###### Abstract  
In this paper, a simple sampling frequency offset (SFO) estimation and compensation scheme based on two phase-conjugated pilots is proposed and experimentally demonstrated in an OFDM-based underwater wireless optical communication (UWOC) system. The phase shift is obtained by simple multiplication for phase-conjugated pilots, and the results are averaged to perform more accurate phase estimation. The experimental results show that the estimation offset is limited within \(\pm\)3 ppm when the SFO ranges from \(-\)1000 ppm to \(+\)1000 ppm over a 1 m tap water channel. Moreover, with the help of the proposed scheme, up to \(\pm\)300 ppm SFO can be well-compensated with error vector magnitude (EVM) penalties below 1 dB after 1 m underwater transmission. In addition, the results demonstrate that, compared with the ideal case without SFO, our proposed SFO compensation scheme can provide nearly negligible bit error rate (BER) penalties in saltwater with the highly scattering property. underwater wireless optical communication; orthogonal frequency-division multiplexing; sampling frequency offset +
Footnote †: journal: _Photonics_  
data-carrying OFDM symbols in each OFDM frame is appropriate and the optimal cyclic prefix/suffix (CP/CS) per OFDM symbol is chosen [16], the SFO-induced ISI can also be avoided. Therefore, the SFO compensation is mainly to correct the SFO-induced subcarrier phase rotation [17]. Several methods have been intensively investigated for SFO estimation and compensation, which can be categorized into the following two types. One is the hardware scheme [18; 19], which realizes sampling clock frequency synchronization by adjusting the voltage-controlled oscillator with feedback/feedforward information. This requires high-precision, stable voltage-controlled oscillators and additional analog circuits. Another way of mitigating the SFO effect is digital signal processing (DSP). Depending on the utilization of assistant information, it can also be divided into blind and data-aided estimation methods. An overhead-free SFO compensation scheme based on inter symbol differential detection (ISDD) is proposed in [20; 21]. However, this method will cause residual phase noise. Then, the fourth-power algorithm is used for SFO estimation in [22; 23]. The application of the method is limited since it is suitable for the OFDM symbols with phases of \(\pm\pi/4\) or \(\pm 3\pi/4\). The data-aided methods estimate the SFO by using the pilot or training sequence (TS). Then the SFO compensation is completed in time or frequency domain [24; 25; 26; 27; 28; 29; 30]. The fourth-order piecewise polynomial interpolation is the most popular time-domain compensation method [24; 25], which can alleviate ICI at the expense of additional DSP computing resources. The pilot-aided SFO estimation method can compensate up to \(\pm 1000\) ppm SFO by correcting the SFO-induced phase rotation in the frequency domain [26; 27]. It is noteworthy that the methods will inevitably reduce SE. In [28; 29; 30], the SFO estimation and compensation scheme based on TSs is proposed. The TSs can also be used for synchronization and channel estimation, which improve the SE. Nevertheless, the rigorous OFDM structure limits the compensation range of SFO to less than \(\pm 200\) ppm. In this brief, to balance the compensation range and spectral efficiency, a simple pilot-aided SFO estimation and compensation scheme is proposed. The SFO compensation performance is experimentally investigated in an LD-based UWOC link with a 3-dB bandwidth of approximately 5.36 MHz. The main contributions of this literature can be summarized as follows:  
1. High accuracy and wide SFO compensation range. Up to \(\pm 1000\) ppm SFO can be well-estimated with an accuracy of less than \(\pm 3\) ppm after 1 m underwater transmission. Moreover, an estimation deviation within \(\pm 2\) ppm can be achieved for the SFO below \(\pm 400\) ppm;
2. Low computational complexity.