On the Densest MIMO Lattices From Cyclic Division Algebras

被引：38
作者：
Vehkalahti, Roope [1 ,2 ]
Hollanti, Camilla [1 ,2 ]
Lahtonen, Jyrki [2 ]
Ranto, Kalle [2 ]
机构：
[1] Turku Ctr Comp Sci, Lab Discrete Math Informat Technol, Turku, Finland
[2] Univ Turku, Dept Math, FI-20014 Turku, Finland
来源：
IEEE TRANSACTIONS ON INFORMATION THEORY | 2009年 / 55卷 / 08期
基金：
芬兰科学院;
关键词：
Cyclic division algebras (CDAs); dense lattices; discriminants; Hasse invariants; maximal orders; multiple-input multiple-output (MIMO) channels; multiplexing; space-time block codes (STBCs); SPACE-TIME CODES; MAXIMAL-ORDERS; PERFECT SPACE; DIVERSITY; NUMBER;
D O I：
10.1109/TIT.2009.2023713
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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.
引用
收藏
页码：3751 / 3780
页数：30
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