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The large untapped spectrum in the sub-THz allows for ultra-high throughputcommunication to realize many seemingly impossible applications in 6G. One ofthe challenges in radio communications in sub-THz is the hardware impairments.Specifically, phase noise is one key hardware impairment, which is accentuatedas we increase the frequency and bandwidth. Furthermore, the modest outputpower of the sub-THz power amplifier demands limits on peak to average powerratio (PAPR) signal design. Single carrier frequency domain equalization(SC-FDE) waveform has been identified as a suitable candidate for sub-THz,although some challenges such as phase noise and PAPR still remain to betackled. In this work, we design a phase noise robust, low PAPR SC-FDE waveformby geometrically shaping the constellation under practical conditions. Weformulate the waveform optimization problem in its augmented Lagrangian formand use a back-propagation-inspired technique to obtain a constellation designthat is numerically robust to phase noise, while maintaining a low PAPR.

Constellation Shaping under Phase Noise Impairment for Sub-THz Communications