## 1 Introduction  
High-speed underwater communication plays an increasingly important role in oceanographic research, information transfer and marine development [1]. With the application of autonomous underwater vehicles (AUVs), underwater wireless sensor networks (UWSNs) and remotely operated vehicles (ROVs), underwater optical wireless communication (UOWC) with advantages of high bandwidth, cost-effectiveness and low latency becomes a promising wireless communication technology for short/middle reach data exchange compared with acoustic and radio frequency (RF) communications [2, 3]. However, seawater, as an enormous and complex physical, chemical and biological system, contains dissolved substances, suspensions and various kinds of active organisms. With the natural characteristics of inhomogeneities of seawater, the transmission light is strongly attenuated because of the absorption and scattering effects that hinder our construction of a precise underwater optical channel model (UOCM) [4, 5]. [PERSON] et al. analyzed the spatial distribution of light energy using the volume scattering function [6], and then the Henyey-Greenstein function-based Monte Carlo method was proved to be an effective means [7]. [PERSON] et al. proposed a double-gamma function based on the mentioned Monte Carlo method, which can describe the UOCM relatively precisely and the impulse responses are calculated [8]. The impulse response calculated from the double-gamma function and Monte Carlo simulation has been shown to have a better fitting effect on real underwater models. On the other hand, orthogonal frequency division multiplexing (OFDM) is widely used in OWC due to its strong capability to resist inter-symbol interference (ISI). However, the transmitted signals in an OWC system should be non-negative and real-valued due to the intensity modulation and direct detection while the conventional OFDM signals are bipolar complex-valued, which requires the modification of conventional OFDM. Therefore, Hermitian symmetry is commonly utilized before the inverse fast Fourier transform (IFFT) to satisfy the real-valued property. To obtain non-negative signals, various optical OFDM schemes are applied. Direct current biased optical OFDM (DCO-OFDM) adds a DC bias [9], and asymmetrically clipped optical OFDM (ACO-OFDM) utilizes the odd-subcarrier modulation and zero clipping [10]. However, DCO-OFDM and ACO-OFDM suffer from the problems of low power efficiency and low spectral efficiency, respectively. Asymmetrically clipped DC-biased optical OFDM (ADO-OFDM) is the performance tradeoff between DCO-OFDM and ACO-OFDM considering power and spectral efficiency [11; 12; 13]. In a conventional ADO-OFDM scheme, the transmitted signals are generated by superimposing the ACO-OFDM signals and DCO-OFDM signals. The zero clipping of the ACO-OFDM branch will introduce clipping noise into the even subcarriers in the transmission of DCO-OFDM signals, bringing difficulties to the demodulation of the DCO-OFDM signals. At the receiver, the ACO-OFDM signals must be demodulated first and subtracted from the reconstructed ADO-OFDM signals, and then the DCO-OFDM signals can be demodulated correctly, which results in high-complexity, delay and error propagation issues in demodulation [14]. The pre-distorted enhanced (PE) operation is applied in PEADO-OFDM to decrease the mutual interference and alleviate the issues caused by the clipping noise of the ACO-OFDM branch [15]. PEADO-OFDM eliminates the inter-carrier interference (ICI) between the ACO-OFDM and the DCO-OFDM branches at the transmitter and is applied as the modulation scheme for downlink in a visible light communication (VLC) system. However, the PE operation requires an additional FFT operation at the transmitter, inducing a more complicated transmitter. Compared with [PERSON]'s works in ref.