Fast Baseband Polynomial Inverse Algorithm for Nonlinear System Compensation Yuelin Ma #1 , Yoshihiko Akaiwa #2 , Yasushi Yamao #3 Advanced Wireless Communication research Center, the University of Electro-Communications 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585 1 enisoc@163.com, 2 akaiwa@awcc.uec.ac.jp, 3 yamao@ieee.org Abstract— Digital predistortion based on nonlinear system modeling and consecutively inverse is an important technique for linearization of radio frequency power amplifiers (PAs). Compensation for the nonlinear systems represented by polynomials involves polynomial inverses. In this paper, we propose a fast algorithm to invert a given baseband memoryless polynomial based on the predefined orthogonal basis. The orthogonal basis is predefined based on the distribution of the signal, which is known a priori. Compared with the well- established pth-order inverse method, the proposed algorithm can find the optimal coefficients of the inverse polynomial. Both numerical simulation and experiment with an actual PA demonstrate that the proposed algorithm can provide very good performance for compensating the nonlinear systems re- presented by baseband polynomial. Keywords- nonliner system, baseband polynomial, digital predistortion, polynomial inverses I. INTRODUCTION In the recent years, many research works have been carried out on identification, behavioral modeling and compensation of nonlinear systems. Especially, nonlinear system modeling and compensation of the radio frequency (RF) power amplifiers (PAs) is an important subject from the viewpoint of practical use. As an effective technique to compensate for the nonlinear distortion in PAs, digital predistortion (DPD) attracts much attention. It always involves inverse modeling of the PA, whether directly or indirectly. Most of the predistortion architectures for PA linearization are based on indirect learning which is more flexible and robust than the direct learning architecture [1]. As noticed by some researchers, however, this method suffers from noisy output of PAs [2]. They suggest more complicated architectures to solve this problem. In [2] and [3], the PA is first modeled using a polynomial model and the predistortion function is calculated based on the inverse of the model. Such scheme is shown in Fig.1, which is also known as “PA modeling and inverse”. In their methods, both modeling and inverse estimation employs adaptive algorithm or least square fitting which are based on the measured data of the PA characteristics, resulting in heavy computation and long executing time. In order to reduce the computation load, more efficient methods for inverting the polynomial model need to be developed. There are several techniques for inverting the polynomials. Schetzen [4] proposed a “pth-order inverse” method to invert the Volterra series which is known as the most general function for representing a weak nonlinear system with memory. In order to increase the speed and decrease the complexity for constructing the Volterra kernels, Sarti et al. [5] proposed the recursive technology for the pth-order inverse. The limitation of the pth-order inverse is that it can only remove the nonlinear distortion introduced by the first pth-order term and leaves residual higher order distortion. It results in ineffective inverses in some circumstances. Tsimbinos [6] derived the method to invert the power series based on Chebyshev polynomial and Hermite polynomial, which provides better performance than pth-order inverse. Tsimbinos's method, however, is difficult to be extended to baseband, and is restricted to sine signal and the signal with Gaussian distribution. In this paper, we propose a fast algorithm that can find the optimum inverse of a given baseband polynomial when the distribution of the signal is known a priori. The appealing hallmark of our approach, compared with the aforementioned methods, is that the higher order distortion that is to be suppressed is tractable with a tunable truncation factor. This results in high flexibility in terms of practical implementation. Fig. 1. Digital predistortion based on direct learning PD PA PA Modeling Inverse Estimation x(t) y(t) error x PD (t)