On the densest MIMO lattices from cyclic division algebras

  • Authors:

  • Roope Vehkalahti;Camilla Hollanti;Jyrki Lahtonen;Kalle Ranto

  • Affiliations:

  • Department of Mathematics, University of Turku, Turku, Finland and Laboratory of Discrete Mathematics for Information Technology, Turku Centre for Computer Science, Turku, Finland;Department of Mathematics, University of Turku, Turku, Finland and Laboratory of Discrete Mathematics for Information Technology, Turku Centre for Computer Science, Turku, Finland;Department of Mathematics, University of Turku, Turku, Finland and Nokia Research Center, Wireless Access Systems, Nokia Group, Finland;Nokia Corporation, Nokia Devices, Salo, Finland and Department of Mathematics, University of Turku, Turku, Finland

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2009

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Abstract

It is shown why the discriminant of a maximal order within a cyclic division algebra must be minimized in order to get the densest possible matrix lattices with a prescribed nonvanishing minimum determinant. Using results from class field theory, a lower bound to the minimum discriminant of a maximal order with a given center and index (= the number of Tx/Rx antennas) is derived. Also numerous examples of division algebras achieving the bound are given. For example, a matrix lattice with quadrature amplitude modulation (QAM) coefficients that has 2.5 times as many codewords as the celebrated Golden code of the same minimum determinant is constructed. Also, a general algorithm due to Ivanyos and Rónyai for finding maximal orders within a cyclic division algebra is described and enhancements to this algorithm are discussed. Also some general methods for finding cyclic division algebras of a prescribed index achieving the lower bound are proposed.