  Intelligent reflective surface (IRS) is an emergent technology for future
wireless communications. It consists of a large 2D array of passive scattering
elements that control the electromagnetic properties of radio-frequency waves
so that the reflected signals add coherently at the intended receiver or
destructively to reduce co-channel interference. The promised gains of
IRS-assisted communications depend on the accuracy of the channel state
information. In this paper, we propose two novel channel estimation methods for
an IRS-assisted multiple-input multiple-output (MIMO) communication system.
Assuming a structured time-domain pattern of pilots and IRS phase shifts, we
show that the received signal follows a parallel factor (PARAFAC) tensor model
that can be exploited to estimate the involved communication channels in
closed-form or iteratively. Numerical results corroborate the effectiveness of
the proposed channel estimation methods and highlight the involved tradeoffs.
