Delay-Stability of Power Control in Wireless Networks

In this thesis, we investigate the stability of uplink power control algorithms in wireless networks. We derive an abstract block-diagram model of the power-control loop similar to the model in [6]. The power control loop regulates the energy output of the mobile devices based on measurements of the incoming signal strengths, background noise and interference. The goal of the implemented algorithm is to maintain a certain Signal-to- Interference Ratio (SIR) for all users. Our analysis is done locally by linearizing the system around a steady state. There, we can use a system-specific multivariate Nyquist criterion to analyze stability. In this framework, we also find bounds on the rate of convergence as a performance measure. A focus in this work lies on the influence of time delays and how one can compensate for them. Consequently, we investigate Time-Delay Compensation (TDC, see [6]) and find an extended version of it. We also extend our model to incorporate binary control feedback to match the realworld system. The emerging oscillatory behavior is then predicted and investigated by multivariate describing-function methods. The work is concluded by evaluating our findings with simulations using a Matlab/ Simulink model.