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This brief demonstrates a new adaptive digital predistortion architecture particularly suited to mobile handset applications. The central idea is to build a lookup table (LUT) that directly captures the static compressive nonlinearity of the power amplifier (PA) and then insert this LUT into the feedback path of a ΔΣ modulator. The oversampled ΔΣ modulator automatically performs both the inversion of the PA nonlinearity and the interpolation between LUT entries, permitting complex modulation strategies to be handled with an absolute minimum of LUT entries and with a dramatically simplified computational structure. The advantages of this architecture over previous methods include: 1) there is no need to explicitly invert the PA nonlinearity, reducing the complexity for the system designer; 2) the LUT training is done with an open-loop method, improving the training speed; 3) there is no need to explicitly employ numerical interpolation between LUT entries; and 4) digital-to-analog converter (DAC) nonlinearity is incorporated into the predistortion, allowing fast low-resolution DACs to be used in the final system. We built a proof-of-concept prototype for a 900-MHz, 27-dBm PA transmitting a 16-ary quadrature amplitude modulation (16-QAM) signal with a bandwidth of 3.4 MHz. The predistortion system reduced out-of-band distortion products by 10 dB and improved the error vector magnitude from 3.5% to 2.0%.