  Integrated sensing and communication (ISAC) is expected to play a prominent
role among emerging technologies in future wireless communications. In
particular, a communication radar coexistence system is degraded significantly
by mutual interference. In this work, given the advantages of promising
reconfigurable intelligent surface (RIS), we propose a simultaneously
transmitting and reflecting RIS (STAR-RIS)-assisted radar coexistence system
where a STAR-RIS is introduced to improve the communication performance while
suppressing the mutual interference and providing full space coverage. Based on
the realistic conditions of correlated fading, and the presence of multiple
user equipments (UEs) at both sides of the RIS, we derive the achievable rates
at the radar and the communication receiver side in closed forms in terms of
statistical channel state information (CSI). Next, we perform alternating
optimization (AO) for optimizing the STAR-RIS and the radar beamforming.
Regarding the former, we optimize the amplitudes and phase shifts of the
STAR-RIS through a projected gradient ascent algorithm (PGAM) simultaneously
with respect to the amplitudes and phase shifts of the surface for both energy
splitting (ES) and mode switching (MS) operation protocols. The proposed
optimization saves enough overhead since it can be performed every several
coherence intervals. This property is particularly beneficial compared to
reflecting-only RIS because a STAR-RIS includes the double number of variables,
which require increased overhead. Finally, simulation results illustrate how
the proposed architecture outperforms the conventional RIS counterpart, and
show how the various parameters affect the performance. Moreover, a benchmark
full instantaneous CSI (I-CSI) based design is provided and shown to result in
higher sum-rate but also in large overhead associated with complexity.
