Power control in cellular systems subject to constraints and time delays

Stability is a fundamental property desirable for any controlled system. We briefly review the root locus and describing function techniques, which are tools for stability analysis, and show how they can be applied to power control algorithms in cellular radio networks. The root locus method is used to find stability limits on controller parameters, and describing functions for predicting the presence of oscillations in the system. Thus these methods can be used to support the design phase, when deciding upon the appropriate controller parameters. These tools are demonstrated for various control algorithms and when different smoothing filters are applied. The analysis reveals that the distributed power control (DPC) algorithm, which works fine under ideal circumstances, yields an unstable system when subject to a small time delay. Furthermore, it is concluded that the performance with respect to stability is better when the measurements are averaged by an exponential forgetting filter than by the moving average filter