Waveform Properties and Spectral Analysis,” in IEEE Internet Things J., vol. 6, no. 5, pp. 8463-8470, Oct. 2019.
14. [14] R. Ghanaatian, O. Afisiadis, M. Cotting and A. Burg, “Lora Digital Receiver Analysis and Implementation,” IEEE ICASSP, Brighton, UK, 2019, pp. 1498-1502.
15. [15] H. Ma, Y. Fang, G. Cai, G. Han and Y. Li, “A New Frequency-Bin-Index LoRa System for High-Data-Rate Transmission: Design and Performance Analysis,” in IEEE Internet Things J., vol. 9, no. 14, pp. 12515-12528, July 2022.
16. [16] T. Elshabrawy and J. Robert, “Interleaved Chirp Spreading LoRa-Based Modulation,” in IEEE Internet Things J., vol. 6, no. 2, pp. 3855-3863, April 2019.
17. [17] M. Hanif and H. H. Nguyen, “Slope-Shift Keying LoRa-Based Modulation,” in IEEE Internet Things J., vol. 8, no. 1, pp. 211-221, 1 Jan.1, 2021.
18. [18] R. V. Şenyuva, “Comparison of LoRa-Based Modulations,” IEEE SIU, Safranbolu, Turkey, 2022, pp. 1-4.
19. [19] O. Afisiadis, M. Cotting, A. Burg and A. Balatsoukas-Stimming, “On the Error Rate of the LoRa Modulation With Interference,” in IEEE Trans. Wireless Comm., vol. 19, no. 2, pp. 1292-1304, Feb. 2020.
20. [20] O. Afisiadis, S. Li, J. Tapparel, A. Burg and A. Balatsoukas-Stimming, “On the Advantage of Coherent LoRa Detection in the Presence of Interference,” in IEEE Internet Things J., vol. 8, no. 14, pp. 11581-11593, July 2021.
21. [21] J. Courjault, B. Vrigneau, O. Berder and M. R. Bhatnagar, “A Computable Form for LoRa Performance Estimation: Application to Ricean and Nakagami Fading,” in IEEE Access, vol. 9, pp. 81601-81611, 2021.