Abstract
In trainable wireless communications systems, the use of deep learning for over-the-air training aims to address the discontinuity in backpropagation learning caused by the channel environment. The primary methods supporting this learning procedure either directly approximate the backpropagation gradients using techniques derived from reinforcement learning, or explicitly model the channel environment by training a generative channel model. In both cases, over-the-air training of transmitter and receiver requires a feedback channel to sound the channel environment and obtain measurements of the learning objective. The use of continuous feedback not only demands extra system resources but also makes the training process more susceptible to adversarial attacks. Conversely, opting for a feedback-free approach to train the models over the forward link, exclusively on the receiver side, could pose challenges to reliably end the training process without intermittent testing over the actual channel environment. In this article, we propose a novel method for the over-the-air training of wireless communication systems that does not require a feedback channel to train the transmitter and receiver. Random samples are transmitted through the channel environment to train a mixture density network to approximate the channel distribution on the receiver side of the network. The transmitter and receiver models are trained with the resulting channel model, and the transmitter can be deployed after training. We show that the block error rate measurements obtained with the simulated channel are suitable for monitoring as a stopping criterion during the training process. The resulting method is demonstrated to have equivalent performance to the end-to-end autoencoder training on small message sequences.