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Construction of Minimum Euclidean Distance MIMO Precoders and Their Lattice Classifications

  • Dzevdan Kapetanovic
  • Fredrik Rusek
  • Traian E. Abrudan
  • Visa Koivunen
Publiceringsår: 2012
Språk: Engelska
Sidor: 4470-4474
Publikation/Tidskrift/Serie: IEEE Transactions on Signal Processing
Volym: 60
Nummer: 8
Dokumenttyp: Artikel i tidskrift
Förlag: IEEE--Institute of Electrical and Electronics Engineers Inc.


This correspondence deals with the construction of minimum Euclidean distance precoders for multiple-input multiple-output (MIMO) systems with up to four transmit antennas. By making use of a state-of-the-art technique for optimization over the unitary group, we can numerically optimize the MIMO precoders. The correspondence then proceeds by identifying the obtained precoders as well-known lattices (square, Z(2), Schlafli D-4, D-6, Gosset E-8). With three transmit antennas, the results are slightly different compared with other numbers of transmit antennas since the obtained precoder is not an instance of the densest 6-dimensional lattice. The overall conclusions of the correspondence are that the found precoders for MIMO transmission are highly structured and that, even with small constellations, lattice theory can be used for the design of MIMO precoders.


  • Electrical Engineering, Electronic Engineering, Information Engineering
  • Lattice theory
  • MIMO
  • minimum Euclidean distance
  • precoding


  • ISSN: 1053-587X

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