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

Hassibi, Babak and Khorrami, Mohammad (2001) Fully-diverse multiple-antenna signal constellations and fixed-point-free Lie groups. In: 2001 IEEE International Symposium on Information Theory. Proceedings. IEEE , Piscataway, NJ, p. 199. ISBN 0-7803-7123-2. https://resolver.caltech.edu/CaltechAUTHORS:20150212-075856105

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Abstract

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 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 2×2 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:Book Section
Related URLs:
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http://dx.doi.org/10.1109/ISIT.2001.936062DOIArticle
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Additional Information:© 2001 IEEE.
Record Number:CaltechAUTHORS:20150212-075856105
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150212-075856105
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ID Code:54765
Collection:CaltechAUTHORS
Deposited By: Shirley Slattery
Deposited On:13 Feb 2015 22:23
Last Modified:03 Oct 2019 08:00

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