Asynchronous Iterative Water-Filling for Gaussian Frequency-Selective Interference Channels

• Published in: IEEE transactions on information theory Vol. 54; no. 7; pp. 2868 - 2878
• Main Authors: Scutari, G., Palomar, D.P., Barbarossa, S.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Channels; Decoding; Density; Density measurement; Distributed algorithms; Electronics; Exact sciences and technology; Frequency; Game theory; Games; Gaussian; Gaussian frequency-selective interference channel; Information rates; Information theory; Information, signal and communications theory; Interference; Interference channels; Interference constraints; Iterative algorithms; iterative water-filling algorithm; Maximization; Nash equilibrium; Nash Equilibrium (NE); Optimization algorithms; Power measurement; Spectra; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; totally asynchronous algorithm; Transmission and modulation (techniques and equipments); Fading channels; Power spectral density; Information rate; Nash equilibrium; Updating; Iterative method; Power allocation; Game theory; Information transmission; Optimization; Nash Equilib- I rium (NE); Frequency selection; Decentralized system; totally asynchronous algorithm; Distributed algorithm; Gaussian frequency-selective interference channel; iterative water-filling algorithm; Power spectrum
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2008.924723

This paper considers the maximization of information rates for the Gaussian frequency-selective interference channel, subject to power and spectral mask constraints on each link. To derive decentralized solutions that do not require any cooperation among the users, the optimization problem is formulated as a static noncooperative game of complete information. To achieve the so-called Nash equilibria of the game, we propose a new distributed algorithm called asynchronous iterative water-filling algorithm. In this algorithm, the users update their power spectral density (PSD) in a completely distributed and asynchronous way: some users may update their power allocation more frequently than others and they may even use outdated measurements of the received interference. The proposed algorithm represents a unified framework that encompasses and generalizes all known iterative water-filling algorithms, e.g., sequential and simultaneous versions. The main result of the paper consists of a unified set of conditions that guarantee the global converge of the proposed algorithm to the (unique) Nash equilibrium of the game.