Iterative D.C. Optimization of Precoding in Wireless MIMO Relaying
Optimizations of precoding matrices in precode-and-forward (PF) MIMO relaying are nonconvex programs in precoding matrix variables. The semidefinite relaxation (SDR) technique, which relaxes the concerned nonconvex quadratic constraints by (convex) semi-definite ones, can locate the optimal solution...
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| Published in: | IEEE transactions on wireless communications Vol. 12; no. 4; pp. 1617 - 1627 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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New York, NY
IEEE
01.04.2013
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1536-1276, 1558-2248 |
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| Abstract | Optimizations of precoding matrices in precode-and-forward (PF) MIMO relaying are nonconvex programs in precoding matrix variables. The semidefinite relaxation (SDR) technique, which relaxes the concerned nonconvex quadratic constraints by (convex) semi-definite ones, can locate the optimal solutions, provided that the numbers of relaying antennas and users are very small. The computational complexity of the SDR grows explosively even with a very moderate increase in the numbers of relaying antennas and/or users, making the existing semidefinite programming (SDP) solvers incapable. In this paper, much more efficient problem formulations of precoding matrix design that exploit the spectral matrix optimization are developed. Such formulations have a low dimensionality and are computationally-tractable nonconvex matrix programs. Furthermore, by exploiting their partial convex structures in the d.c. (difference of two convex functions) framework, new effective iterative solutions are obtained. Extensive simulation results are presented to support the computational advantage of the proposed approach and show that the proposed approach can effectively handle all three considered optimization problems of precoding matrices in MIMO PF relaying, while the SDR approach either is computationally impractical or fails. |
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| AbstractList | Optimizations of precoding matrices in precode-and-forward (PF) MIMO relaying are nonconvex programs in precoding matrix variables. The semidefinite relaxation (SDR) technique, which relaxes the concerned nonconvex quadratic constraints by (convex) semi-definite ones, can locate the optimal solutions, provided that the numbers of relaying antennas and users are very small. The computational complexity of the SDR grows explosively even with a very moderate increase in the numbers of relaying antennas and/or users, making the existing semidefinite programming (SDP) solvers incapable. In this paper, much more efficient problem formulations of precoding matrix design that exploit the spectral matrix optimization are developed. Such formulations have a low dimensionality and are computationally-tractable nonconvex matrix programs. Furthermore, by exploiting their partial convex structures in the d.c. (difference of two convex functions) framework, new effective iterative solutions are obtained. Extensive simulation results are presented to support the computational advantage of the proposed approach and show that the proposed approach can effectively handle all three considered optimization problems of precoding matrices in MIMO PF relaying, while the SDR approach either is computationally impractical or fails. |
| Author | Nguyen, Ha H. Tuan, H. D. Phan, A. H. Kha, H. H. |
| Author_xml | – sequence: 1 givenname: A. H. surname: Phan fullname: Phan, A. H. email: anh.phan@student.uts.edu.au organization: Fac. of Eng. & Inf. Technol., Univ. of Technol. Sydney, Sydney, NSW, Australia – sequence: 2 givenname: H. D. surname: Tuan fullname: Tuan, H. D. email: tuan.hoang@uts.edu.au organization: Fac. of Eng. & Inf. Technol., Univ. of Technol. Sydney, Sydney, NSW, Australia – sequence: 3 givenname: H. H. surname: Kha fullname: Kha, H. H. email: khahoang.ha@uts.edu.au organization: Fac. of Eng. & Inf. Technol., Univ. of Technol. Sydney, Sydney, NSW, Australia – sequence: 4 givenname: Ha H. surname: Nguyen fullname: Nguyen, Ha H. email: ha.nguyen@usask.ca organization: Dept. of Electr. & Comput. Eng., Univ. of Saskatchewan, Saskatoon, SK, Canada |
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| Keywords | MIMO system Relaying Dimensionality Relay Wireless telecommunication Iterative method Computational complexity Convex programming Optimization semidefinite programming Relaxation precode-and-forward (PF) relaying Simulation Coding Optimal solution d.c (difference of convex functions) programming Convex function Pretreatment MIMO relay Antenna Software radio |
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| SubjectTerms | Algorithms Antennas Applied sciences Coding, codes Computation d.c. (difference of convex functions) programming Exact sciences and technology Information, signal and communications theory Interference Linear programming Mathematical analysis Mathematical models Matrices Matrix methods MIMO MIMO relay Optimization precode-and-forward (PF) relaying Radiocommunication specific techniques Radiocommunications Relaying Relays semidefinite programming Signal and communications theory Signal to noise ratio Studies Telecommunications Telecommunications and information theory Vectors |
| Title | Iterative D.C. Optimization of Precoding in Wireless MIMO Relaying |
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