Probabilistic stability of power control systems with Nakagami-m fading channels

ABSTRACT

This paper analyses the probabilistic stability of power control systems under Nakagami-m fading channels caused by multi-path propagation. First, the Nakagami-m fading model is utilised to capture the feature of shadowed fading channels. The Foschini–Miljanic algorithm is utilised to achieve the desired quality-of-service, and a stability condition is given for the power control system. Then, the probability of the system being stable is obtained for power control systems. Afterwards, the monotonicity of the probability with respect to the communication distance is revealed, which sheds light on the node configuration. Furthermore, it is shown that Nakagami-m fading links can model the channel gains better than Rayleigh fading links by adjusting the shape parameter. Finally, an example is given to illustrate the effectiveness of the theoretical results.

KEYWORDS:

• Nakagami-m fading channel
• power control
• Foschini–Miljanic algorithm
• positive systems

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article.

Disclosure statement

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

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [Grant Numbers 61973156 and 61603180], in part by the Natural Science Foundation of Jiangsu Province, China [Grant Number BK20200068].

Notes on contributors

Shoujin Huang

Shoujin Huang received the B.Sc. degree in automation from Shandong University of Science and Technology, Qingdao, China, in 2019, the M.Sc. degree in control engineering from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 2022, where he is currently pursuing the Ph.D. degree in control science and engineering. His research interests include positive systems and its applications.

Jun Shen

Jun Shen received the B.Sc. and M.Sc. degrees from Southeast University, Nanjing, China, in 2008 and 2011, respectively, and the Ph.D. degree from the Department of Mechanical Engineering, the University of Hong Kong, Hong Kong, China, in 2015. Since 2021 he has been a Professor in the College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China. He is Associate Editor or Editorial Board Member of Journal of the Franklin Institute, IEEE Access, Cogent Engineering, IET Journal of Engineering, International Journal of Sensors, Wireless Communications and Control, Guest Editor of IET Control Theory and Applications. He is a Senior Member of IEEE and a Member of IET. His current research interests include positive systems, monotone systems, fractional-order systems, model reduction and robust control and filtering.