# Research on Underwater Wireless Optical Communication Channel Model and Its Application
## 2 Modeling of the Communication Channel of UWOC
### Analysis of \"Effective Communication Space\" in UWOC
However, varying amounts of energy are reflected from objects such as the water surface, seabed, and fish. These reflections cover longer ranges to reach the receiver, resulting in a delay phenomenon. Specifically, we aim to identify the most detrimental light path in terms of delay. The propagation velocity of light in a body of water is 2.25 \(\times\) 10\({}^{8}\) m/s. When transmitting an optical signal in water at a frequency of 10 MHz, which corresponds to a symbol duration of 100 ns, the multipath effect of the preceding signal extends up to a range of 22.5 m before two adjacent pulses completely overlap at the receiver. Beyond this transmission range, the optical signal is significantly attenuated and does not cause significant interference. Hence, we opt to disregard the multipath effect for communication speeds below 10 Mb/s [18]. Overall, the power of the optical signal received by the receiver at the specific position indicated in the figure can be determined using Equation (8) [19]. \[P_{R}=P_{T}\times\eta_{t}\times\eta_{r}\times e^{-K(\lambda)\times\frac{d}{cos \theta}}\times\frac{A\times cos\theta}{2\pi d^{2}\times\left[1-cos(\Phi/2) \right]} \tag{8}\]  
In the above equation, \(P_{R}\), \(P_{T}\), \(\eta_{t}\), \(\eta_{r}\), \(K(\lambda)\), \(d\) have the same meaning as in Equation (6) and denote the aperture area of the receiver. This equation takes into account not only the energy loss caused by the absorption scattering effect, but also the energy change caused by the source having a diffusion angle and the misalignment of the transceiver. However, the formula is simple in structure and can only describe the received power in the case of uniform beam energy distribution from the transmitter. In reality, the energy distribution of the UWOC beam is not uniform, resulting in the receiver receiving a smaller light signal than the calculated value of the equation for larger angles, and a larger light signal than the calculated value for smaller angles. In Equation (9), to join the consideration of the light distribution, \(f(\theta)\) is a function of the light source distribution. \[P_{R}=P_{T}\times\eta_{t}\times\eta_{r}\times e^{-K(\lambda)\times\frac{d}{cos \theta}}\times\frac{A\times cos\theta}{2\pi d^{2}\times\left[1-cos(\Phi/2) \right]}\times f(\theta) \tag{9}\]  
The model expressed by Equation (9) allows for the determination of the optical signal power received at specific locations. By utilizing the sensitivity value of the receiver, representing the minimum power, one can outline the contours of the minimum power across different positions. This graphical representation facilitates the calculation of the effective communication space. The model takes into account crucial parameters, including the transmission distance, representing the distance covered by the optical signal in water. It also considers the beam diffusion angle, reflecting the spread of the emitted light beam from the transmitter. Additionally, the relative position of the transmitter and receiver, which includes spatial relationships and angular deviations, is a crucial factor. Moreover, the model incorporates water quality characteristics, encompassing the impact of absorption and scattering on the transmission of optical signals. By comprehensively considering these parameters, the model provides a robust framework for understanding the spatial dynamics of optical wireless communication. It enables the determination of the effective communication space, essential for planning and optimizing underwater communication systems.