  Reconfigurable intelligent surface (RIS) has become a focal point of
extensive research due to its remarkable "squared gain". However, achieving a
substantial beamforming gain typically requires a significant number of
elements, which leads to a non-negligible overhead that forwards the coherent
phase shift to the RIS. Different from previous works, which primarily focus on
the information transmission phase, we consider the phase delivery overhead
during the phase-shift delivery phase to explore the trade-off between
performance and overhead. To reduce the phase delivery overhead via the control
link, we introduce a hybrid phase shift mechanism, encompassing both the
coherent and fixed phase shifts. Specifically, a beamforming problem is
formulated for maximizing the throughput. In light of the intractability of the
problem, we develop an alternating optimization-based iterative algorithm by
combining quadratic transformation and successive convex approximation. To gain
more insights, we derive the closed-form expression of the number of elements
adopting the coherent phase shift in the large signal-to-noise ratio region.
This expression serves as a valuable guide for the practical implementation of
the RIS technology. Our simulation results conclusively demonstrate the
effectiveness of the proposed algorithm in achieving a favorable trade-off
between throughput and overhead. Furthermore, the introduction of the hybrid
phase shift approach significantly reduces phase delivery overhead while
concurrently enhancing the system throughput.
