Upper and Lower Bounds on the Capacity of Amplitude-Constrained MIMO Channels

In this work, novel upper and lower bounds on the capacity of channels with arbitrary constraints on the support of the channel input symbols are derived. As an immediate practical application, the case of multiple-input multiple-output channels with amplitude constraints is considered. The bounds are shown to be within a constant gap if the channel matrix is invertible and are tight in the high amplitude regime for arbitrary channel matrices. Moreover, in the high amplitude regime, it is shown that the capacity scales linearly with the minimum of the numbers of transmit and receive antennas, similarly to the case of average power-constrained inputs.