On the Impact of Mutual Coupling on RIS-Assisted Channel Estimation

Amid the demand for densely integrated elements in holographic reconfigurable intelligent surfaces (RISs), the mutual coupling effect has gained prominence. By performing a misspecified Cram\'er-Rao bound analysis within an electromagnetics-compliant communication model, this letter offers a quantitative evaluation of the impact of mutual coupling on RIS-assisted channel estimation. Our analysis provides insights into situations where mutual coupling can be disregarded safely. The numerical results reveal that within practical scenarios, closer integration of RIS elements or the enlargement of RIS size accentuates the impact of neglecting mutual coupling. In addition, even with mutual coupling-aware setups, excessively tight RIS element spacing can lead to substantial degradation in the channel estimation performance.