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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.

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