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Local Stability of High Order Power Control in Cellular Networks
University of Stuttgart.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2011 (English)In: 2011 50th IEEE Conference on Decision and Control and European Control Conference, 2011, 4528-4534 p.Conference paper, Published paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
2011. 4528-4534 p.
Series
Proceedings of the IEEE Conference on Decision and Control, ISSN 0191-2216
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-93264DOI: 10.1109/CDC.2011.6161275ISI: 000303506205024Scopus ID: 2-s2.0-84860661277ISBN: 978-1-61284-801-3 (print)OAI: oai:DiVA.org:kth-93264DiVA: diva2:515488
Conference
2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011; Orlando, FL;
Note

QC 20140905

Available from: 2012-04-13 Created: 2012-04-13 Last updated: 2014-09-05Bibliographically approved
In thesis
1. Modeling and Stability Analysis of Rate and Power Control Systems in Wireless Communication Networks
Open this publication in new window or tab >>Modeling and Stability Analysis of Rate and Power Control Systems in Wireless Communication Networks
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. xiv, 34 p.
Series
Trita-MAT. OS, ISSN 1401-2294 ; 2012:01
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-93222 (URN)987-91-7501-302-2 (ISBN)
Public defence
2012-05-04, F3, Lindstedtsvägen 26, Stockholm, 10:00 (English)
Opponent
Supervisors
Funder
ICT - The Next Generation
Note

QC 201204013

Available from: 2012-04-13 Created: 2012-04-12 Last updated: 2013-04-15Bibliographically approved

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Citation style
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