  We characterize the capacity of Rayleigh block-fading multiple-input
multiple-output (MIMO) channels in the noncoherent setting where transmitter
and receiver have no a priori knowledge of the realizations of the fading
channel. We prove that unitary space-time modulation (USTM) is not
capacity-achieving in the high signal-to-noise ratio (SNR) regime when the
total number of antennas exceeds the coherence time of the fading channel
(expressed in multiples of the symbol duration), a situation that is relevant
for MIMO systems with large antenna arrays (large-MIMO systems). This result
settles a conjecture by Zheng & Tse (2002) in the affirmative. The
capacity-achieving input signal, which we refer to as Beta-variate space-time
modulation (BSTM), turns out to be the product of a unitary isotropically
distributed random matrix, and a diagonal matrix whose nonzero entries are
distributed as the square-root of the eigenvalues of a Beta-distributed random
matrix of appropriate size. Numerical results illustrate that using BSTM
instead of USTM in large-MIMO systems yields a rate gain as large as 13% for
SNR values of practical interest.
