scispace - formally typeset
Search or ask a question
Journal ArticleDOI

A simple distributed autonomous power control algorithm and its convergence

01 Nov 1993-IEEE Transactions on Vehicular Technology (IEEE)-Vol. 42, Iss: 4, pp 641-646
TL;DR: For wireless cellular communication systems, one seeks a simple effective means of power control of signals associated with randomly dispersed users that are reusing a single channel in different cells, and the authors demonstrate exponentially fast convergence to these settings whenever power settings exist for which all users meet the rho requirement.
Abstract: For wireless cellular communication systems, one seeks a simple effective means of power control of signals associated with randomly dispersed users that are reusing a single channel in different cells. By effecting the lowest interference environment, in meeting a required minimum signal-to-interference ratio of rho per user, channel reuse is maximized. Distributed procedures for doing this are of special interest, since the centrally administered alternative requires added infrastructure, latency, and network vulnerability. Successful distributed powering entails guiding the evolution of the transmitted power level of each of the signals, using only focal measurements, so that eventually all users meet the rho requirement. The local per channel power measurements include that of the intended signal as well as the undesired interference from other users (plus receiver noise). For a certain simple distributed type of algorithm, whenever power settings exist for which all users meet the rho requirement, the authors demonstrate exponentially fast convergence to these settings. >
Citations
More filters
Book
01 Jan 2005

9,038 citations

Journal ArticleDOI
Roy D. Yates1
TL;DR: It is shown that systems in which transmitter powers are subject to maximum power limitations share these common properties, which permit a general proof of the synchronous and totally asynchronous convergence of the iteration p(t+1)=I(p(t)) to a unique fixed point at which total transmitted power is minimized.
Abstract: In cellular wireless communication systems, transmitted power is regulated to provide each user an acceptable connection by limiting the interference caused by other users. Several models have been considered including: (1) fixed base station assignment where the assignment of users to base stations is fixed, (2) minimum power assignment where a user is iteratively assigned to the base station at which its signal to interference ratio is highest, and (3) diversity reception where a user's signal is combined from several or perhaps all base stations. For the above models, the uplink power control problem can be reduced to finding a vector p of users' transmitter powers satisfying p/spl ges/I(p) where the jth constraint p/sub j//spl ges/I/sub j/(p) describes the interference that user j must overcome to achieve an acceptable connection. This work unifies results found for these systems by identifying common properties of the interference constraints. It is also shown that systems in which transmitter powers are subject to maximum power limitations share these common properties. These properties permit a general proof of the synchronous and totally asynchronous convergence of the iteration p(t+1)=I(p(t)) to a unique fixed point at which total transmitted power is minimized. >

2,526 citations


Cites background from "A simple distributed autonomous pow..."

  • ...[19], Zander [20], and Foschini and Miljanic [12] use p(t + 1) = IFA(p(t))to solve the subproblem of nding a feasible power vector p....

    [...]

  • ...[19], Zander [20], and Foschini and Miljanic [12] use p(t + 1) = IFA(p(t)) to solve the subproblem of nding a feasible power vector p....

    [...]

  • ...[12] G.J. G.J. Foschini and Z. Miljanic....

    [...]

Journal ArticleDOI
TL;DR: This tutorial paper first reviews the basics of convexity, Lagrange duality, distributed subgradient method, Jacobi and Gauss-Seidel iterations, and implication of different time scales of variable updates, and introduces primal, dual, indirect, partial, and hierarchical decompositions, focusing on network utility maximization problem formulations.
Abstract: A systematic understanding of the decomposability structures in network utility maximization is key to both resource allocation and functionality allocation. It helps us obtain the most appropriate distributed algorithm for a given network resource allocation problem, and quantifies the comparison across architectural alternatives of modularized network design. Decomposition theory naturally provides the mathematical language to build an analytic foundation for the design of modularized and distributed control of networks. In this tutorial paper, we first review the basics of convexity, Lagrange duality, distributed subgradient method, Jacobi and Gauss-Seidel iterations, and implication of different time scales of variable updates. Then, we introduce primal, dual, indirect, partial, and hierarchical decompositions, focusing on network utility maximization problem formulations and the meanings of primal and dual decompositions in terms of network architectures. Finally, we present recent examples on: systematic search for alternative decompositions; decoupling techniques for coupled objective functions; and decoupling techniques for coupled constraint sets that are not readily decomposable

1,725 citations

Journal ArticleDOI
TL;DR: This tutorial paper collects together in one place the basic background material needed to do GP modeling, and shows how to recognize functions and problems compatible with GP, and how to approximate functions or data in a formcompatible with GP.
Abstract: A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions that have a special form. Recently developed solution methods can solve even large-scale GPs extremely efficiently and reliably; at the same time a number of practical problems, particularly in circuit design, have been found to be equivalent to (or well approximated by) GPs. Putting these two together, we get effective solutions for the practical problems. The basic approach in GP modeling is to attempt to express a practical problem, such as an engineering analysis or design problem, in GP format. In the best case, this formulation is exact; when this is not possible, we settle for an approximate formulation. This tutorial paper collects together in one place the basic background material needed to do GP modeling. We start with the basic definitions and facts, and some methods used to transform problems into GP format. We show how to recognize functions and problems compatible with GP, and how to approximate functions or data in a form compatible with GP (when this is possible). We give some simple and representative examples, and also describe some common extensions of GP, along with methods for solving (or approximately solving) them.

