  In this paper, channel estimation of an active intelligent reflecting surface
(IRS) aided uplink Internet of Things (IoT) network is investigated. Firstly,
the least square (LS) estimators for the direct channel and the cascaded
channel are presented, respectively. The corresponding mean square errors (MSE)
of channel estimators are derived. Subsequently, in order to evaluate the
influence of adjusting the transmit power at the IoT devices or the reflected
power at the active IRS on Sum-MSE performance, two situations are considered.
In the first case, under the total power sum constraint of the IoT devices and
active IRS, the closed-form expression of the optimal power allocation factor
is derived. In the second case, when the transmit power at the IoT devices is
fixed, there exists an optimal reflective power at active IRS. To further
improve the estimation performance, the convolutional neural network
(CNN)-based direct channel estimation (CDCE) algorithm and the CNN-based
cascaded channel estimation (CCCE) algorithm are designed. Finally, simulation
results demonstrate the existence of an optimal power allocation strategy that
minimizes the Sum-MSE, and further validate the superiority of the proposed
CDCE / CCCE algorithms over their respective traditional LS and minimum mean
square error (MMSE) baselines.
