A system for linearly transmitting an amplified output signal using predistortion is disclosed. The system uses a straight inverse modeling scheme with orthogonal predictor variables to more easily and accurately determine the inverse of the distortion caused by a power amplifier of a RF transmitter. The direct inverse modeling scheme of the present invention indexes the LUT using the modulated input signals instead of the potentially noisier output signals, which helps to increase the accuracy of the predistortion. The predistorter system stores complex coefficients in the LUT, which are then used as the tap weights of a non-linear digital filter implementing the predistorter. Finally, the trainer uses a modified version of the power amplifier output signal which results in better predistortion performance. The modified power amplifier output signal has the in-band distortion removed from the power amplifier output signal.