Coverage probability of energy harvesting enabled LoRa networks with stochastic geometry

ABSTRACT

The average transmit power and coverage probability (Pcov) of uplink energy harvesting-enabled long-range networks are investigated in the present paper. Particularly, we model the end-device (EDs) according to the homogeneous Poisson point process while the power beacon is randomly distributed on the circle in the middle of the network. All EDs rely on the harvested energy to perform their operations and transmissions. Under this context, the upper bound of the average transmit power of an end-device is derived in the closed-form expression. The signal-to-noise-ratio condition of the coverage probability is given in the closed-form expression as well. Simulation results are provided to corroborate the accuracy of the derived mathematical framework as well as to feature the impact of some key parameters on the considered metrics. Our findings unveil that increasing either the number of power beacons or their transmit power will monotonically ameliorate the Pcov. Nevertheless, rising the average number of EDs will significantly decline the Pcov's performance.

KEYWORDS:

• Coverage probability
• energy harvesting
• LoRa networks
• performance analysis

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Here we consider a finite network radius $R<\mathrm{\infty }$, if the network's radius approaches infinity, the system performance will, of course, degrade owing to the severe impact of large-scale path-loss. To mitigate such an ultra-long transmission, multiple gateways are one of the most effective solutions since they dramatically reduce the transmission distance (Tu et al., 2022b). Nonetheless, we leave such an interesting network for future work.

2 Other performance metrics such as average lifetime, and spectral efficiency can be effortlessly extended from the coverage probability (Nguyen et al., 2023b). Nonetheless, to comprehensively study these metrics, we leave it for the future work.

3 It is noted that the derived framework can be considered as an upper bound of the exact framework (Tu et al., 2020).

Additional information

Funding

This research is funded by Posts and Telecommunications Institute of Technology [grant number 19-2023-HV-TH2].

Notes on contributors

Thi-Tuyet-Hai Nguyen

Thi-Tuyet-Hai Nguyen (Email: [email protected]) got the Ph.D. degree from La Rochelle University, La Rochelle, France, in 2020. She has been working at the Faculty of Information Technology 2, Posts and Telecommunications Institute of Technology, HCM campus, Vietnam since 2012. Her research interests are natural language processing, machine learning, information retrieval, chatbot, and LoRa networks.

Tan N. Nguyen

Tan N. Nguyen (Email: [email protected]) was born in 1986 in Nha Trang City, Vietnam. He received a BS degree in electronics in 2008 from Ho Chi Minh University of Natural Sciences and an MS degree in telecommunications engineering in 2012 from Vietnam National University. He received a Ph.D. in communications technologies in 2019 from the Faculty of Electrical Engineering and Computer Science at VSB – Technical University of Ostrava, Czech Republic. He joined the Faculty of Electrical and Electronics Engineering of Ton Duc Thang University, Vietnam, in 2013, and since then has been lecturing. His major interests are cooperative communications, cognitive radio, physical layer security and signal processing.

Tran Trung Duy

Tran Trung Duy (Email: [email protected]) received the Ph.D degree in electrical engineering from University of Ulsan, South Korea in 2013. In 2013, he joined Posts and Telecommunications Institute of Technology, HoChiMinh city campus (PTIT-HCM), as a lecturer. From 2022, he is an associate Professor of Wireless Communications at PTIT-HCM. His major research interests are cooperative communications, cooperative multi-hop, cognitive radio, physical-layer security, energy harvesting, hardware impairments and Fountain codes.

Nguyen Hong Son

Nguyen Hong Son (Email: [email protected]) received his B.Sc. in Computer Engineering from The University of Technology in HCM city, and his M.Sc. and Ph.D. in Communication Engineering from the Post and Telecommunication Institute of Technology in Hanoi, Vietnam. His research interests include communication engineering, machine learning, network security, and cloud computing.

Tan Hanh

Tan Hanh (Email: [email protected]) received the PhD degree from Grenoble Institute of Technology, France. Currently, he is vice president of Posts and Telecommunications Institute of Technology (PTIT), in charge of Ho Chi Minh city campus. His research interests are machine learning, information retrieval, and data mining.

Minh Bui Vu

Minh Bui Vu (Email: [email protected]) was born on March 02, 1991 in Dong Nai, Vietnam. He graduated in Electrical and Electronic Engineering in 2014 from Nguyen Tat Thanh University, Ho Chi Minh City, Vietnam. End of 2014, he joined the Faculty of Electrical and Electronics of Nguyen Tat Thanh University as Laboratory-Practice management, until in 2017 he was a lecturer. In 2019, he received Master degree in Engineering Electrical from Ho Chi Minh City University of Technology and Education. His major research interests are Artificial Neuron Network, Fuzzy Logic, Wireless Networks.

Lam-Thanh Tu

Lam-Thanh Tu (Email: [email protected]) received the Ph.D. degree from the University of Paris Sud, Paris-Saclay University, France, in 2018. From 2022, he has been with the Faculty of Electrical and Electronics Engineering, at Ton Duc Thang University, Vietnam. His research interests include stochastic geometry, LoRa networks, reconfigurable intelligent surfaces, covert communications, and artificial intelligence applications for wireless communications.