Hassibi, Babak and Khorrami, Mohammad (2000) Fully-diverse multiple-antenna signal constellations and fixed-point-free Lie groups. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20150302-171200624
![]() |
PDF
- Draft Version
See Usage Policy. 10MB |
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20150302-171200624
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.
Item Type: | Report or Paper (Report) |
---|---|
Record Number: | CaltechAUTHORS:20150302-171200624 |
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20150302-171200624 |
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
ID Code: | 55445 |
Collection: | CaltechAUTHORS |
Deposited By: | Shirley Slattery |
Deposited On: | 03 Mar 2015 01:55 |
Last Modified: | 03 Oct 2019 08:05 |
Repository Staff Only: item control page