Orthogonal frequency division multiplexing (OFDM) has been widely adopted in communications systems due to its high spectral efficiency and resistance to multipath fading and impulse noise. However, because of its large peak-to-average power ratio (PAPR), OFDM is highly sensitive to nonlinear distortion. In wireless systems, where to achieve acceptable power efficiency, the high power amplifiers (HPAs) operate near the saturation point, OFDM signals cause spectral regrowth leading to prohibitively high levels of adjacent channel interference (ACI). This paper investigates two signal predistortion techniques that attempt to mitigate these effects. The first approach assumes the HPA is memoryless, meaning that the output only depends on the current input. A predistorter using a one-dimensional (1-D) look up table (LUT) which has non-uniform bin spacing in amplitude is proposed. This non-uniform spacing allows the LUT to produce a better estimate of the inverse gain characteristic of the HPA. The second approach attempts to utilizes a two dimensional (2-D) LUT which is capable of linearizing amplifiers with memory effects where the amplifier gain has a dependency on the short-term average power of the input signal. Multiple LUTs are constructed over the range of the input signal with each LUT being employed over a specific range of short-term average power.