Abstract—Transmission signals of modern communication systems, such as orthogonal frequency-division multiplexing signals, usually have large peak-to-average power ratio. These signals are sensitive to the power amplifier’s nonlinearity, which generates both in-band distortion and out-of-band spectral regrowth. The adaptive digital predistortion (DPD) is an efficient linearization technique without sacrificing the power efficiency. To estimate the DPD coefficients, numerical instability and computational complexity are bottlenecks. In this paper, we propose a general approach to derive orthonormal basis functions, which can improve the numerical stability during the coefficients estimation. By applying the orthonormal basis functions, we further propose an adaptive algorithm that exhibits a low computation complexity of least mean squares algorithm while retaining the fast convergence speed of recursive least squares algorithm. Both simulation and experimental results validate the effectiveness of the proposed algorithm. Index Terms—Power amplifiers, adaptive digital predistortion, orthonormal basis functions, low-complexity.