Higher Order Constellations for Channels with Residual Phase Noise and Nonlinear Power Amplifiers

In satellite transponders, hardware impairments play a significant role when transmission at very high data rates is desired. Two components in satellite transponders causing such impairments are the power amplifier and the oscillator. Particularly for high data rates, the power amplifier needs to be driven as close to saturation as possible, as doing so maximizes transmit power. Operation close to saturation, however, causes clipping effects. The local oscillator, on the other hand, poses challenges to synchronization at the receiver particularly at high data rates. Hence, imperfect synchronizers can result in high residual phase noise which needs to be taken into account as additional hardware impairment. When it comes to designing optimal transmit constellations, past research has treated these problems individually, resulting in spiral constellations for channels with high phase noise and amplitude and phase-shift keying (APSK) constellations for channels with amplifiers operating close to saturation. In this work, we optimize high order constellation, i.e., with order 256, for channels with joint impairment of power amplifier and residual phase noise. We optimize our constellations using neural networks, and propose an extension of spiral constellation optimization using a feedforward network. We compare our proposed constellations to APSK constellations from DVB-S2X and spiral constellations and provide information rates for different severities of each impairment.