# An Optical Differential Method for Underwater Wireless Communication in Turbid Environments
## 1 Introduction  
As Earth's terrestrial resources become increasingly depleted, people shift increasing attention toward the oceans. Serving as an intermediator for information exchange in water, underwater wireless communications are one of the indispensable components of ocean equipment. In recent years, optical communication has emerged as a popular research topic for underwater wireless communication due to its high data rate, negligible delay in the signal channel, and compact equipment volume [1]. For instance, [PERSON] et al. achieved underwater optical communications at a distance of 5 m and a speed of 16.6 Gbps in tap water [2]. The light source they used was a 450 nm laser diode with a power of 120 mW, resulting in an average power consumption of 24 mW/m. [PERSON] et al. used a cascaded micro-light-emitting diode (mLED) array combined with orthogonal frequency division multiplexing modulation to achieve transmission rates of 4.92 Gbps, 3.22 Gbps, and 3.4 Gbps at distances of 1.5 m, 3 m, and 4.5 m in clean water, respectively [3]. The totalpower consumption of mLEDs is about 20 mW. [PERSON] et al. experimented with a white LED with a power of 48 W in water with a turbidity of 6.8 NTU, which is representative of the water quality of the Red Sea. The experimental results show that the system can communicate within a range of 60 cm [4]. The experiments were performed in coastal water, achieving successful communication over a distance of 1.5 m. The results demonstrated that the multiple-input, multiple-output configuration significantly reduced the bit error rate (BER) compared to the single-input, multiple-output configuration. [PERSON] et al. utilized polarization division multiplexing and conducted experiments in water with an attenuation coefficient of 0.8 m\({}^{-1}\), demonstrating that this method exhibits greater stability in turbid water compared to traditional OOK [5]. [PERSON] et al. proposed a full-duplex underwater wireless optical communication system based on a 450 nm laser, achieving a communication speed of 250 Mbps in the turbid harbor water. The average power consumption was around 41.7 mW/m [6]. [PERSON] et al. proposed the application of Ince-Gaussian beams in underwater optical communication. The team conducted communication experiments in water with different attenuation coefficients over a distance of 3 m. The final results demonstrated that Ince-Gaussian beams exhibit more stable propagation and reduced attenuation in turbid environments [7]. [PERSON] et al. achieved a data rate of 1 Gbps at a distance of 12 m in turbid harbor water using a 532 nm laser with a power of 1 W [8]. [PERSON] et al. employed coherent detection at the receiver to achieve communication over a distance of 0.6 m in water with an attenuation coefficient of 0.4 m\({}^{-1}\). This study demonstrated that coherent detection exhibits better sensitivity compared to traditional intensity detection in turbid environments [9]. [PERSON] et al. used the technique of optical code division multiple access to achieve a maximum speed of 30 Gbps using a 31.6 mW green laser in pure seawater, clear seawater, coastal seawater, and turbid port seawater [10]. [PERSON] et al. successfully achieved 9 m communication in water with an attenuation coefficient of 0.18 m\({}^{-1}\) using orbital angular momentum multiplexing and photon counting, with a power of only 0.5 mW at the transmitter. The use of a photon-counting detector significantly enhanced the detection capability for weak signals, providing a solution for low-power visible light communication in turbid water environments [11]. [PERSON] et al. experimented with a white LED with a power of 48 W in water with a turbidity of 6.8 NTU, which is representative of the water quality of the Red Sea [12]. The experimental results showed that the system could communicate within a range of 60 cm. In terms of channel simulation, progress has been made in recent years in the study of BER caused by turbulence. [PERSON] et al.