  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.
