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Upper bounds on the capacity of vector Gaussian channels affected by fadingare derived under peak amplitude constraints at the input. The focus is onconstraint regions that can be decomposed in a Cartesian product ofsub-regions. This constraint models a transmitter configuration employing anumber of power amplifiers less than or equal to the total number oftransmitting antennas. In general, the power amplifiers feed distinct subsetsof the transmitting antennas and partition the input in independent subspaces.Two upper bounds are derived: The first one is suitable for highsignal-to-noise ratio (SNR) values and, as we prove, it is tight in thisregime; The second upper bound is accurate at low SNR. Furthermore, the derivedupper bounds are applied to the relevant case of amplitude constraints inducedby employing a distinct power amplifier for each transmitting antenna.

The Capacity of Fading Vector Gaussian Channels Under Amplitude Constraints on Antenna Subsets