Local stability of high order power control in cellular networks

We address three major control challenges present in power control of wireless cellular networks: time-delays, interference and the binary control feedback. The power control is distributed and based on measurements of the Signal-to-Interference Ratio (SIR). This implies that the users are coupled through the mutual interference. In this paper we show that the interference feedback plays a fundamental role for system stability and behavior. The interference is captured by the so-called feasibility matrix, which contains the interference couplings weighted with SIR-requirements. First, we consider a simplified system and derive a Nyquist stability criterion which separates the system dynamics from the eigenvalues of the feasibility matrix. This criterion is also used to derive bounds on the rate of convergence. Second, we investigate oscillations caused by the binary feedback using harmonic balance techniques. Here, we obtain a similar separation result. Using the structure of the feasibility matrix we derive bounds on the eigenvalue location, which can be seen as a robustness result to disturbances. In an example we illustrate the stability results and predict and observe oscillation modes that are caused by the interference feedback.