  The large untapped spectrum in the sub-THz allows for ultra-high throughput
communication to realize many seemingly impossible applications in 6G. One of
the challenges in radio communications in sub-THz is the hardware impairments.
Specifically, phase noise is one key hardware impairment, which is accentuated
as we increase the frequency and bandwidth. Furthermore, the moderate output
power of the sub-THz power amplifier demands limits on peak to average power
ratio (PAPR) signal design. Single carrier frequency domain equalization
(SC-FDE) has been identified as a suitable candidate for sub-THz, although some
challenges such as phase noise and PAPR still remain to be tackled. In this
work, we design a phase noise robust, modest PAPR SC waveform by geometrically
shaping the constellation under practical conditions. We formulate the waveform
optimization problem in its augmented Lagrangian form and use a
back-propagation-inspired technique to obtain a constellation design that is
numerically robust to phase noise, while maintaining a relatively low PAPR
compared to the conventional waveforms.
