In this paper, we propose to model the digital predistortion as an adding signal technique in the Orthogonal Frequency Division Multiplexing (OFDM) context. The additional signal is then the predistortion signal for the Power Amplifier's (PA) non-linearity compensation. Two different algorithms are investigated for this signal generation. The first one is based on the Bussgang theorem for a memoryless predistortion where a preliminary step of PA's characteristic estimation is needed. The second algorithm doesn't need a priori PA's characteristic estimation; it is based on an iterative compensation of the error between the amplified signal and the OFDM signal. Thanks to the well known performance of Peak-to Average Power Ratio (PAPR) reduction methods based on the adding signal technique, this new formulation of predistortion by adding signal will allow us to have a common vision of both PAPR reduction and predistortion and by the way an optimal compromise between PA's efficiency and linearity. Simulations results in terms of Error Vector Magnitude (EVM), Adjacent Channel Power Ratio (ACPR) and Power Spectral Density (PSD) criteria show that both algorithms have close performances. Moreover, the second algorithm has a fast convergence; after 2 iterations, its performance is almost identical to that of the traditional predistortion.