  This letter develops a novel transmit beamforming (BF) design for canceling
self-interference (SI) in analog in-band full-duplex phased arrays. Our design
maximizes transmit BF gain in a desired direction while simultaneously reducing
SI power to below a specified threshold on per-antenna basis to avoid
saturating receive-chain components, such as LNAs. Core to our approach is that
it accounts for real-world phase shifters used in analog phased array systems,
whose limited resolution imposes non-convex constraints on BF design. We
overcome this by transforming these non-convex constraints into convex polygon
constraints, which we then solve through semidefinite relaxation and a rank
refinement procedure. Numerical results show that our proposed BF scheme
reliably cancels SI to the target power threshold at each receive antenna while
sacrificing little in transmit BF gain, even with modest phase shifter
resolution.
