Full duplex (FD), which allows bidirectional transmission over the same resources, has the potential to reduce latency and double spectral efficiency. Recently, FD has been studied in 5G LTE millimeter wave cellular communications for New Radio in 3GPP releases 15--17. The primary drawback of FD is self-interference (SI). SI arises in the receiver for system 1 because it receives transmissions from itself and system 2. Because system 1 is much closer, SI can be 100-1000x the received power from system 2, thereby severely degrading communication. In this paper, we investigate a FD relay extending mmWave coverage to a single user. We propose to use alternating projections in designing the precoder and combiner to maximize the sum of the uplink and downlink spectral efficiency while bringing the SI below the noise floor. Our contributions include (1) all-digital and hybrid beamforming design algorithms for SI cancellation; and (2) communication performance analysis in terms of spectral efficiency, energy efficiency and outage probability. We compare the proposed algorithms against beam steering, singular value decomposition, and angle search techniques.