Varying the antenna locations to optimize the capacity of multi-antenna Gaussian channels

In this paper we investigate the problem of maximizing the capacity of multi-antenna Gaussian channels when one has the freedom of moving the transmit/receive antennas so as to modify individual singular values of the transfer matrix (subject to an overall energy conservation constraint). We solve this maximization problem and make some interesting observations. Namely that with n transmit and n receive antennas, when the signal-to-noise ratio is sufficiently large, the optimal solution corresponds to creating n parallel channels, all of which have the same strength. On the other extreme, when the signal-to-noise ratio is sufficiently small, the optimal solution boils down to creating a single channel. This is done by using the transmit and receive antennas to create focused beams. Perhaps the most interesting lesson is that beamforming is optimal only in the low signal-to-noise regime.