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This paper tries to reduce the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signal using a method that combines the use of convex optimization and amplitude predistortion. To reduce the peak of the OFDM signal, the proposed method applies one of the techniques on free carriers and the other one on the data carriers. Depending on the method used in each carrier, two different variants of it can be identify. Throughout this article, it is demonstrated that a significant improvement of ht performance can be obtained with a combination of the two methods with a slight increase in the computational complexity.