Single carrier (SC) modulation is a promising candidate for sub-THz (90–300 GHz) communication due to its relaxed hardware requirements. However, MIMO precoding increases the peak-to-average power ratio (PAPR) in SC systems. Recent works have addressed this challenge by introducing a PAPR reduction signal (PRS), which is transmitted alongside the precoded information symbols. In existing works, the PRS is designed to minimize the PAPR by solving a constrained optimization problem. While this approach effectively reduces PAPR, current methods to solve the optimization problem suffer from high computational complexity. In this letter, we propose a novel low complexity algorithm for designing the PRS. We adopt a projected gradient descent method that converges toward the optimal solution while maintaining significantly lower computational complexity. Simulation results demonstrate that our algorithm achieves a 33-fold reduction in computation time compared to existing methods.