  We derive bounds on the noncoherent capacity of a very general class of
multiple-input multiple-output channels that allow for selectivity in time and
frequency as well as for spatial correlation. The bounds apply to
peak-constrained inputs; they are explicit in the channel's scattering
function, are useful for a large range of bandwidth, and allow to coarsely
identify the capacity-optimal combination of bandwidth and number of transmit
antennas. Furthermore, we obtain a closed-form expression for the first-order
Taylor series expansion of capacity in the limit of infinite bandwidth. From
this expression, we conclude that in the wideband regime: (i) it is optimal to
use only one transmit antenna when the channel is spatially uncorrelated; (ii)
rank-one statistical beamforming is optimal if the channel is spatially
correlated; and (iii) spatial correlation, be it at the transmitter, the
receiver, or both, is beneficial.
