Skip to main content
Erschienen in: Journal of Combinatorial Optimization 4/2017

28.06.2016

A new effective branch-and-bound algorithm to the high order MIMO detection problem

verfasst von: Ye Tian, Ke Li, Wei Yang, Zhiyong Li

Erschienen in: Journal of Combinatorial Optimization | Ausgabe 4/2017

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

This paper develops a branch-and-bound method based on a new convex reformulation to solve the high order MIMO detection problem. First, we transform the original problem into a \(\{-1,1\}\) constrained quadratic programming problem with the smallest size. The size of the reformulated problem is smaller than those problems derived by some traditional transformation methods. Then, we propose a new convex reformulation which gets the maximized average objective value as the lower bound estimator in the branch-and-bound scheme. This estimator balances very well between effectiveness and computational cost. Thus, the branch-and-bound algorithm achieves a high total efficiency. Several simulations are used to compare the performances of our method and other benchmark methods. The results show that this proposed algorithm is very competitive for high accuracy and relatively good efficiency.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Billionnet A, Elloumi S (2007) Using a mixed integer quadratic programming solver for the unconstrained quadratic 0–1 problem. Math Program 109:55–68MathSciNetCrossRefMATH Billionnet A, Elloumi S (2007) Using a mixed integer quadratic programming solver for the unconstrained quadratic 0–1 problem. Math Program 109:55–68MathSciNetCrossRefMATH
Zurück zum Zitat Bunse-Gerstner A, Kubaliń D, Vossen G, Wilczek D (2010) \(h_2\)-norm optimal model reduction for large scale discrete dynamical MIMO systems. J Comput Appl Math 233:1202–1216MathSciNetCrossRefMATH Bunse-Gerstner A, Kubaliń D, Vossen G, Wilczek D (2010) \(h_2\)-norm optimal model reduction for large scale discrete dynamical MIMO systems. J Comput Appl Math 233:1202–1216MathSciNetCrossRefMATH
Zurück zum Zitat Damen M, El Gamal H, Caire G (2003) On maximum-likelihood detection and the search for the closest lattice point. IEEE Trans Inf Theory 49:2389–2402MathSciNetCrossRefMATH Damen M, El Gamal H, Caire G (2003) On maximum-likelihood detection and the search for the closest lattice point. IEEE Trans Inf Theory 49:2389–2402MathSciNetCrossRefMATH
Zurück zum Zitat Fincke U, Pohst M (1985) Improved methods for calculating vectors of short length in a lattice, including a complexity analysis. Math Computat 44:463–471MathSciNetCrossRefMATH Fincke U, Pohst M (1985) Improved methods for calculating vectors of short length in a lattice, including a complexity analysis. Math Computat 44:463–471MathSciNetCrossRefMATH
Zurück zum Zitat El Gamal H, Caire G, Damen M (2004) Lattice coding and decoding achieve the optimal diversity-multiplexing tradeoff of MIMO channels. IEEE Trans Inf Theory 50:968–985MathSciNetCrossRefMATH El Gamal H, Caire G, Damen M (2004) Lattice coding and decoding achieve the optimal diversity-multiplexing tradeoff of MIMO channels. IEEE Trans Inf Theory 50:968–985MathSciNetCrossRefMATH
Zurück zum Zitat Goldberger J, Leshem A (2011) MIMO detection for high-order QAM based on a Gaussian tree approximation. IEEE Trans Inf Theory 57:4973–4982MathSciNetCrossRef Goldberger J, Leshem A (2011) MIMO detection for high-order QAM based on a Gaussian tree approximation. IEEE Trans Inf Theory 57:4973–4982MathSciNetCrossRef
