High power efficiency is an important requirement in cellular transmitter radios. OFDM systems require very linear transmission because of high peak-to-average power-ratio (PAPR). However, linear power amplifiers (PA) have very low efficiency. To enhance the power efficiency, non-linear PAs are applied and even forced to work near the saturation point. This generates inevitably huge non-linear distortion and spectrum re-growth. In this paper we propose a novel scheme to enhance the power efficiency of the mobile OFDM radio using polynomial-based pre-distortion and post-compensation. We estimate both the non-linearity and inverse non-linearity of the RF transmitter modeled by a memory-less polynomial with Least Square Error (LSE) method. These parameters can then be used to either construct a closed-form pre-distorter or easily generate the post-compensation signal to cancel the non-linear distortion at the RF output.