In this paper, we study the performance of the continuous phase modulation (CPM)-based orthogonal frequency division multiplexing (CPM-OFDM) system. Also, we propose a CPM-based single-carrier frequency domain equalization (CPM-SC-FDE) structure for broadband wireless communication systems. The proposed structure combines the advantages of the low complexity of SC-FDE, in addition to exploiting the channel frequency diversity and the power efficiency of CPM. Both the CPM-OFDM system and the proposed system are implemented with FDE to avoid the complexity of the equalization. Two types of frequency domain equalizers are considered and compared for performance evaluation of both systems; the zero forcing (ZF) equalizer and the minimum mean square error (MMSE) equalizer. Simulation experiments are performed for a variety of multipath fading channels. Simulation results show that the performance of the CPM-based systems with multipath fading is better than their performance with single path fading. The performance over a multipath channel is at least 5 and 12 dB better than the performance over a single path channel, for the CPM-OFDM system and the proposed CPM-SC-FDE system, respectively. The results also show that, when CPM is utilized in SC-FDE systems, they can outperform CPM-OFDM systems by about 5 dB. Copyright © 2010 John Wiley & Sons, Ltd.