  This paper develops a novel methodology for designing analog beamforming
codebooks for full-duplex millimeter wave (mmWave) transceivers, the first such
codebooks to the best of our knowledge. Our design reduces the
self-interference coupled by transmit-receive beam pairs and simultaneously
delivers high beamforming gain over desired coverage regions, allowing mmWave
full-duplex systems to support beam alignment while minimizing
self-interference. To do so, our methodology allows some variability in
beamforming gain to strategically shape beams that reject self-interference
while still having substantial gain. We present an algorithm for approximately
solving our codebook design problem while accounting for the non-convexity
posed by digitally-controlled phase shifters and attenuators. Numerical results
suggest that our design can outperform or nearly match existing codebooks in
sum spectral efficiency across a wide range of self-interference power levels.
Results show that our design offers an extra 20-50 dB of robustness to
self-interference, depending on hardware constraints.
