Universal Approximation with XL MIMO Systems: OTA Classification via Trainable Analog Combining

Abstract--In this paper, we show that an eXtremely Large (XL) Multiple-Input Multiple-Output (MIMO) wireless system with appropriate analog combining components exhibits the properties of a universal function approximator, similar to a feedforward neural network. By treating the channel coefficients as the random nodes of a hidden layer and the receiver's analog combiner as a trainable output layer, we cast the XL MIMO system to the Extreme Learning Machine (ELM) framework, leading to a novel formulation for Over-The-Air (OT A) edge inference without requiring traditional digital processing nor pre-processing at the transmitter . Through theoretical analysis and numerical evaluation, we showcase that XL-MIMO-ELM enables near-instantaneous training and efficient classification, even in varying fading conditions, suggesting the paradigm shift of beyond massive MIMO systems as OT A artificial neural networks alongside their profound communications role. Compared to deep learning approaches and conventional ELMs, the proposed framework achieves on par performance with orders of magnitude lower complexity, making it highly attractive for inference tasks with ultra low power wireless devices. Future device-to-device and Goal-Oriented (GO) networks will facilitate the communication of sensory data from Transmitter (Tx) to Receiver (Rx) devices, not solely for the purpose of conventional information decoding and storage, but also for extracting features that guide autonomous devices towards desired actions [1], [2].