  The theoretic capacity of a communication system constituted of several
transmitting/receiving elements is determined by the singular values of its
transfer matrix. Results based on an independent identically distributed
channel model, representing an idealized rich propagation environment, state
that the capacity is directly proportional to the number of antennas.
Nevertheless there is growing experimental evidence that the capacity gain can
at best scale at a sub-linear rate with the system size. In this paper, we show
under appropriate assumptions on the transfer matrix of the system, that the
theoretic information-capacity of multi-antenna systems is upper bounded by a
sub-linear function of the number of transmitting/receiving links.
