Over-the-Air Split Learning with MIMO-Based Neural Network and Constellation-Based Activation

This paper investigates a communication-efficient split learning (SL) over multiple-input multiple-output (MIMO) communication system. In particular, we mathematically decompose the inter-layer connection of a neural network (NN) to a series of linear precoding and combining transformations using over-the-air computation (OAC), which synergistically form a linear layer in NNs. The precoding and combining matrices are trainable parameters in such a system, whereas the MIMO channel is implicit. The proposed system eliminates the implicit channel estimation through exploiting the channel reciprocity and properly casting the backpropagation process, significantly saving the system costs and further improving the overall efficiency. The practical constellation diagrams are used as the activation function to avoid sending arbitrary analog signals as in the traditional OAC system. Numerical results are illustrated to demonstrate the effectiveness of the proposed scheme.