Capacity bounds for peak-constrained multiantenna wideband channels

Bounds are derived on the noncoherent capacity of a very general class of multiple-input multiple-output fading channels that are selective in time and frequency as well as correlated in space. 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 one to coarsely identify the capacity-optimal combination of bandwidth and number of transmit antennas. Furthermore, a closed-form expression is obtained for the first-order Taylor series expansion of capacity in the limit of infinite bandwidth. From this expression, it is concluded 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.