Two subspaces of a vector space are here called ``nonintersecting'' if they
meet only in the zero vector. The following problem arises in the design of
noncoherent multiple-antenna communications systems. How many pairwise
nonintersecting M_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 subseteq F? The most
important case is when F is the field of complex numbers C; then M_t is the
number of antennas. If A = F = GF(q) it is shown that the number of
nonintersecting subspaces is at most (q^m-1)/(q^{M_t}-1), and that this bound
can be attained if and only if m is divisible by M_t. Furthermore these
subspaces remain nonintersecting when ``lifted'' to the complex field. Thus the
finite field case is essentially completely solved. In the case when F = C only
the case M_t=2 is considered. It is shown that if A is a PSK-configuration,
consisting of the 2^r complex roots of unity, the number of nonintersecting
planes is at least 2^{r(m-2)} and at most 2^{r(m-1)-1} (the lower bound may in
fact be the best that can be achieved).Comment: 14 page