A rank-one optimization framework and its applications to transmit beamforming

Article

Le, T., Ng, D. and Yang, X. 2024. A rank-one optimization framework and its applications to transmit beamforming. IEEE Transactions on Vehicular Technology. 73 (1), pp. 620-636. https://doi.org/10.1109/TVT.2023.3303623
TypeArticle
TitleA rank-one optimization framework and its applications to transmit beamforming
AuthorsLe, T., Ng, D. and Yang, X.
Abstract

This paper proposes an elegant optimization framework consisting of a mix of linear-matrix-inequality and second-order-cone constraints. The proposed framework generalizes the semidefinite relaxation (SDR) enabled solution to the typical transmit beamforming problems presented in the form of quadratically constrained quadratic programs (QCQPs) in the literature. It is proved that the optimization problems subsumed under the framework always admit a rank-one optimal solution when they are feasible and their optimal solutions are not trivial. This finding indicates that the relaxation is tight as the optimal solution of the original beamforming QCQP can be straightforwardly obtained from that of the SDR counterpart without any loss of optimality. Four representative examples of transmit beamforming, i.e., transmit beamforming with perfect channel state information (CSI), transmit beamforming with imperfect CSI, chance-constraint approach for imperfect CSI, and reconfigurable-intelligent-surface (RIS) aided beamforming, are shown to demonstrate how the proposed optimization framework can be realized in deriving the SDR counterparts for different beamforming designs.

KeywordsQuadratically constrained quadratic program; semidefinite relaxation; transmit beamforming; reconfigurable intelligent surfaces; Array signal processing; Optimization; Linear matrix inequalities; Simultaneous wireless information and power transfer; Receivers; Probabilistic logic ; Transforms
Sustainable Development Goals9 Industry, innovation and infrastructure
Middlesex University ThemeCreativity, Culture & Enterprise
PublisherIEEE
JournalIEEE Transactions on Vehicular Technology
ISSN0018-9545
Electronic1939-9359
Publication dates
Online09 Aug 2023
Print17 Jan 2024
Publication process dates
Submitted20 Nov 2022
Accepted05 Aug 2023
Deposited10 Aug 2023
Output statusPublished
Accepted author manuscript
File Access Level
Open
Copyright Statement

© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

Digital Object Identifier (DOI)https://doi.org/10.1109/TVT.2023.3303623
Web of Science identifierWOS:001166813500096
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Chaotic bat algorithm
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Mathematical modelling and parameter optimization of pulsating heat pipes
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A firefly-inspired method for protein structure prediction in lattice models
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True global optimality of the pressure vessel design problem: a benchmark for bio-inspired optimisation algorithms
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Flower pollination algorithm: a novel approach for multiobjective optimization
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Random walks, Lévy flights, Markov chains and metaheuristic optimization
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Metaheuristic algorithms for self-organizing systems: a tutorial
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Downlink optimization with interference pricing and statistical CSI
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Optimal test sequence generation using firefly algorithm
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Flower pollination algorithm for global optimization
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Benchmark problems in structural optimization
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Bat algorithm for topology optimization in microelectronic applications
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Efficiency analysis of swarm intelligence and randomization techniques
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Modelling of a pulsating heat pipe and start up asymptotics
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Free lunch or no free lunch: that is not just a question?
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Coupled eagle strategy and differential evolution for unconstrained and constrained global optimization
Gandomi, A., Yang, X., Talatahari, S. and Deb, S. 2012. Coupled eagle strategy and differential evolution for unconstrained and constrained global optimization. Computers and Mathematics with Applications. 63 (1), pp. 191-200. https://doi.org/10.1016/j.camwa.2011.11.010
Bat algorithm: a novel approach for global engineering optimization
Yang, X. and Gandomi, A. 2012. Bat algorithm: a novel approach for global engineering optimization. Engineering Computations. 29 (5), pp. 464-483. https://doi.org/10.1108/02644401211235834
Evolutionary boundary constraint handling scheme
Gandomi, A. and Yang, X. 2012. Evolutionary boundary constraint handling scheme. Neural Computing and Applications. 21 (6), pp. 1449-1462. https://doi.org/10.1007/s00521-012-1069-0
Two-stage eagle strategy with differential evolution
Yang, X. and Deb, S. 2012. Two-stage eagle strategy with differential evolution. International Journal of Bio-Inspired Computation. 4 (1), pp. 1-5. https://doi.org/10.1504/IJBIC.2012.044932
Firefly Algorithm for solving non-convex economic dispatch problems with valve loading effect
Yang, X., Hosseini, S. and Gandomi, A. 2012. Firefly Algorithm for solving non-convex economic dispatch problems with valve loading effect. Applied Soft Computing. 12 (3), pp. 1180-1186. https://doi.org/10.1016/j.asoc.2011.09.017
User position aware multicell beamforming for a distributed antenna system
Le, T. and Nakhai, M. 2011. User position aware multicell beamforming for a distributed antenna system. IEEE 22nd International Symposium on Personal, Indoor and Mobile Radio Communications. Toronto, ON, Canada 11 - 14 Sep 2011 IEEE. pp. 1423-1427 https://doi.org/10.1109/PIMRC.2011.6139736
An iterative algorithm for downlink multi-cell beam-forming
Le, T. and Nakhai, M. 2011. An iterative algorithm for downlink multi-cell beam-forming. 2011 IEEE Global Telecommunications Conference. Houston, TX, USA 05 - 09 Dec 2011 IEEE. pp. 1-6 https://doi.org/10.1109/GLOCOM.2011.6133913
Throughput analysis of network coding enabled wireless backhauls
Le, T. and Nakhai, M. 2011. Throughput analysis of network coding enabled wireless backhauls. IET Communications. 5 (10), pp. 1318-1327. https://doi.org/10.1049/iet-com.2010.0223
Green radio: radio techniques to enable energy-efficient wireless networks
Han, C., Harrold, T., Armour, S., Krikidis, I., Videv, S., Grant, P., Haas, H., Thompson, J., Ku, I., Wang, C., Le, T., Nakhai, M., Zhang, J. and Hanzo, L. 2011. Green radio: radio techniques to enable energy-efficient wireless networks. IEEE Communications Magazine. 49 (6), pp. 46-54. https://doi.org/10.1109/MCOM.2011.5783984
Power-efficient downlink transmission in multicell networks with limited wireless backhaul
Le, T., Nasseri, S., Zarrebini-Esfahani, A., Nakhai, M. and Mills, A. 2011. Power-efficient downlink transmission in multicell networks with limited wireless backhaul. IEEE Wireless Communications. 18 (5), pp. 82-88. https://doi.org/10.1109/MWC.2011.6056696
Accelerated particle swarm optimization and support vector machine for business optimization and applications
Yang, X., Deb, S. and Fong, S. 2011. Accelerated particle swarm optimization and support vector machine for business optimization and applications. Fong, S. (ed.) NDT 2011: International Conference on Networked Digital Technologies. Macau, China 11 - 13 Jul 2011 Springer. pp. 53-66 https://doi.org/10.1007/978-3-642-22185-9_6
Bat algorithm for multi-objective optimisation
Yang, X. 2011. Bat algorithm for multi-objective optimisation. International Journal of Bio-Inspired Computation. 3 (5), pp. 267-274. https://doi.org/10.1504/IJBIC.2011.042259
Mixed variable structural optimization using Firefly Algorithm
Gandomi, A., Yang, X. and Alavi, A. 2011. Mixed variable structural optimization using Firefly Algorithm. Computers and Structures. 89 (23-24), pp. 2325-2336. https://doi.org/10.1016/j.compstruc.2011.08.002
Possible power-saving gains by dividing a cell into tiers of smaller cells
Le, T. and Nakhai, M. 2010. Possible power-saving gains by dividing a cell into tiers of smaller cells. Electronics Letters. 46 (16), pp. 1163-1165. https://doi.org/10.1049/el.2010.1509
A new metaheuristic bat-inspired algorithm
Yang, X. 2010. A new metaheuristic bat-inspired algorithm. in: González, J., Pelta, D., Cruz, C., Terrazas, G. and Krasnogor, N. (ed.) Nature Inspired Cooperative Strategies for Optimization (NISCO 2010) Berlin Springer.
Eagle strategy using Lévy walk and firefly algorithm for stochastic optimization
Yang, X. and Deb, S. 2010. Eagle strategy using Lévy walk and firefly algorithm for stochastic optimization. in: González, J., Pelta, D, Cruz, C., Terrazas, G. and Krasnogor, N. (ed.) Nature Inspired Cooperative Strategies for Optimization (NICSO 2010) Springer. pp. 101-111
Optimization and data mining for fracture prediction in geosciences
Shi, G. and Yang, X. 2010. Optimization and data mining for fracture prediction in geosciences. Procedia Computer Science. 1 (1), pp. 1359-1366. https://doi.org/10.1016/j.procs.2010.04.151
Firefly algorithm, stochastic test functions and design optimisation
Yang, X. 2010. Firefly algorithm, stochastic test functions and design optimisation. International Journal of Bio-Inspired Computation. 2 (2), pp. 78-84. https://doi.org/10.1504/IJBIC.2010.032124
Oil and gas assessment of the Kuqa depression of Tarim Basin in western China by simple fluid flow models of primary and secondary migrations of hydrocarbons
Shi, G., Zhang, Q., Yang, X. and Mi, S. 2010. Oil and gas assessment of the Kuqa depression of Tarim Basin in western China by simple fluid flow models of primary and secondary migrations of hydrocarbons. Journal of Petroleum Science and Engineering. 75 (1-2), pp. 77-90. https://doi.org/10.1016/j.petrol.2010.10.009
Firefly algorithms for multimodal optimization
Yang, X. 2009. Firefly algorithms for multimodal optimization. in: Stochastic Algorithms: Foundations and Applications; 5th International Symposium, SAGA 2009, Sapporo, Japan, October 26-28, 2009. Proceedings Springer.
Cuckoo search via Lévy flights
Yang, X. and Deb, S. 2009. Cuckoo search via Lévy flights. in: World Congress on Nature & Biologically Inspired Computing (NaBIC 2009) IEEE Publications. pp. 210-214