MIMO Over-the-Air Computation for Device-Edge Collaborative Inference

Device-edge collaborative inference, which deploys well-trained artificial intelligence (AI) models at the network edge via the cooperation of edge devices and edge servers, emerges as a promising technique to provide ubiquitous intelligent services. In this paper, a multiple-input multiple-output (MIMO) over-the-air computation (AirComp) scheme is proposed for the efficient implementation of device-edge collaborative inference. In the considered system, the technique of MIMO AirComp is utilized to aggregate local feature vectors, extracted from noise-corrupted sensory data on devices, at the server to efficiently derive a denoised global one for completing the downstream inference task. Device-edge collaborative inference features a task-oriented property, that concerns the effectiveness and efficiency of the task execution. In this case, the traditional AirComp criterion, i.e., minimum mean square error (MMSE), is not effective, since the same distortion level on different feature elements may have different influences on the inference performance. To this end, this paper directly adopts inference accuracy as the design objective. As the instantaneous inference accuracy is unknown during the design stage, an approximated but tractable metric, called discriminant gain, which measures the discernibility of different classes, is adopted. To maximize the inference accuracy measured by discriminant gain, a MIMO AirComp technique is proposed to jointly optimize all feature elements. The problem is nonconvex because of the complicated form of the objective function and the constraints. The solution based on semidefinite relaxation (SDR) and successive convex approximation (SCA) is employed to design a joint transmit precoding and receive beamforming scheme. Besides, to enhance the robustness of practical AI models in the inference stage, a post-processing design of feature magnitude normalization is proposed. Extensive experiments are conducted based on a practical human motion recognition task, which verifies our theoretical analysis and the superiority of our proposed scheme.