  We explore the potential of a simultaneously transmitting and reflecting
reconfigurable intelligent surface (STAR-RIS) to enhance the performance of
wireless surveillance systems. The STAR-RIS is deployed between a full-duplex
(FD) multi-antenna legitimate eavesdropper (E) and a suspicious communication
pair. It reflects the suspicious signal towards the suspicious receiver (SR),
while simultaneously transmitting the same signal to E for interception
purposes. Additionally, it enables the forwarding of a jamming signal from E to
SR, which is located on the back side of the STAR-RIS. To enhance the
eavesdropping non-outage probability, we formulate a non-convex joint
optimization problem to design the beamforming vectors at E and
reflection/transmission phase shift matrices at the STAR-RIS. We adopt the
block coordinate descent (BCD) algorithm and propose an approach, mainly based
on semi-definite relaxation (SDR) and successive convex approximation (SCA),
for solving the resulting decoupled sub-problems. Finally, we compare the
performance of the proposed design against low-complexity zero-forcing
(ZF)-based beamforming designs.
