Digital communication systems which use Orthogonal Frequency Division Multiplexing (OFDM) are now widely used and have many advantages. The main disadvantage is the requirement for highly linear analogue electronics including the high power amplifier (HPA). This requirement cannot be met in all circumstances because of the occurrence of symbols with high peak to average power ratio (PAPR). Such symbols may be non-linearly distorted by limiting. Approaches to solve this problem have been either to reduce the PAPR at the transmitter or to try to mitigate the effect of the non-linearity at the receiver. Soft-limiting, i.e. applying limiting in software prior to the HPA is a simple way to reduce the PAPR. It produces non-linear distortion which will cause an increase in the bit-error-rate (BER) at the receiver. This thesis surveys existing alternatives ways of reducing the effect of non-linearity and proposes some new ones. Two iterative receiver techniques, based on statistical analysis of the nature of the non-linearity, have been implemented and investigated. These are the 'Bussgang Noise Cancellation' (BNC) technique and the 'Decision Aided Reconstruction' (DAR) techniques. As these techniques are valid for any memory-less nonlinearity, an alternative form of limiting, named as Inverted-Wraparound (IWRAP) has been included in the BNC investigation.A new method is proposed which is capable of correcting the received time-domain samples that are clipped, once they have been identified. This is named the 'Equation-Method' and it works by identifying constellation symbols that are likely to be correct at the receiver. If there are a sufficient number of these and they are correctly identified, the FFT may be partitioned to produce a set of equations that may be solved for the clipped time-domain samples. The thesis proposes four enhancements to this new method which improve its effectiveness. It is shown that the best form of this method outperforms conventional techniques especially for severe clipping levels. The performance of these four enhancements is evaluated over channels with additive white Gaussian noise (AWGN) in addition to clipping distortion. A technique based on a 'margin factor' is designed to make these methods work more effectively in the presence of AWGN noise. A new combining algorithm referred as 'HARQ for Clipping' is presented where soft bit decisions are combined from multiple transmissions. 'HARQ for Clipping' has been combined with the best version of the Equation-Method, and the performance of this approach is evaluated in terms of the BER with different levels of AWGN. It has been compared to other approaches from the literature and was found to out-perform the BNC iterative receiver by 3dB at signal to noise ratios around 10dB. Without HARQ, the best version of the Equation-Method performs better than the BNC receiver, at signal-to-nose ratios above about 17dB.