Constant Envelope OFDM provides a solution to the issue of a high peak-to-average power ratio in OFDM by using angle modulation to transform the OFDM signal to a constant envelope signal. However, Constant Envelope OFDM is based on nonlinear angle modulation and therefore presents its own unique set of challenges. These challenges are studied in this dissertation and addressed through the application of signal reception, equalization and error correction coding techniques to enable robust Constant Envelope OFDM performance. The impact of the threshold effect on Constant Envelope OFDM is studied. More specifically, the impact of cycle slip noise, both due to the threshold effect and phase wrapping issues, on Constant Envelope OFDM performance is considered. A novel cycle slip mitigation technique is developed which results in significant threshold extension. Novel receivers for Constant Envelope OFDM are also developed which allow for a lower complexity receiver implementation. These receivers alleviate the need to employ a phase demodulator at the receiver also resulting in immunity from the threshold effect and phase wrapping issues. The performance of these linear receivers is studied in additive white Gaussian noise (AWGN) and multipath fading channels and they are shown to perform well compared to the conventional arctangent based receiver. In frequency selective fading channels, a frequency domain equalizer is applied to Constant Envelope OFDM and shown to provide good performance in all cases. Since the performance of the frequency domain equalizer depends on the quality of the channel estimate, the effect of the amplifier nonlinearities on the channel estimate is studied for the case of alternate channel estimation training symbols. Furthermore, the application of error correction coding to Constant Envelope OFDM is also studied for the alternate receivers in AWGN and multipath fading channels. Finally, the impact of narrowband interference on Constant Envelope OFDM is studied. A prediction error filter (PEF) is employed to mitigate the narrowband interference resulting in significant performance improvement at low signal to interference ratios