We consider the problem of peak-to-average power ratio (PAPR) reduction for orthogonal frequency-division multiplexing (OFDM) based large-scale multiple-input multipleoutput (MIMO) systems. A novel perturbation-assisted scheme is developed to reduce the PAPRs of the transmitted signals by exploiting the redundant degrees-of-freedom (DoFs) inherent in the large-scale antenna array... Specifically, we introduce artificial perturbation signals to the frequency-domain precoded signals, with the aim of reducing the PAPRs of their time-domain counterpart signals. Meanwhile, the additive perturbation signal associated with each tone is constrained to lie in the null-space of its associated channel matrix, such that it does not cause any multi-user inference or out-of-band radiations. Such a problem is formulated as a convex optimization problem, and an efficient algorithm is developed by resorting to the variable splitting and alterative direction method of multipliers (ADMM) techniques. Simulation results show that the proposed method has a fast convergence rate and achieves substantial PAPR reduction within only tens of iterations. In addition, unlike other precoding-based PAPR reduction methods, our proposed method which introduces perturbation signals to the precoded signals is independent of the precoding stage and thus could be more suitable for practical systems. (read more)