Over-the-Air Multi-View Pooling for Distributed Sensing

Abstract

Sensing is envisioned as a key network function of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sixth-generation</i> (6G) mobile networks. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Artificial intelligence</i> (AI)-empowered sensing fuses features of multiple sensing views from devices distributed in edge networks for the edge server to perform accurate inference. This process, known as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multi-view pooling</i> , creates a communication bottleneck due to multi-access by many devices. To alleviate this issue, we propose a task-oriented simultaneous access scheme for distributed sensing called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Over-the-Air Pooling</i> (AirPooling). The existing <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Over-the-Air Computing</i> (AirComp) technique can be directly applied to enable Average-AirPooling, which exploits the waveform superposition property of a multi-access channel to implement fast over-the-air averaging of pooled features. However, despite being most popular in practice, the over-the-air maximization, called Max-AirPooling, is not AirComp realizable given the fact that AirComp addresses only a limited subset of functions. We tackle the challenge by proposing the novel generalized AirPooling framework that can be configured to support both Max- and Average-AirPooling by controlling a configuration parameter and extended to even other pooling functions. The former is realized by adding to AirComp the designed pre-processing at devices and post-processing at the server. To characterize the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">End-to-End</i> (E2E) sensing performance in object recognition, the theory of classification margin is applied to relate the classification accuracy and the AirPooling error, which allows the latter to be a tractable surrogate of the former. Furthermore, the analysis reveals an inherent tradeoff of Max-AirPooling between the accuracy of the pooling-function approximation and the effectiveness of noise suppression. Using the tradeoff, we make an attempt to optimize the configuration parameter of Max-AirPooling, yielding a sub-optimal closed-form method of adaptive parametric control. Experimental results obtained on real-world datasets show that AirPooling provides sensing accuracies close to those achievable by the traditional digital air interface but dramatically reduces the communication latency, by up to an order of magnitude.