  This paper studies the role of the joint transmit-receive antenna array
geometry in shaping the self-interference (SI) channel in full-duplex
communications. We consider a simple spherical wave SI model and two
prototypical linear array geometries with uniformly spaced transmit and receive
antennas. We show that the resulting SI channel matrix has a regular (Toeplitz)
structure in both of these cases. However, the number of significant singular
values of these matrices - an indication of the severity of SI - can be
markedly different. We demonstrate that both reduced SI and high angular
resolution can be obtained by employing suitable sparse array configurations
that fully leverage the available joint transmit-receive array aperture without
suffering from angular ambiguities. Numerical electromagnetic simulations also
suggest that the worst-case SI of such sparse arrays need not increase - but
can actually decrease - with the number of antennas. Our findings provide
preliminary insight into the extent to which the array geometry alone can
mitigate SI in full-duplex massive MIMO communications systems employing a
large number of antennas.
