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In this work, we focus on simultaneous transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs) with coupled transmission and reflection phase shifts. We demonstrate how to achieve full diversity for users on both sides by proposing a practical phase-shift design, namely, the diversity preserving design. To evaluate the performance, a STAR-RIS-aided two-user downlink communication system is investigated for both orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA). The outage probabilities, diversity orders, and power scaling laws under this design are studied and compared with the performance upper and lower bounds. Numerical simulations show that the proposed diversity preserving phase-shift configuration strategy for the STAR-RIS achieves the same diversity order as the STAR-RISs assuming independent phase-shift, and achieves a comparable power …