Neural constellation shaping and back-off training for memoryless power amplifiers

Traveling-wave tube amplifiers (TWTAs) are common power amplifiers in satellite communications. Saturation and warping effects caused by the nonlinearity make constellation shaping a non-trivial task, when nonlinear amplifiers are involved in the channel. Constellation shaping optimizes geometry and probability of occurrence of constellation points to maximize the mutual information. This paper newly introduces constellation shaping using neural networks to satellite communications by showing its benefits on channels with TWTAs. We study how the TWTA nonlinearity impacts learned constellations both in terms of geometry and point probability of occurrence. The peak-power constraint introduced by TWTA saturation leads to a decreased impact of probabilistic shaping compared to geometric shaping which is illustrated using mutual information curves and displayed constellations. The tuning of the input backoff (IBO) of the TWTA causes an additional trade-off between transmit power at the cost of more severe nonlinear effects. This paper makes a new contribution by training IBO and transmit constellation jointly for TWTAs. By displaying constellations at different IBOs the interdependency of constellation shaping and IBO optimization is motivated. Total degradation analysis on mutual information curves resulting from the cross-entropy loss of the autoencoder illustrates the impact of joint IBO training and constellation shaping. A study of coded bit error rate performance and comparison to conventional constellations with memoryless predistortion emphasizes the effectiveness of training IBO and constellation jointly using autoencoders.