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

Abstract 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.

[1]  Niranjan Suri,et al.  Investigating LoRa for the Internet of Battlefield Things: A Cyber Perspective , 2018, MILCOM 2018 - 2018 IEEE Military Communications Conference (MILCOM).

[2]  Qi Li,et al.  A Data Collection Collar for Vital Signs of Cows on the Grassland Based on LoRa , 2018, 2018 IEEE 15th International Conference on e-Business Engineering (ICEBE).

[3]  Sergio Verdu,et al.  Multiuser Detection , 1998 .

[4]  Jiansheng Zhang,et al.  Experimental Analysis of LoRa CSS Wireless Transmission Characteristics for Forestry Monitoring and Sensing , 2018, 2018 International Symposium in Sensing and Instrumentation in IoT Era (ISSI).

[5]  Alexios Balatsoukas-Stimming,et al.  Coded LoRa Frame Error Rate Analysis , 2019, ICC 2020 - 2020 IEEE International Conference on Communications (ICC).

[6]  Bruce C. Berndt,et al.  The determination of Gauss sums , 1981 .

[7]  Luca Rugini,et al.  Performance of nonorthogonal FSK for the Internet of Things , 2019, Digit. Signal Process..

[8]  Izzat Darwazeh,et al.  Non-Orthogonal Narrowband Internet of Things: A Design for Saving Bandwidth and Doubling the Number of Connected Devices , 2018, IEEE Internet of Things Journal.

[9]  Olivier Berder,et al.  Accurate LoRa Performance Evaluation Using Marcum Function , 2019, 2019 IEEE Global Communications Conference (GLOBECOM).

[10]  Sofie Pollin,et al.  Chirp spread spectrum as a modulation technique for long range communication , 2016, 2016 Symposium on Communications and Vehicular Technologies (SCVT).

[11]  Alexios Balatsoukas-Stimming,et al.  On the Error Rate of the LoRa Modulation With Interference , 2020, IEEE Transactions on Wireless Communications.

[12]  Marco Chiani,et al.  On the LoRa Modulation for IoT: Waveform Properties and Spectral Analysis , 2019, IEEE Internet of Things Journal.

[13]  Ajay Dholakia,et al.  Reduced-complexity decoding of LDPC codes , 2005, IEEE Transactions on Communications.

[14]  Jörg Robert,et al.  Enhancing LoRa Capacity using Non-Binary Single Parity Check Codes , 2018, 2018 14th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob).

[15]  Ingrid Moerman,et al.  LoRa indoor coverage and performance in an industrial environment: Case study , 2017, 2017 22nd IEEE International Conference on Emerging Technologies and Factory Automation (ETFA).

[16]  Boualem Boashash,et al.  Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals , 1992, Proc. IEEE.

[17]  Luca Rugini,et al.  An IoT Architecture for Continuous Livestock Monitoring Using LoRa LPWAN , 2019, Electronics.

[18]  Peter G. Casazza,et al.  Fourier Transforms of Finite Chirps , 2006, EURASIP J. Adv. Signal Process..

[19]  John G. Proakis,et al.  Digital Communications , 1983 .

[20]  Tareq Y. Al-Naffouri,et al.  Sensor placement and resource allocation for energy harvesting IoT networks , 2019, Digit. Signal Process..

[21]  Lorenzo Vangelista,et al.  Frequency Shift Chirp Modulation: The LoRa Modulation , 2017, IEEE Signal Processing Letters.

[22]  Ramesh Annavajjala,et al.  On the optimality of bit detection of certain digital modulations , 2005, IEEE Transactions on Communications.

[23]  Luca Rugini,et al.  Tight Upper Bounds on the Probability of Error of Quaternary Simplex Signals , 2015, IEEE Communications Letters.

[24]  Thomas Watteyne,et al.  Understanding the Limits of LoRaWAN , 2016, IEEE Communications Magazine.

[25]  Joerg Robert,et al.  Closed-Form Approximation of LoRa Modulation BER Performance , 2018, IEEE Communications Letters.

[26]  Audrey Giremus,et al.  LoRa Physical Layer Principle and Performance Analysis , 2018, 2018 25th IEEE International Conference on Electronics, Circuits and Systems (ICECS).

[27]  Thomas H. Clausen,et al.  A Study of LoRa: Long Range & Low Power Networks for the Internet of Things , 2016, Sensors.

[28]  Luca Rugini,et al.  Coded LoRa Performance in Wireless Channels , 2019, 2019 IEEE 30th Annual International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC).

[29]  Vincent Lefèvre,et al.  MPFR: A multiple-precision binary floating-point library with correct rounding , 2007, TOMS.

[30]  Mahesh Sooriyabandara,et al.  Low Power Wide Area Networks: An Overview , 2016, IEEE Communications Surveys & Tutorials.

[31]  Konstantin Mikhaylov,et al.  Evaluation of LoRa LPWAN technology for remote health and wellbeing monitoring , 2016, 2016 10th International Symposium on Medical Information and Communication Technology (ISMICT).