  Channel estimation is one of the main tasks in realizing practical
intelligent reflecting surface-assisted multi-user communication (IRS-MC)
systems. However, different from traditional communication systems, an IRS-MC
system generally involves a cascaded channel with a sophisticated statistical
distribution. In this case, the optimal minimum mean square error (MMSE)
estimator requires the calculation of a multidimensional integration which is
intractable to be implemented in practice. To further improve the channel
estimation performance, in this paper, we model the channel estimation as a
denoising problem and adopt a deep residual learning (DReL) approach to
implicitly learn the residual noise for recovering the channel coefficients
from the noisy pilot-based observations. To this end, we first develop a
versatile DReL-based channel estimation framework where a deep residual network
(DRN)-based MMSE estimator is derived in terms of Bayesian philosophy. As a
realization of the developed DReL framework, a convolutional neural network
(CNN)-based DRN (CDRN) is then proposed for channel estimation in IRS-MC
systems, in which a CNN denoising block equipped with an element-wise
subtraction structure is specifically designed to exploit both the spatial
features of the noisy channel matrices and the additive nature of the noise
simultaneously. In particular, an explicit expression of the proposed CDRN is
derived and analyzed in terms of Bayesian estimation to characterize its
properties theoretically. Finally, simulation results demonstrate that the
performance of the proposed method approaches that of the optimal MMSE
estimator requiring the availability of the prior probability density function
of channel.
