Optimized Design For Over-the-Air Computation System with Imperfect Channel State Information

Over-the-air computation (OAC) can leverage the interference between multiple users of multi-access channels (MAC) to perform function computation during the transmission process. This helps overcome the high latency issues caused by a large amount of data access in the applications of Internet of Things (IoT). The majority of current studies solely focus on air computation with the assumption of full channel state information (CSI). However, in practical applications, due to quantization and feedback errors, calibration mismatches, and various factors leading to delay errors and noise, the central end often can only obtain imperfect CSI. Therefore, we have a strong interest in optimizing the design of OAC with channel estimation errors to enhance its performance under adverse channel conditions. This papeer suggests a superior design strategy for OAC, considering total power limitations and flawed CSI. Specifically, we formulate the problem as a minimum mean square error (MSE) and transform the original non-convex problem into a convex problem using alternating optimization methods, and obtain the closed-form solution for the optimal transceiver factors. Numerical results are presented to validate the effectiveness of the proposed method.