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The digital baseband predistorter is an effective technique to compensate for the nonlinearity of power amplifiers (PAs) with memory effects. However, most available adaptive predistorters based on direct learning architectures suffer from slow convergence speeds. In this paper, the recursive prediction error method is used to construct an adaptive Hammerstein predistorter based on the direct learning architecture, which is used to linearize the Wiener PA model. The effectiveness of the scheme is demonstrated on a digital video broadcasting-terrestrial system. Simulation results show that the predistorter outperforms previous predistorters based on direct learning architectures in terms of convergence speed and linearization. A similar algorithm can be applied to estimate the Wiener PA model, which will achieve high model accuracy.