  Intelligent reflecting surfaces (IRSs)-assisted wireless communication
promises improved system performance, while posing new challenges in channel
estimation (CE) due to the passive nature of the reflecting elements. Although
a few CE protocols for IRS-assisted multiple-input single-output (MISO) systems
have appeared, they either require long channel training times or are developed
under channel sparsity assumptions. Moreover, existing works focus on a single
IRS, whereas in practice multiple such surfaces should be installed to truly
benefit from the concept of reconfiguring propagation environments. In light of
these challenges, this paper tackles the CE problem for the distributed
IRSs-assisted multi-user MISO system. An optimal CE protocol requiring
relatively low training overhead is developed using Bayesian techniques under
the practical assumption that the BS-IRSs channels are dominated by the
line-of-sight (LoS) components. An optimal solution for the phase shifts
vectors required at all IRSs during CE is determined and the minimum mean
square error (MMSE) estimates of the BSusers direct channels and the IRSs-users
channels are derived. Simulation results corroborate the normalized MSE (NMSE)
analysis and establish the advantage of the proposed protocol as compared to
benchmark scheme in terms of training overhead.
