In my Master's thesis work, I performed measurement-based study of the capabilities and limitations of three key mechanisms for passive self-interference suppression: directional isolation, absorptive shielding, and cross-polarization. The study demonstrates that more than 70 dB of passive suppression can be achieved in certain environments, but also establishes two results on the limitations of passive suppression: (1) environmental reflections limit the amount of passive suppression that can be achieved, and (2) passive suppression, in general, increases the frequency selectivity of the residual self-interference signal. These results suggest two design implications: (1) deployments of full-duplex infrastructure nodes should minimize near-antenna reflectors, and (2) active cancellation in concatenation with passive suppression should employ higher-order filters or per-subcarrier cancellation. See our paper, "Passive Self-Interference Suppression for Full-Duplex Infrastructure Nodes," in IEEE Transaction on Wireless Communication.
Check out this video on our information theoretic approach to the problem of full-duplex communication in the presence of fading self-interference. It's a slightly modified version of the talk I gave at the 2011 Allerton Conference on Communication, Control, and Computing.