  This paper investigates simultaneous transmission and reflection
reconfigurable intelligent surface (STAR-RIS) aided physical layer security
(PLS) in multiple-input multiple-output (MIMO) systems, where the base station
(BS) transmits secrecy information with the aid of STAR-RIS against multiple
eavesdroppers equipped with multiple antennas. We aim to maximize the secrecy
rate by jointly optimizing the active beamforming at the BS and passive
beamforming at the STAR-RIS, subject to the hardware constraint for STAR-RIS.
To handle the coupling variables, a minimum mean-square error (MMSE) based
alternating optimization (AO) algorithm is applied. In particular, the
amplitudes and phases of STAR-RIS are divided into two blocks to simplify the
algorithm design. Besides, by applying the Majorization-Minimization (MM)
method, we derive a closed-form expression of the STAR-RIS's phase shifts.
Numerical results show that the proposed scheme significantly outperforms
various benchmark schemes, especially as the number of STAR-RIS elements
increases.
