用无线中继网络实现深层神经网络，功率放大器当激活函数。

Wireless physical neural networks (WPNNs) embed neural computation directly into analog hardware, offering lower energy consumption and latency than conventional digital implementations. In this paper, we propose a deep WPNN in which nonlinear activations are realized by a multi-hop multiple-input multiple-output (MIMO) relay network, in which each relay implements a trainable complex linear gain and bias, followed by the power amplifier's intrinsic nonlinearity acting as an activation function. The cascade of multiple relays therefore realizes an over-the-air fully connected network whose parameters can be trained end-to-end. We develop two transceiver designs for different channel state information (CSI) availability scenarios: a least squares (LS)-based scheme requiring only receiver-side CSI, and a singular-value-decomposition (SVD)-based scheme requiring both transmitter-side and receiver-side CSI. Simulation results show that the proposed architecture enables accurate over-the-air inference for image classification. In particular, the results highlight the advantage of exploiting hardware nonlinearity for enhanced inference capability.