One key weakness of multicarrier signals such as OFDM (Orthogonal frequency division multiplexing) is the high peak-to-average power ratio (PAPR). Nonlinear distortions caused by the power amplifier are aggravated by high PAPR, which in turn affects the OFDM signal. These nonlinearities in amplifiers cause both inter-Symbol interference (ISI) and inter-carrier interference (ICI) in the system. A “power back-off” is required to prevent spectral broadening and performance degradation from inter-modulation distortion. Constant Envelope OFDM (CE-OFDM) provides a solution to the high PAPR issue in OFDM. OFDM signal is transformed, by way of phase modulation (PM), to a constant envelope signal, thereby alleviating the need for a power back-off (IBO) and allowing for the most efficient power amplifier operation possible. In this paper the implementation of MLSE (Maximum-Likelihood Sequence Estimation) channel equalization in CE-OFDM-CPM is proposed, a performance gain comparison and evaluation over fast fading channels well be presented and discussed.