  The opening of the millimeter wave (mmWave) spectrum bands for 5G
communications has motivated the need for novel spectrum sharing solutions at
these high frequencies. In fact, reconfigurable intelligent surfaces (RISs)
have recently emerged to enable spectrum sharing while enhancing the
incumbents' quality-of-service (QoS). Nonetheless, co-existence over mmWave
bands remains persistently challenging due to their unfavorable propagation
characteristics. Hence, initiating mmWave spectrum sharing requires the RIS to
further assist in improving the QoS over mmWave bands without jeopardizing
spectrum sharing demands. In this paper, a novel simultaneous transmitting and
reflecting RIS (STAR-RIS)-aided solution to enable mmWave spectrum sharing is
proposed. In particular, the transmitting and reflecting abilities of the
STAR-RIS are leveraged to tackle the mmWave spectrum sharing and QoS
requirements separately. The STAR-RIS-enabled spectrum sharing problem between
a primary network (e.g. a radar transmit-receive pair) and a secondary network
is formulated as an optimization problem whose goal is to maximize the downlink
sum-rate over a secondary multiple-input-single-output (MISO) network, while
limiting interference over a primary network. Moreover, the STAR-RIS response
coefficients and beamforming matrix in the secondary network are jointly
optimized. To solve this non-convex problem, an alternating iterative algorithm
is employed, where the STAR-RIS response coefficients and beamforming matrix
are obtained using the successive convex approximation method. Simulation
results show that the proposed solution outperforms conventional RIS schemes
for mmWave spectrum sharing by achieving a 14.57% spectral efficiency gain.
