Math @ Duke

Publications [#235854] of Robert Calderbank
Papers Published
 Oggier, FE; Sloane, NJA; Diggavi, SN; Calderbank, AR, Nonintersecting subspaces based on finite alphabets,
IEEE Transactions on Information Theory, vol. 51 no. 12
(2005),
pp. 43204325, ISSN 00189448 [doi]
(last updated on 2018/03/21)
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 multipleantenna communications systems, we consider the following question. How many pairwise nonintersecting Mtdimensional subspaces of an mdimensional 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 PSKconfiguration, consisting of the 2r complex roots of unity, the number of nonintersecting planes is at least 2r(m2) and at most 2r(m1)1 (the lower bound may in fact be the best that can be achieved. © 2005 IEEE.


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