  Over-the-air computation (AirComp) shows great promise to support fast data
fusion in Internet-of-Things (IoT) networks. AirComp typically computes desired
functions of distributed sensing data by exploiting superposed data
transmission in multiple access channels. To overcome its reliance on channel
station information (CSI), this work proposes a novel blind over-the-air
computation (BlairComp) without requiring CSI access, particularly for low
complexity and low latency IoT networks. To solve the resulting non-convex
optimization problem without the initialization dependency exhibited by the
solutions of a number of recently proposed efficient algorithms, we develop a
Wirtinger flow solution to the BlairComp problem based on random
initialization. To analyze the resulting efficiency, we prove its statistical
optimality and global convergence guarantee. Specifically, in the first stage
of the algorithm, the iteration of randomly initialized Wirtinger flow given
sufficient data samples can enter a local region that enjoys strong convexity
and strong smoothness within a few iterations. We also prove the estimation
error of BlairComp in the local region to be sufficiently small. We show that,
at the second stage of the algorithm, its estimation error decays exponentially
at a linear convergence rate.
