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Fully-diverse multiple-antenna signal constellations and fixed-point-free Lie groups

Hassibi, Babak and Khorrami, Mohammad (2000) Fully-diverse multiple-antenna signal constellations and fixed-point-free Lie groups. . (Unpublished)

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A group of unitary matrices is called fixed-point-free (fpf) if all non-identity elements of the group have no eigenvalues at unity. Such groups are useful in multiple-antenna communications, especially in multiple-antenna differential modulation, since they constitute a fully-diverse constellation. In [1] all finite fpf groups have been cla8Hified. In this note we consider infinite groups and, in particular, their most interesting case; Lie groups. Two such fpf Lie groups are currently widely used in communications: the group of unit modulus scalars, from which various phase modulation schemes, such as QPSK, are derived, and the 2 x 2 orthogonal designs of Alamouti, on which many two-transmit-antenna schemes are based. In Lie-group-theoretic jargon these are referred to as U(1) and SU(2). A natural question is whether there exist other fpf Lie groups. We answer this question in the negative: U(1) and SU(2) are all there are.

Item Type:Report or Paper (Report)
Record Number:CaltechAUTHORS:20150302-171200624
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55445
Deposited By: Shirley Slattery
Deposited On:03 Mar 2015 01:55
Last Modified:03 Oct 2019 08:05

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