Sum-Rate Maximization in Two-Way AF MIMO Relaying: Polynomial Time Solutions to a Class of DC Programming Problems
Sum-rate maximization in two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying belongs to the class of difference-of-convex functions (DC) programming problems. DC programming problems occur also in other signal processing applications and are typically solved using differe...
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| Veröffentlicht in: | IEEE transactions on signal processing Jg. 60; H. 10; S. 5478 - 5493 |
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| Sprache: | Englisch |
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IEEE
01.10.2012
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1053-587X, 1941-0476 |
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| Abstract | Sum-rate maximization in two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying belongs to the class of difference-of-convex functions (DC) programming problems. DC programming problems occur also in other signal processing applications and are typically solved using different modifications of the branch-and-bound method which, however, does not have any polynomial time complexity guarantees. In this paper, we develop two efficient polynomial time algorithms for the sum-rate maximization in two-way AF MIMO relaying. The first algorithm guarantees to find at least a Karush-Kuhn-Tucker (KKT) solution. There is a strong evidence, however, that such a solution is actually globally optimal. The second algorithm that is based on the generalized eigenvectors shows the same performance as the first one with reduced computational complexity. The objective function of the problem is represented as a product of quadratic fractional ratios and parameterized so that its convex part (versus the concave part) contains only one (or two) optimization variables. One of the algorithms is called POlynomial Time DC (POTDC) and is based on semi-definite programming (SDP) relaxation, linearization, and an iterative Newton-type search over a single parameter. The other algorithm is called RAte-maximization via Generalized EigenvectorS (RAGES) and is based on the generalized eigenvectors method and an iterative search over two (or one, in its approximate version) optimization variables. We derive an upper-bound for the optimal value of the corresponding optimization problem and show by simulations that this upper-bound is achieved by both algorithms. It provides an evidence that the algorithms find a global optimum. The proposed methods are also superior to other state-of-the-art algorithms. |
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| AbstractList | Sum-rate maximization in two-way amplify-and- forward (AF) multiple-input multiple-output (MIMO) relaying belongs to the class of difference-of-convex functions (DC) programming problems. DC programming problems occur also in other signal processing applications and are typically solved using different modifications of the branch-and-bound method which, however, does not have any polynomial time complexity guarantees. In this paper, we develop two efficient polynomial time algorithms for the sum-rate maximization in two-way AF MIMO relaying. The first algorithm guarantees to find at least a Karush-Kuhn-Tucker (KKT) solution. There is a strong evidence, however, that such a solution is actually globally optimal. The second algorithm that is based on the generalized eigenvectors shows the same performance as the first one with reduced computational complexity. Sum-rate maximization in two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relaying belongs to the class of difference-of-convex functions (DC) programming problems. DC programming problems occur also in other signal processing applications and are typically solved using different modifications of the branch-and-bound method which, however, does not have any polynomial time complexity guarantees. In this paper, we develop two efficient polynomial time algorithms for the sum-rate maximization in two-way AF MIMO relaying. The first algorithm guarantees to find at least a Karush-Kuhn-Tucker (KKT) solution. There is a strong evidence, however, that such a solution is actually globally optimal. The second algorithm that is based on the generalized eigenvectors shows the same performance as the first one with reduced computational complexity. The objective function of the problem is represented as a product of quadratic fractional ratios and parameterized so that its convex part (versus the concave part) contains only one (or two) optimization variables. One of the algorithms is called POlynomial Time DC (POTDC) and is based on semi-definite programming (SDP) relaxation, linearization, and an iterative Newton-type search over a single parameter. The other algorithm is called RAte-maximization via Generalized EigenvectorS (RAGES) and is based on the generalized eigenvectors method and an iterative search over two (or one, in its approximate version) optimization variables. We derive an upper-bound for the optimal value of the corresponding optimization problem and show by simulations that this upper-bound is achieved by both algorithms. It provides an evidence that the algorithms find a global optimum. The proposed methods are also superior to other state-of-the-art algorithms. |
| Author | Roemer, F. Haardt, M. Khabbazibasmenj, A. Vorobyov, S. A. |
| Author_xml | – sequence: 1 givenname: A. surname: Khabbazibasmenj fullname: Khabbazibasmenj, A. email: khabbazi@ualberta.ca organization: Dept. of Electr. & Comput. Eng., Univ. of Alberta, Edmonton, AB, Canada – sequence: 2 givenname: F. surname: Roemer fullname: Roemer, F. email: roemer@tu-ilmenau.de organization: Commun. Res. Lab., Ilmenau Univ. of Technol., Ilmenau, Germany – sequence: 3 givenname: S. A. surname: Vorobyov fullname: Vorobyov, S. A. email: svorobyo@ualberta.ca organization: Dept. of Electr. & Comput. Eng., Univ. of Alberta, Edmonton, AB, Canada – sequence: 4 givenname: M. surname: Haardt fullname: Haardt, M. email: martin.haardt@tu-ilmenau.de organization: Commun. Res. Lab., Ilmenau Univ. of Technol., Ilmenau, Germany |
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| Keywords | Performance evaluation Relaying Iterative method Polynomial method Convex programming Optimization Call time Relaxation Convex function Routing protocols two-way relaying Linearization MIMO system semi-definite programming relaxation Branch and bound method Eigenvector Transmission protocol Algorithm Computational complexity Polynomial time non-convex programming sum-rate maximization Algorithm performance Signal processing Objective function Time complexity Difference-of-convex functions (DC) programming |
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| SubjectTerms | Algorithms Applied sciences Complexity Detection, estimation, filtering, equalization, prediction Difference-of-convex functions (DC) programming Direct current Exact sciences and technology Information, signal and communications theory Mathematical models Maximization Noise non-convex programming Optimization Polynomials Programming Relaying Relays semi-definite programming relaxation Signal and communications theory Signal processing Signal processing algorithms Signal, noise sum-rate maximization Telecommunications and information theory two-way relaying Vectors |
| Title | Sum-Rate Maximization in Two-Way AF MIMO Relaying: Polynomial Time Solutions to a Class of DC Programming Problems |
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