  In the intelligent reflecting surface (IRS) assisted communication systems,
the acquisition of channel state information (CSI) is a crucial impediment for
achieving the passive beamforming gain of IRS because of the considerable
overhead required for channel estimation. Specifically, under the current
beamforming design for IRS-assisted communications, $KMN+KM$ channel
coefficients should be estimated if the passive IRS cannot estimate its
channels with the base station (BS) and users due to its lack of radio
frequency (RF) chains, where $K$, $N$ and $M$ denote the number of users,
reflecting elements of the IRS, and antennas at the BS, respectively. This
number can be extremely large in practice considering the current trend of
massive MIMO (multiple-input multiple-output), i.e., a large $M$, and massive
connectivity, i.e., a large $K$. To accurately estimate such a large number of
channel coefficients within a short time interval, we devote our endeavour in
this paper to investigating the efficient pilot-based channel estimation method
in IRS-assisted uplink communications. Building upon the observation that the
IRS reflects the signals from all the users to the BS via the same channels, we
analytically verify that a time duration consisting of $K+N+\max(K-1,\lceil
(K-1)N/M \rceil)$ pilot symbols is sufficient for the BS to perfectly recover
all the $KMN+KM$ channel coefficients in the case without noise. In contrast to
the conventional uplink communications without IRS in which the minimum pilot
sequence length for channel estimation is independent with the number of
receive antennas, our study reveals the significant role of massive MIMO in
reducing the channel training time for IRS-assisted communication systems.
