By Topic

Nonintersecting subspaces based on finite alphabets

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

4 Author(s)
Oggier, F.E. ; Dept. de Math., Ecole Polytechnique Fed. de Lausanne, Switzerland ; Sloane, N.J.A. ; Diggavi, S.N. ; Calderbank, A.R.

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 Mt-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⊆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 (qm-1)/(qMt-1), and that this bound can be attained if and only if m is divisible by Mt. 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 Mt=2 is considered. It is shown that if A is a PSK-configuration, consisting of the 2r complex roots of unity, the number of nonintersecting planes is at least 2r(m-2) and at most 2r(m-1)-1 (the lower bound may in fact be the best that can be achieved).

Published in:

Information Theory, IEEE Transactions on  (Volume:51 ,  Issue: 12 )