A method of wireless communication by a transmitting device transforms a transmit waveform by an encoder neural network to control power amplifier (PA) operation with respect to non-linearities. The method also transmits the transformed transmit waveform across a propagation channel. A method of wireless communication by a receiving device receives a waveform transformed by an encoder neural network. The method also recovers, with a decoder neural network, the encoder input symbols from the received waveform. A transmitting device for wireless communication calculates distortion error based on a non-distorted digital transmit waveform and a distorted digital transmit waveform. The transmitting device also compresses the distortion error with an encoder neural network of an auto-encoder. The transmitting device transmits to a receiving device the compressed distortion error to compensate for power amplifier (PA) non-linearity.