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On the densest MIMO lattices from cyclic division algebras

C. Hollanti·J. Lahtonen·K. Ranto·R. Vehkalahti
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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 our bound are given. E.g. we construct a matrix lattice with QAM coefficients that has 2.5 times as many codewords as the celebrated Golden code of the same minimum determinant. We describe a general algorithm due to Ivanyos and Ronyai for finding maximal orders within a cyclic division algebra and discuss our enhancements to this algorithm. We also consider general methods for finding cyclic division algebras of a prescribed index achieving our lower bound.

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C. Hollanti, J. Lahtonen, K. Ranto, R. Vehkalahti. 2007-03-12. On the densest MIMO lattices from cyclic division algebras. https://arxiv.org/abs/cs/0703052

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