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

In this work, novel upper and lower bounds for the capacity of channels with\narbitrary constraints on the support of the channel input symbols are derived.\nAs an immediate practical application, the case of multiple-input\nmultiple-output channels with amplitude constraints is considered. The bounds\nare shown to be within a constant gap if the channel matrix is invertible and\nare tight in the high amplitude regime for arbitrary channel matrices.\nMoreover, in the high amplitude regime, it is shown that the capacity scales\nlinearly with the minimum between the number of transmit and receive antennas,\nsimilarly to the case of average power-constrained inputs.\n