Abstract: To solve the issues of the high complexity and poor performance in the equalization of high order and partial response Continuous Phase Modulation (CPM) signals, a new framework of tilted phase CPM transmitted signals is designed from the perspective of Rimoldi decomposition. A novel frequency domain equalization algorithm for high order CPM signals is proposed[0] based on the combination of single-carrier Frequency Domain Equalization (FDE) and Turbo equalization. This algorithm avoids the large matrix inversions in computation of the equalizer coefficients in time domain by transforming the signal equalization to frequency domain. Simultaneously, it improves the system performance by soft information iterative process. The analysis and simulation results show that in multipath fading channels with serious inter-symbol interference the proposed algorithm provides a relatively lower computational complexity and a performance gain of about 1.5 dB in signal-noise ratio compared with the previously proposed FDE algorithm based on symbol for fourth-order and partial response CPM signals.