  In this paper, we derive upper and lower bounds as well as a simple
closed-form approximation for the capacity of the continuous-time, bandlimited,
additive white Gaussian noise channel in a three-dimensional free-space
electromagnetic propagation environment subject to constraints on the total
effective antenna aperture area of the link and a total transmitter power
constraint. We assume that the communication range is much larger than the
radius of the sphere containing the antennas at both ends of the link, and we
show that, in general, the capacity can only be achieved by transmitting
multiple spatially-multiplexed data streams simultaneously over the channel.
Furthermore, the lower bound on capacity can be approached asymptotically by
transmitting the data streams between a pair of physically-realizable
distributed antenna arrays at either end of the link. A consequence of this
result is that, in general, communication at close to the maximum achievable
data rate on a deep-space communication link can be achieved in practice if and
only if the communication system utilizes spatial multiplexing over a
distributed MIMO antenna array. Such an approach to deep-space communication
does not appear to be envisioned currently by any of the international space
agencies or any commercial space companies. A second consequence is that the
capacity of a long-range free-space communication link, if properly utilized,
grows asymptotically as a function of the square root of the received SNR
rather than only logarithmically in the received SNR.
