  In this work, novel upper and lower bounds for 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 between the number of transmit and receive antennas,
similarly to the case of average power-constrained inputs.
