Keyholes, correlations and capacities of multi-element transmit and receive antennas

Multi-element system capacities are usually thought of as being limited only by correlations between elements. We show that degenerate channel phenomena, called "keyholes" may arise under realistic assumptions which have zero correlation between the entries of the channel matrix H and yet only a single degree of freedom. Canonical physical examples of keyholes are presented. For indoor environments, it is shown that the number of communication modes in a hallway may not exceed the number of waveguide modes.