1,215 citations


Cites background from "A simple distributed autonomous pow..."

  • ...Several problems involving power control in communications systems can be cast as GPs (see,e.g., [74, 72, 55 ])....

    [...]

  • ...4.1 Power control Several problems involving power control in communications systems can be cast as GPs (see, e.g., Kandukuri and Boyd 2002; Julian et al. 2002; Foschini and Miljanic 1993)....

    [...]

Journal ArticleDOI
TL;DR: The iterative water-filling algorithm can be implemented distributively without the need for centralized control, and it reaches a competitively optimal power allocation by offering an opportunity for loops to negotiate the best use of power and frequency with each other.
Abstract: This paper considers the multiuser power control problem in a frequency-selective interference channel. The interference channel is modeled as a noncooperative game, and the existence and uniqueness of a Nash equilibrium are established for a two-player version of the game. An iterative water-filling algorithm is proposed to efficiently reach the Nash equilibrium. The iterative water-filling algorithm can be implemented distributively without the need for centralized control. It implicitly takes into account the loop transfer functions and cross couplings, and it reaches a competitively optimal power allocation by offering an opportunity for loops to negotiate the best use of power and frequency with each other. When applied to the upstream power backoff problem in very-high bit-rate digital subscriber lines and the downstream spectral compatibility problem in asymmetric digital subscriber lines, the new power control algorithm is found to give a significant performance improvement when compared with existing methods.

946 citations


Cites background from "A simple distributed autonomous pow..."

  • ...Nevertheless, power control schemes designed for wireless systems [ 2 ], [6], [4] still provide us with considerable insight....

    [...]

  • ...The power control problem in DSL systems differs from the more widely studied power control problem in wireless systems (e.g., [ 2 ]‐[5]) in two key aspects....

    [...]

References
More filters
Book
30 Nov 1961
TL;DR: In this article, the authors propose Matrix Methods for Parabolic Partial Differential Equations (PPDE) and estimate of Acceleration Parameters, and derive the solution of Elliptic Difference Equations.
Abstract: Matrix Properties and Concepts.- Nonnegative Matrices.- Basic Iterative Methods and Comparison Theorems.- Successive Overrelaxation Iterative Methods.- Semi-Iterative Methods.- Derivation and Solution of Elliptic Difference Equations.- Alternating-Direction Implicit Iterative Methods.- Matrix Methods for Parabolic Partial Differential Equations.- Estimation of Acceleration Parameters.

5,317 citations

Journal ArticleDOI
TL;DR: In order to derive upper performance bounds for transmitter power control schemes, algorithms that are optimum in the sense that the interference probability is minimized are suggested.
Abstract: Most cellular radio systems provide for the use of transmitter power control to reduce cochannel interference for a given channel allocation. Efficient interference management aims at achieving acceptable carrier-to-interference ratios in all active communication links in the system. Such schemes for the control of cochannel interference are investigated. The effect of adjacent channel interference is neglected. As a performance measure, the interference (outage) probability is used, i.e., the probability that a randomly chosen link is subject to excessive interference. In order to derive upper performance bounds for transmitter power control schemes, algorithms that are optimum in the sense that the interference probability is minimized are suggested. Numerical results indicate that these upper bounds exceed the performance of conventional systems by an order of magnitude regarding interference suppression and by a factor of 3 to 4 regarding the system capacity. The structure of the optimum algorithm shows that efficient power control and dynamic channel assignment algorithms are closely related. >

1,256 citations


"A simple distributed autonomous pow..." refers background or methods in this paper

  • ...3References [ 3 ] and [4] take a preliminary look at the effect of fast fading on the power control scheme reported there, and suggest that it does not undermine control accuracy very much....

    [...]

  • ...For analytical work on power control in wireless systems see [1]-[9].l J. Zander, in [ 3 ], (which builds on the basic reference [2]) as well as Zander’s companion paper, [4], report interesting initial work on distributed power control.2 Namely, an iterative scheme is presented that operates under the assumption that the transmitter power is sufficiently high in order to allow receiver noise to be neglected....

    [...]

  • ...Also, as we have already mentioned, we will work with a prefixed target p that our algorithm will succeed or fail in attaining for all users, rather than the interesting, but different, floating “best-we-cando-under-the-circumstances’’ type of objective considered in [ 3 ] and [4]....

    [...]

  • ...As will be apparent to those readers familiar with the iterative scheme in [ 3 ] and [4], while there are strong similarities, key features differ from the algorithm that will occupy us here....

    [...]

  • ...‘References [ 3 ], [7], and, [Sj provide an up-to-date listing of references, including several of special interest for the area of spread spectrum communications....

    [...]

Book
16 Sep 2010
TL;DR: This book presents an enormous amount of information in a concise and accessible format and begins with the assumption that the reader has never seen a matrix.

1,236 citations

Book
22 Nov 2021
TL;DR: Numerical Methods: Concepts.
Abstract: (Chapter Headings) Definitions and Concepts. Transformations. Exact Analytical Methods. Exact Methods for ODEs. Exact Methods for PDEs. Approximate Analytical Methods. Numerical Methods: Concepts. Numerical Methods for ODEs. Numerical Methods for PDEs. List of Tables. List of Programs. List of Figures. Subject Index.

917 citations