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Phase modulation based systems have the advantages of constant envelope (CE) signals and the ability to improve the diversity of multipath channels. In this paper, we study the performance of single-carrier (SC) and orthogonal frequency-division multiplexing (OFDM) systems using phase modulation (PM). Both systems are implemented with frequency domain equalization (FDE) to obtain high diversity gains over the frequency selective multipath fading channels. FDE performance using both zero forcing (ZF) and minimum mean square error (MMSE) is studied over a wide range of multipath fading channel models. Simulation results show that, the PM based systems performance with multipath fading can outperform their performance with single path fading. The performance over the multipath channels is at least 5 dB and 12 dB better than the performance over the single path channel, using PM based OFDM and SC-FDE systems, respectively. The results also show that, when PM is utilized, SC-FDE systems can outperform OFDM systems by about 5 dB.