## 1 Introduction
The system experienced a dramatic degradation of performance since severe inter-subcarrier interference and inter-symbol interference were caused. Under normal circumstances, a long-time cyclic prefix was added to overcome these adverse impacts. In recent years, underwater acoustic communications systems have been extensively investigated taking cyclic prefix orthogonal frequency division multiplexing (CP-OFDM), a multicarrier transmission technique into account, to overcome the harsh underwater channel [12]. Compared with traditional single carrier system, the CP-OFDM system has many advantages. For example, excellent spectral efficiency, robustness against multi-path channels, and the possibility of implementing low-cost transceivers. The CP-OFDM system is capable of converting a multipath channel in the time domain into a one-tap response for each subcarrier in the frequency domain, so it has the robustness against a multipath channel. In [13], cyclic prefix correlation was introduced to estimate Doppler factors, and time frequency two-dimensional pilot insertion was adopted to realize channel estimation and equalization. A transmission rate of 4.8 kbps was achieved for the transmission distance of ten kilometers. Nevertheless, a cyclic prefix would cause a waste of bandwidth if it did not transmit effective information, and would restrict the advantages of OFDM. In order to eliminate the adverse effects of redundant cyclic prefixed in CP-OFDM systems, a frequency-domain equalization algorithm for underwater acoustic communication OFDM with high channel utilization is proposed in this paper. In particular, we focus on the optimal design of cycle prefixes in OFDM system. Following the principles of a cyclic prefix, a frequency domain equalization algorithm is proposed to reduce the number of cyclic prefixes in the OFDM. The proposed algorithm effectively eliminates the adverse multipath effect on underwater acoustic channels without using any cyclic prefix. Additionally, it greatly improves the frequency band utilization of the OFDM-based underwater acoustic communication system, so as to guarantee high-speed data transmission with limited bandwidth. The main contributions of this paper are as follows:  
1. The model of CP-OFDM communication system is deeply studied, and the influence of multipath fading on signal transmission is analyzed. It is found that the influence of multipath effect on OFDM signal can be divided into three aspects: the first is frequency selective fading caused by multipath channel, the second is intercarrier interference, which is caused by multipath effect destroying the orthogonality of OFDM subcarriers, and the third is inter-symbol interference ISI. 2. In view of the fact that the traditional frequency domain equalization algorithm is only suitable for the case that the maximum delay length is not greater than the cyclic prefix length, and it relies on the longer cyclic prefix to \"avoid\" the inter-symbol interference and inter-carrier interference caused by multipath effect. In this paper, a new frequency domain equalization algorithm is proposed, which can compensate for frequency selective fading and \"proactively\" overcome the adverse effects of inter-symbol interference and inter-carrier interference under the premise of less redundant cyclic prefix. 3. 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 complex multiplication number of each iteration, which greatly reduces the hardware requirements of the system, and is more conducive to practical application.