Abstract
Over-the-air computation (AirComp) is considered a transformative enabler for next-generation artificial intelligence (AI) services and wireless data aggregation via the electromagnetic waveform-superposition property of wireless multi-access channels (MAC). However, the conventional distortion metric, minimum square error (MSE), is imperfect and not universally applicable in specific AirComp scenarios in a low-signal-to-noise ratio (SNR) regime and under power budget constraint. Conversely, the average discriminant gain is studied for task-oriented AirComp AI services like classification but with inaccurate performance indication. To solve these problems, this work establishes a novel framework for AirComp systems from the mutual information (MI) perspective. First, we categorize the AirComp model into two distinct classes based on the source (sensing) data independence, namely diverse-targets (DT) AirComp and homogeneous-target (HT) AirComp. Both categories with different inputs like classical Gaussian and classification-based Gaussian mixture model (GMM), can be unified and assessed via MI criterion. Next, for the DT AirComp system, we introduce a novel MI-aided AirComp beamforming scheme employing majorization-minimization (MM) relaxation. As for the HT AirComp, we present a heuristic successive approximation (SA)-based beamforming method considering complex GMM inputs. We also provide the feedback and update protocol for AirComp tracking. Simulations validate the superior performance on AirComp throughput and task-oriented metrics such as classification accuracy with our proposed MI-aided beamforming schemes.