  Recently, simultaneously transmitting and reflecting reconfigurable
intelligent surfaces (STAR-RISs) have received significant research interest.
The employment of large STAR-RIS and high-frequency signaling inevitably make
the near-field propagation dominant in wireless communications. In this work, a
STAR-RIS aided near-field multiple-input multiple-multiple (MIMO) communication
framework is proposed. A weighted sum rate maximization problem for the joint
optimization of the active beamforming at the base station (BS) and the
transmission/reflection-coefficients (TRCs) at the STAR-RIS is formulated. The
non-convex problem is solved by a block coordinate descent (BCD)-based
algorithm. In particular, under given STAR-RIS TRCs, the optimal active
beamforming matrices are obtained by solving a convex quadratically constrained
quadratic program. For given active beamforming matrices, two algorithms are
suggested for optimizing the STAR-RIS TRCs: a penalty-based iterative (PEN)
algorithm and an element-wise iterative (ELE) algorithm. The latter algorithm
is conceived for STAR-RISs with a large number of elements. Numerical results
illustrate that: i) near-field beamforming for STAR-RIS aided MIMO
communications significantly improves the achieved weighted sum rate compared
with far-field beamforming; ii) the near-field channels facilitated by the
STAR-RIS provide enhanced degrees-of-freedom and accessibility for the
multi-user MIMO system; and iii) the BCD-PEN algorithm achieves better
performance than the BCD-ELE algorithm, while the latter has a significantly
lower computational complexity.
