An Optimal Channel Estimation Scheme for Intelligent Reflecting Surfaces based on a Minimum Variance Unbiased Estimator

In a wireless system with Intelligent Reflective Surfaces (IRS) containing many passive elements, we consider the problem of channel estimation. All the links from the transmitter to the receiver via each IRS elements (or groups) are estimated. As the estimation performance are dependent on the setting of the IRS, we design an optimal channel estimation scheme where the IRS elements follow an optimal series of activation patterns. The optimal design is guided by results for the minimum variance unbiased estimation. The IRS setting during the channel estimation period mimics a series of discrete Fourier transforms. We show theoretically and with simulations that the estimation variance is one order smaller compared to existing on/off methods proposed in the literature.