Zurück zum Zitat Jaldén J, Elia P (2010) DMT optimality of LR-aided linear decoders for a general class of channels, lattice designs, and system models. IEEE Trans Inf Theory 56:4765–4780MathSciNetCrossRef Jaldén J, Elia P (2010) DMT optimality of LR-aided linear decoders for a general class of channels, lattice designs, and system models. IEEE Trans Inf Theory 56:4765–4780MathSciNetCrossRef
Zurück zum Zitat Jaldén J, Ottersten B (2005) On the complexity of sphere decoding in digital communications. IEEE Trans Signal Process 53:1474–1484MathSciNetCrossRef Jaldén J, Ottersten B (2005) On the complexity of sphere decoding in digital communications. IEEE Trans Signal Process 53:1474–1484MathSciNetCrossRef
Zurück zum Zitat Kisialiou M, Luo Z (2005) Performance Analysis of Quasi-Maximum-Likelihood Detector Based on Semidefinite Programming. In: Proceedings of the IEEE International Conference on Acoustics Speech and Signal Process, vol III, pp 433–436 Kisialiou M, Luo Z (2005) Performance Analysis of Quasi-Maximum-Likelihood Detector Based on Semidefinite Programming. In: Proceedings of the IEEE International Conference on Acoustics Speech and Signal Process, vol III, pp 433–436
Zurück zum Zitat Liu S, Ling C, Stehlé D (2011) Decoding by sampling: A randomized lattice algorithm for bounded-distance decoding. IEEE Trans Inf Theory 57:5933–5945MathSciNetCrossRef Liu S, Ling C, Stehlé D (2011) Decoding by sampling: A randomized lattice algorithm for bounded-distance decoding. IEEE Trans Inf Theory 57:5933–5945MathSciNetCrossRef
Zurück zum Zitat Lu C, Guo X (2015) Convex reformulation for binary quadratic programming problems via average objective value maximization. Optim Lett 9:523–535MathSciNetCrossRefMATH Lu C, Guo X (2015) Convex reformulation for binary quadratic programming problems via average objective value maximization. Optim Lett 9:523–535MathSciNetCrossRefMATH
Zurück zum Zitat Luzzi L, Stehlé D, Ling C (2013) Decoding by embedding: Correct decoding radius and DMT optimality. IEEE Trans Inf Theory 59:960–2973MathSciNetCrossRef Luzzi L, Stehlé D, Ling C (2013) Decoding by embedding: Correct decoding radius and DMT optimality. IEEE Trans Inf Theory 59:960–2973MathSciNetCrossRef
Zurück zum Zitat Ma W, Davidson T, Wong K, Ching P (2004) A block alternating likelihood maximization approach to multiuser detection. IEEE Trans Signal Process 52:2600–2611MathSciNetCrossRef Ma W, Davidson T, Wong K, Ching P (2004) A block alternating likelihood maximization approach to multiuser detection. IEEE Trans Signal Process 52:2600–2611MathSciNetCrossRef
Zurück zum Zitat Ma W, Su C, Jaldém J, Chang T, Chi C (2009) The equivalence of semidefinite relaxation MIMO detectors for higher-order QAM. IEEE J Select Top Signal Process 3:1038–1052CrossRef Ma W, Su C, Jaldém J, Chang T, Chi C (2009) The equivalence of semidefinite relaxation MIMO detectors for higher-order QAM. IEEE J Select Top Signal Process 3:1038–1052CrossRef
Zurück zum Zitat Mao Z, Wang X, Wang X (2007) Semidefinite programming relaxation approach for multiuser detection of QAM signals. IEEE Trans Wire Commun 6:4275–4279CrossRef Mao Z, Wang X, Wang X (2007) Semidefinite programming relaxation approach for multiuser detection of QAM signals. IEEE Trans Wire Commun 6:4275–4279CrossRef
Zurück zum Zitat Pan J, Ma W, Jaldém J (2014) MIMO detection by Lagrangian dual maximum-likilihood relaxation: Reinterpreting regularized lattice decoding. IEEE Trans Signal Process 62:511–524MathSciNetCrossRef Pan J, Ma W, Jaldém J (2014) MIMO detection by Lagrangian dual maximum-likilihood relaxation: Reinterpreting regularized lattice decoding. IEEE Trans Signal Process 62:511–524MathSciNetCrossRef
