Design of Non-uniform Constellations in the Channel with Phase Noise

The performance of sub-TeraHertz(sub-THz) system is severely degraded by strong oscillator phase noise. Highorder constellation is one of the methods in which transmission rates can be increased and non-uniform constellation (NUC) is considered to be an effective way of increasing block error rate (BLER) performance. In this paper, we design a series of constellations for single-carrier and multi-carrier systems under phase noise (PN). In order to improve the BLER performance under PN channel, we formulate an optimization problem to maximize the channel capacity by changing the complex plane coordinates of the constellation points. To calculate the channel capacity, single-carrier PN and multi-carrier PN are modeled separately in this paper. In particular, a series of derivations are carried out for multi-carrier PN. Numerical results demonstrate that NUC can be considered as a commitment technique for channels with PN, and a series of NUCs with different code rates are obtained, with a maximum gain of 4.10 dB in the single-carrier system and 1.65 dB in the multi-carrier system.