  Recently, full duplex (FD) has been studied in 5G LTE millimeter wave
(mmWave) cellular communications for New Radio in 3GPP releases 15-17. FD
allows bidirectional transmission over the same resources and has the potential
to reduce latency and double spectral efficiency. Self-interference (SI) is the
primary drawback. SI can be several orders of magnitude greater than the
received signal power, saturate the analog-to-digital converters (ADCs) and
degrade communication performance severely. Massive mmWave antenna arrays may
provide enough degrees of freedom for spatial multiplexing and SI suppression.
In this paper, we design spatial beamformers for the phased arrays already
built into the FD basestation/relay to extend mmWave coverage to a single user.
We propose alternating projections to design the precoder and combiner to
maximize the sum of the uplink and downlink spectral efficiencies while
bringing SI below the noise floor. Our contributions include (1) hybrid
analog/digital beamformer design algorithm to cancel SI in the analog domain to
avoid ADC saturation and in the digital domain on each subcarrier; (2)
full-digital beamformer design algorithm; and (3) analysis of spectral
efficiency, energy efficiency and outage probability. In simulation, the
proposed algorithms outperform beamsteering, singular value decomposition,
angle search, and half-duplex techniques.
