Blind Over-the-Air Computation and Data Fusion via Provable Wirtinger Flow

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.