  IoT systems typically involve separate data collection and processing, and
the former faces the scalability issue when the number of nodes increases. For
some tasks, only the result of data fusion is needed. Then, the whole process
can be realized in an efficient way, integrating the data collection and fusion
in one step by over-the-air computation (AirComp). Its shortcoming, however, is
signal distortion when channel gains of nodes are different, which cannot be
well solved by transmission power control alone in times of deep fading. To
address this issue, in this paper, we propose a multi-slot over-the-air
computation (MS-AirComp) framework for the sum estimation in fading channels.
Compared with conventional data collection (one slot for each node) and AirComp
(one slot for all nodes), MS-AirComp is an alternative policy that lies between
them, exploiting multiple slots to improve channel gains so as to facilitate
power control. Specifically, the transmissions are distributed over multiple
slots and a threshold of channel gain is set for distributed transmission
scheduling. Each node transmits its signal only once, in the slot when its
channel gain first gets above the threshold, or in the last slot when its
channel gain remains below the threshold. Theoretical analysis gives the
closed-form of the computation error in fading channels, based on which the
optimal parameters are found. Noticing that computation error tends to be
reduced at the cost of more transmission power, a method is suggested to
control the increase of transmission power. Simulations confirm that the
proposed method can effectively reduce computation error, compared with
state-of-the-art methods.
