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This paper is concerned with offline digital predistortion (DPD) for linearization of radio frequency (RF) high power amplifiers (PAs). We propose an adaptive scheme for selecting basis functions for both direct and indirect learning digital predistortion architectures. The adaptive scheme has the advantage of reducing the complexity and, at the same time, increasing the convergence rate and stability of offline digital predistoriton. In this paper we also present simulation results and lab experiment results of using adaptive basis functions in a hardware platform with a solid state high power amplifier.