## 6 Conclusions  
The existing OFDM-based frequency domain equalization algorithm faces a limitation, that is, its dependence on longer redundant cyclic prefixes. For this reason, an OFDM-based frequency domain decision feedback equalization algorithm is proposed in this paper, which can compensate for frequency selective fading and \"proactively\" over-come the adverse effects of inter-symbol interference and inter-carrier interference under the premise of less redundant cyclic prefix. Based on the limitations of the existing frequency domain equalization algorithm, this paper first highlighted the influence of the multipath effect on the OFDM signal transmission. Subsequently, the principles of the OFDM-based frequency domain equalization were further explored for an improved structural model design of the communication system. On this basis, a novel frequency domain adaptive equalization algorithm was put forward. In the end, the proposed algorithm was optimized to address the problem of increased computation.  
In addition, the computational complexity of the proposed method is analyzed, and an optimization method to reduce the computational complexity of the algorithm is proposed according to the principle of decision feedback equalization algorithm in frequency domain. Simulation results show that the BER performance of the simplified algorithm is not much different from that of the original algorithm. In addition, it can significantly reduce the  
Figure 6: Symbol error ratio curve for Channel 2 with two frequency domain equalization algorithms.  
complex multi-plication number of each iteration, which greatly reduces the hardware requirements of the system, and is more conducive to practical application.  
The simulation results reveal that this novel algorithm delivers a better symbol error ratio and a stronger capability of compensation for the frequency selective fading under multipath effect compared with the existing algorithm. Moreover, the proposed algorithm can realize the information transmission at a low symbol error ratio when fewer cyclic prefixes are used. This can effectively overcome the dependence of the OFDM communication system on cyclic prefixes. The proposed algorithm is therefore more suitable for the underwater acoustic channels characterized by limited energy and bandwidth. In the end, the novel algorithm is simplified to address the increased computation.  
Since Doppler compensation is not the focus of this paper, the method proposed in this paper is mainly suitable for stationary conditions. There are related methods to deal with the Doppler effect, which can estimate and compensate the Doppler shift caused by movement. Later, according to the research progress, the optimization method under the Doppler effect will be further considered.  
[PERSON] has been the project leader and responsible for defining the scientific requirements that meet the research goals. The authors' individual contributions, are summarized below: conceptualization, C.F. and Y.L.; data curation, C.F.; formal analysis, J.Z.; funding acquisition, Y.L. and H.L.; methodology, J.Z.; writing-original draft, C.F.; writing-review and editing, H.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Science Foundation for Outstanding Young Scholars (grant number 42122025), Natural Science Foundation for Distinguished Young Scholars of Hubei Province of China (grant number 2019 CFA086) and Natural Science Foundation of Hubei Province of China (grant number 2017 CFB377).  
Not applicable.  
The original contributions presented in the study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.