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Nonintersecting subspaces based on finite alphabets

Authors :
Oggier, Frederique E.
Sloane, N.J.A.
Diggavi, Suhas N.
Calderbank, A.R.
Source :
IEEE Transactions on Information Theory. Dec, 2005, Vol. 51 Issue 12, p4320, 6 p.
Publication Year :
2005

Abstract

Two subspaces of a vector space are here called "nonintersecting" if they meet only in the zero vector. Motivated by the design of noncoherent multiple-antenna communications systems, we consider the following question. How many pairwise nonintersecting [M.sub.t]-dimensional subspaces of an m-dimensional vector space V over a field F can be found, if the generator matrices for the subspaces may contain only symbols from a given finite alphabet A [subset] F? The most important case is when F is the field of complex numbers C; then Mt is the number of antennas. If A = F = GF (q) it is shown that the number of nonintersecting subspaces is at most ([q.sup.m] - 1) / ([q.sup.[M.sub.t] - 1), and that this bound can be attained if and only if m is divisible by Mr. Furthermore, these subspaces remain nonintersecting when "lifted" to the complex field. It follows that the finite field case is essentially completely solved. In the case when F = C only the case [M.sub.t] = 2 is considered. It is shown that if A is a PSK-configuration, consisting of the [2.sup.r] complex roots of unity, the number of nonintersecting planes is at least [2.sup.r] (m - 2) and at most [2.sup.r] (m - 1) - 1 (the lower bound may in fact be the best that can he achieved). Index Terms--Multiple-antenna communications, noncoherent systems, nonintersecting subspaces, space-time codes.

Details

Language :
English
ISSN :
00189448
Volume :
51
Issue :
12
Database :
Gale General OneFile
Journal :
IEEE Transactions on Information Theory
Publication Type :
Academic Journal
Accession number :
edsgcl.140015529