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Modeling and Stability Analysis of Rate and Power Control Systems in Wireless Communication Networks
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
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: urn:nbn:se:kth:diva-93222ISBN: 987-91-7501-302-2 OAI: oai:DiVA.org:kth-93222DiVA: diva2:515417
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
List of papers
1. A Stability of High Order Distributed Power Control
Open this publication in new window or tab >>A Stability of High Order Distributed Power Control
(English)Manuscript (preprint) (Other academic)
Abstract [en]

A major challenge in power control of wireless networks is higher order dynamics introduced in implementations. In this paper we propose an extended distributed power control algorithm for wireless networks with high order dynamics included. A general class of interference functions is considered and sufficient conditions for stability are derived using two approaches. First stability is addressed using analysis in linear scale and then using logarithmic variables in a control theoretic approach with Lyapunov theory. Furthermore we prove local exponential convergence for the extended system model.

National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-93259 (URN)
Note
Parts of the material is previously published in Proceedings of the European Control Conference 2009 and Proceedings of the 48th IEEE Conference on Decision and Control 2009. QC 201204113Available from: 2012-04-13 Created: 2012-04-13 Last updated: 2012-04-13Bibliographically approved
2. Input-Output Analysis of Power Controlin Wireless Networks
Open this publication in new window or tab >>Input-Output Analysis of Power Controlin Wireless Networks
2010 (English)In: Proceedings of the IEEE Conference on Decision and Control, 2010, 6451-6456 p.Conference paper, Published paper (Refereed)
Abstract [en]

In a wireless communication network different users share a common resource. An objective of radio resource management is to assign the resources in an effective way between the users. Power control is an important component in this setting that has been extensively studied over the last two decades. In many real networks there are inherent time delays due to filtering of signals and control signaling. Time delays can affect stability and convergence properties of the power control algorithms. We therefore consider power control laws of higher order to include models with delays and delay compensation. The main contribution of this paper is to prove less conservative conditions for system stability. Our primary tool to reduce conservativeness is to use scalings in an input-output framework for stability analysis.

National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-93260 (URN)10.1109/CDC.2010.5717842 (DOI)000295049107050 ()2-s2.0-79953146753 (Scopus ID)978-1-4244-7746-3 (ISBN)
Conference
2010 49th IEEE Conference on Decision and Control, CDC 2010;Atlanta, GA
Note

QC 20120904

Available from: 2012-04-13 Created: 2012-04-13 Last updated: 2012-09-04Bibliographically approved
3. Local Stability of High Order Power Control in Cellular Networks
Open this publication in new window or tab >>Local Stability of High Order Power Control in Cellular Networks
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.

Series
Proceedings of the IEEE Conference on Decision and Control, ISSN 0191-2216
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-93264 (URN)10.1109/CDC.2011.6161275 (DOI)000303506205024 ()2-s2.0-84860661277 (Scopus ID)978-1-61284-801-3 (ISBN)
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
4. A Stability of High Order Distributed Power Control Algorithms in Cellular Networks
Open this publication in new window or tab >>A Stability of High Order Distributed Power Control Algorithms in Cellular Networks
(English)Manuscript (preprint) (Other academic)
Abstract [en]

In radio resource management for cellular networks a trade-off has to be made between the congestion level, related to the cell coverage and the intercell interference, and the Quality of Service (QoS), or data rates of the users. This is implemented by using a fast inner power control algorithm and an outer rate control algorithm, working on a slower time scale.

Due to the distributed nature of the network, both the information and the control are distributed. Measurements of the congestion and the QoS are used in the control algorithms and this introduces a nonlinear feedback. Another complicating factor is that filtering, computations and information exchange in the network introduce time delays.

In this paper we propose a general high order model as a cascade system with an outer and inner control loop. The control algorithms use distributed information available in the network. The full system model includes the nonlinear feedback from congestion and QoS measurements, time delays and time-scale modeling. We provide sufficient conditions for stability and convergence of the system. Our primary analysis tool is input output theory.

National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-93268 (URN)
Note

Parts of the material is previously published in Proceedings of the 50th IEEE Conference on Decision and Control 2011 and Proceedings of IEEE Global Communications Conference 2011. QC 20120413

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

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