  Full-duplex (FD) systems gained enormous attention because of the potential
to double the spectral efficiency. In the context of 5G technology, FD systems
operating at millimeter-wave (mmWave) frequencies become one of the most
promising solutions to further increase the spectral efficiency and reduce the
latency. However, such systems are vulnerable to the self-interference (SI)
that significantly degrades the performance. To overcome this shortcoming,
analog-only beamforming techniques have been developed to mitigate the SI.
Because of the huge power consumption, systems operating at mmWave frequencies
beamform the power by only tunning the phase shifters while maintaining
constant amplitudes. Such a hardware constraint, known as the constant
amplitude (CA) constraint, severely limits the system performance. In this
work, we propose a digital and analog hybrid beamforming design that completely
eliminates the SI while substantially minimizing the losses imposed by the CA
constraint. Further, we develop a fully-digital beamforming design and derive
the upper bound for the spectral efficiency as benchmarking tools to quantify
the losses of our proposed hybrid design.