Zurück zum Zitat Pardalos P, Rodgers G (1990) Computational aspects of a branch and bound algorithm for quadratic zero-one programming. Computing 45:131–144MathSciNetCrossRefMATH Pardalos P, Rodgers G (1990) Computational aspects of a branch and bound algorithm for quadratic zero-one programming. Computing 45:131–144MathSciNetCrossRefMATH
Zurück zum Zitat Sidiropoulos N, Luo Z (2006) A semidefinite relaxation approach to MIMO detection for higher-order constellations. IEEE Signal Process lett 13:525–528CrossRef Sidiropoulos N, Luo Z (2006) A semidefinite relaxation approach to MIMO detection for higher-order constellations. IEEE Signal Process lett 13:525–528CrossRef
Zurück zum Zitat Singh A, Elia P, Jaldén J (2012) Achieving a vanishing SNR gap to exact lattice decoding at a subexponential complexity. IEEE Trans Inf Theory 58:3692–3707MathSciNetCrossRef Singh A, Elia P, Jaldén J (2012) Achieving a vanishing SNR gap to exact lattice decoding at a subexponential complexity. IEEE Trans Inf Theory 58:3692–3707MathSciNetCrossRef
Zurück zum Zitat Taherzadeh M, Khandani A (2010) On the limitations of the naive lattice decoding. IEEE Trans Inf Theory 56:4820–4826MathSciNetCrossRef Taherzadeh M, Khandani A (2010) On the limitations of the naive lattice decoding. IEEE Trans Inf Theory 56:4820–4826MathSciNetCrossRef
Zurück zum Zitat Tan P, Rasmussen L (2001) The application of semidefinite programming for detection in CDMA. IEEE J Select Areas Commun 19:1442–1449CrossRef Tan P, Rasmussen L (2001) The application of semidefinite programming for detection in CDMA. IEEE J Select Areas Commun 19:1442–1449CrossRef
Zurück zum Zitat Tse D, Viswanath P (2005) Fundamentals of wireless communication. Cambridge University Press, CambridgeCrossRefMATH Tse D, Viswanath P (2005) Fundamentals of wireless communication. Cambridge University Press, CambridgeCrossRefMATH
Zurück zum Zitat Verdú S (1998) Multiuser detectection. Cambridge University Press, Cambridge Verdú S (1998) Multiuser detectection. Cambridge University Press, Cambridge
Zurück zum Zitat Wang Z, Fang SC, Gao D, Xing W (2008) Global extremal conditions for multi-integer quadratic programming. J Ind Manage Optim 4:213–225MathSciNetCrossRefMATH Wang Z, Fang SC, Gao D, Xing W (2008) Global extremal conditions for multi-integer quadratic programming. J Ind Manage Optim 4:213–225MathSciNetCrossRefMATH
Zurück zum Zitat Wiesel A, Eldar Y, Shamai S (2005) Semidefinite relaxation for detection of 16-QAM signaling in MIMO channels. IEEE Signal Process Lett 13:525–528 Wiesel A, Eldar Y, Shamai S (2005) Semidefinite relaxation for detection of 16-QAM signaling in MIMO channels. IEEE Signal Process Lett 13:525–528
Zurück zum Zitat Wübben D, Seethaler D, Jaldén J, Matz G (2011) Lattice reduction. IEEE Signal Process Mag 28:70–91CrossRef Wübben D, Seethaler D, Jaldén J, Matz G (2011) Lattice reduction. IEEE Signal Process Mag 28:70–91CrossRef
Metadaten
Titel
A new effective branch-and-bound algorithm to the high order MIMO detection problem
verfasst von
Ye Tian
Ke Li
Wei Yang
Zhiyong Li
Publikationsdatum
28.06.2016
Verlag
Springer US
Erschienen in
Journal of Combinatorial Optimization / Ausgabe 4/2017
Print ISSN: 1382-6905
Elektronische ISSN: 1573-2886
DOI
https://doi.org/10.1007/s10878-016-0045-5

Weitere Artikel der Ausgabe 4/2017

Journal of Combinatorial Optimization 4/2017 Zur Ausgabe

Premium Partner