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A Stability of High Order Distributed Power Control
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
(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: urn:nbn:se:kth:diva-93259OAI: oai:DiVA.org:kth-93259DiVA: diva2:515473
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
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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CiteExportLink to record
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