Capacity of the Aperture-Constrained AWGN Free-Space Communication Channel

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.