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This paper presents a combined table look-up and polynomial-based predistortion (TLPPD) scheme for M-QAM transmission using non-linear power amplifiers. By applying a table look-up approach, the overall AM/AM and AM/PM distortion characteristics of the amplifier are divided into a small number of segments so that the non-linear behavior of each segment can be modeled by polynomials of lower order. As a result, the proposed scheme can offer both reduced complexity and faster convergence while maintaining the required accuracy as compared to the table look-up and polynomial-based techniques. Performance evaluation using simulation and experiments is presented. Power spectra and out-of-band emission of M-QAM systems using the proposed scheme and nonlinear power amplifier to achieve both high power and bandwidth efficiencies are also examined by simulation and experiments. Results indicate that the proposed scheme is suitable for applications of bandwidth-efficient M-QAM to PCS systems using non-linear amplifiers.