Modeling and Stability Analysis of Rate and Power Control Systems in Wireless Communication Networks

Sammanfattning: Wireless data traffic in cellular networks is currently undergoing a strong global expansion and the demand for high and reliable data throughput increases. Capacity is, however, a limited resource, and in radio resource management a trade-off has to be made between the congestion level, related to cell coverage and interference levels, and the Quality of Service (QoS) or data rates of the users. The radio channel conditions vary on a fast time scale and the measurements of the received signals are subject to disturbances and uncertainties. This motivates the use of control strategies to update the transmission powers. In fact, in implementations of uplink in cellular networks, the performance of the network is ensured by using a fast inner power control algorithm to track a QoS-target and a slower outer control algorithm to limit congestion. Several theoretical challenges arise in this problem setting. Due to the nature of the network, both information and control are distributed. Furthermore, measurements of the congestion and the QoS are used in the control loops, which introduces nonlinear feedback. Another complicating factor is that filtering, computations and information exchange in the network cause time-delays and dynamics. In this thesis we address these challenges by using modeling and analysis tools in systems and control. The objective is to provide systematic methods to quantify the fundamental limitations of the system and to point out the trade-offs for a given system design. We perform stability analysis on a high mathematical level that provides results that are simple to compute and that reveal the system structure.In Paper A we extend existing power control models and stability frameworks to include dynamics. For this we use a general definition of the interference. Moreover, stability is addressed by a monotonicity approach and by proposing a Lyapunov function. Paper B provides less conservative stability results using input-output analysis for the same system model. Stability of a linearization of the system model is studied in Paper C with the multivariate Nyquist criterion. Moreover, we use discrete multivariate describing functions to analyze the equilibrium oscillations that arise due to binary feedback. In Paper D we extend the model with an outer control loop, which dynamically sets the reference value to the control algorithm studied in Papers A to C. The main analysis tool for stability is input-output theory.