Orthogonal frequency-division multiplexing (OFDM) is a digital modulation scheme that has resilience to multipath effects and is one of the most widely adopted schemes for modern wireless systems. The scheme is critically dependent on linearity in hardware systems due to the Fourier transformation and its inherently high peak-to-average power ratio, which makes minimisation of non-linearity a priority. This work investigates the effect of non-linearity caused by a typical radio frequency high-power amplifier on the performance of an OFDM signal based on the WLAN 802.11a standard. To overcome the non-linear distortion, an adaptive baseband predistorter (PD) based on the Hammerstein system and new parameter estimation technique is developed. The performance of the predistorter is assessed using S-band lateral MOSFET transistor amplifier as transmitter, of 40-dBm peak envelope power. The effectiveness of the compensator is investigated with measurement of the error vector magnitude (EVM) in an additive white Gaussian noise (AWGN) channel and the adjacent channel power ratio (ACPR). The experimental results confirm the accurate prediction of PA nonlinear behaviour with memory effect and a useful trade-off between accuracy and convergence speed in the reduction of nonlinear distortion, as well as good suppression of spectrum regrowth.