Fully-diverse multiple-antenna signal constellations and fixed-point-free Lie groups
- Creators
- Hassibi, Babak
- Khorrami, Mohammad
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 [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.
Attached Files
Draft - ully-diverse_multiple-antenna_signal_constellations_and_fixed-point-free_Lie_groups.pdf
Files
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Additional details
- Eprint ID
- 55445
- Resolver ID
- CaltechAUTHORS:20150302-171200624
- Created
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2015-03-03Created from EPrint's datestamp field
- Updated
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2019-10-03Created from EPrint's last_modified field