The continuous phase modulation (CPM) is a adaptive phase modulation technique which performs a vital role in OFDM system than constant envelope based on OFDM. The system combines the frequency diversity and low complexity type of equalizer. The attractive digital modulation adopted two types of equalizers; zero forcing and MMSE equalizer. The constant envelope modulation also used to attract the OFDM in future communications. The digital modulations QPSK, DPSK, 4-FSK and 4-PAM are analyzed to achieve good error rate and QPSK/QAM outperforms the PAM and FSK. The constant envelope OFDM (CE-OFDM) propagates the signal with near ideal PAPR than conventional systems and gives good performance with suitable FDE. In this paper, we proposed CE- CPM based FDE which is feasible than CE –CPM based OFDM and non OFDM systems. The error rate can minimize via selected equalizer which will results in good performance under channel conditions.