  In this letter, we study efficient uplink channel estimation design for a
simultaneously transmitting and reflecting reconfigurable intelligent surface
(STAR-RIS) assisted two-user communication systems. We first consider the time
switching (TS) protocol for STAR-RIS and propose an efficient scheme to
separately estimate the channels of the two users with optimized training
(transmission/reflection) pattern. Next, we consider the energy splitting (ES)
protocol for STAR-RIS under the practical coupled phase-shift model and devise
a customized scheme to simultaneously estimate the channels of both users.
Although the problem of minimizing the resultant channel estimation error for
the ES protocol is difficult to solve, we propose an efficient algorithm to
obtain a high-quality solution by jointly designing the pilot sequences,
power-splitting ratio, and training patterns. Numerical results show the
effectiveness of the proposed channel estimation designs and reveal that the
STAR-RIS under the TS protocol achieves a smaller channel estimation error than
the ES case.
