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An algebraic family of complex lattices for fading channels with application to space-time codes

机译：衰落信道的复格的代数族，应用于时空编码

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摘要

A new approach is presented for the design of full modulation diversity (FMD) complex lattices for the Rayleigh-fading channel. The FMD lattice design problem essentially consists of maximizing a parameter called the normalized minimum product distance d/sub p//sup 2/ of the finite signal set carved out of the lattice. We approach the problem of maximizing d/sub p//sup 2/ by minimizing the average energy of the signal constellation obtained from a new family of FMD lattices. The unnormalized minimum product distance for every lattice in the proposed family is lower-bounded by a nonzero constant. Minimizing the average energy of the signal set translates to minimizing the Frobenius norm of the generator matrices within the proposed family. The two strategies proposed for the Frobenius norm reduction are based on the concepts of successive minima (SM) and basis reduction of an equivalent real lattice. The lattice constructions in this paper provide significantly larger normalized minimum product distances compared to the existing lattices in certain dimensions. The proposed construction is general and works for any dimension as long as a list of number fields of the same degree is available.
机译：提出了一种新方法，用于设计瑞利衰落信道的全调制分集（FMD）复杂晶格。 FMD晶格设计问题主要包括最大化从晶格中雕刻出来的有限信号集的称为归一化最小乘积距离d / sub p // sup 2 /的参数。我们通过最小化从新的FMD族获得的信号星座图的平均能量来解决使d / sub p // sup 2 /最大化的问题。所提出族中每个晶格的未归一化最小乘积距离由一个非零常数下界。使信号集的平均能量最小化将使拟议族内的发生器矩阵的Frobenius范数最小化。为Frobenius范数约简提出的两种策略均基于连续极小值（SM）和等效实格的基本约简的概念。与某些尺寸的现有晶格相比，本文中的晶格结构提供了更大的归一化最小乘积距离。所提出的构造是通用的，并且可以在任何维度上使用，只要有相同程度的数字字段列表可用即可。

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