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Constructing the capacity bound of a multiple-input multiple-output wireless system is often performed by assuming specified antenna configurations and a propagation environment and determining the signaling strategy which maximizes throughput. This paper extends this approach to further determine the optimal antenna characteristics which maximize the capacity for the propagation scenario, with the resulting capacity bound representing the ultimate maximum achievable value if optimal antenna design and signaling are used. In this approach, the spatially-continuous transmit currents and receive fields are represented using eigenfunctions of appropriate operators. It is shown that, except under certain conditions where array supergain solutions emerge, the capacity remains bounded for finite transmit power. The approach also shows how to limit supergain effects using practical constraints. Model problems and numerical computations are provided for different power constraints at the transmitter and noise characteristics at the receiver.