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On the Densest MIMO Lattices From Cyclic Division Algebras

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4 Author(s)
Roope Vehkalahti ; Lab. of Discrete Math. for Inf. Technol., Turku Centre for Comput. Sci., Turku, Finland ; Camilla Hollanti ; Jyrki Lahtonen ; Kalle Ranto

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 Ronyai 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.

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IEEE Transactions on Information Theory  (Volume:55 ,  Issue: 8 )