We consider the design of Amplify & Forward Full-Duplex (FD) relay-assisted communication systems. The FD mode has potential for significant improvements in spectral efficiency, but it suffers from large self-interference (SI) levels.

Beamforming-based SI mitigation is attractive for millimeter wave (mmWave) systems due to the large number of degrees of freedom available with large antenna arrays. We first develop an all-digital beamformer design by imposing a zero-forcing constraint on SI, performing quasi-optimally in terms of spectral efficiency. The design is then modified to fit the hardware-related constraints usually found when operating at mmWave, so that the beamformers can be implemented in the analog domain by using phase shifters, with an acceptable performance loss.