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Publication# Method and wireless communication using unitary space-time signal constellations

Abstract

Disclosed is a method for wireless signal transmission of signals from an array of two or more antennas, in which each signal to be transmitted is selected from a constellation of unitary space-time signals. Each unitary space-time signal is a unitary matrix, in which each column represents a respective antenna, each row represents a respective time interval, and each element represents a complex amplitude to be transmitted by a given antenna during a given time interval. In specific embodiments of the invention, the matrices of the signal constellation form a non-Abelian group having a positive diversity product, or a coset of such a group. In other embodiments, the signal constellation is a subset of such a group, and its multiplicative closure forms a finite non-Abelian group having a positive diversity product. In still other embodiments, the signal constellation is an extension of any of the preceding types of constellations, formed by adding one or more further elements that do not belong to and are not derived from the group or group subset.

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Abelian group

In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after early 19th century mathematician Niels Henrik Abel.

Group action

In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism group of the structure. It is said that the group acts on the space or structure. If a group acts on a structure, it will usually also act on objects built from that structure. For example, the group of Euclidean isometries acts on Euclidean space and also on the figures drawn in it.

Finitely generated abelian group

In abstract algebra, an abelian group is called finitely generated if there exist finitely many elements in such that every in can be written in the form for some integers . In this case, we say that the set is a generating set of or that generate . Every finite abelian group is finitely generated. The finitely generated abelian groups can be completely classified. The integers, , are a finitely generated abelian group. The integers modulo , , are a finite (hence finitely generated) abelian group.

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