Over-the-Air Inference Through Analog Computation Over Multi-Hop MIMO Networks

A novel over-the-air machine learning framework over multi-hop multiple-input and multiple-output (MIMO) relay networks is proposed. The core idea is to imitate fully connected (FC) neural network layers by employing analog over-the-air computation over MIMO channels by carefully designing the precoding matrices at the transmitting nodes. A neural network, dubbed PrototypeNet, consisting of multiple FC layers is employed, with the number of neurons of each layer equal to the number of antennas of the corresponding terminal. PrototypeNet is trained with a loss function consisting of classification error accounting for the transmit power constraints, and with noise injection during training. We also propose a multiple-block extension when the number of antennas at the relay terminals is limited. Numerical results verify that the proposed over-the-air transmission scheme can achieve satisfactory classification accuracy under a power constraint while satisfying low latency requirements.