Due to the increasing ocean exploration by a large number of scientific activities and military operations, researchers are investigating high-speed, stable, and long-range underwater wireless communication technologies. Compared with traditional acoustic and radio frequency communications, underwater wireless optical communication (UWOC) systems are attracting a great deal of interest from researchers due to their advantages of big bandwidth, high information transmission rate, and sound confidentiality. However, UWOC systems are not only affected by water absorption but also suffer from the loss caused by misalignment between receiving and transmitting systems or the loss caused by pointing error, which cannot be neglected. Additionally, ocean turbulence also causes flickering of received light intensity, affecting the system performance. However, the inconsistency of salinity diffusion and heat diffusion mechanisms in real marine environments causes unstable seawater stratification, which results in the scintillation effect of the Gaussian beam in the ocean turbulence channel deviating significantly from the actual marine environment. Therefore, a pointing-jitter error model in UWOC is developed by the unstable Yue ocean power spectrum with ocean water stratification. The model takes into account water body attenuation, pointing-jitter error loss, and link attenuation caused by seawater turbulence, and finally investigates the effect of aperture averaging technique on system performance.

To more accurately model underwater wireless communication systems, we discuss the effect of pointing-jitter error on the performance of laser communication systems based on a turbulent seawater fading channel. Firstly, for the pointing error, we introduce the relative position parameter of the laser transmitter and the deflection angle parameter to determine the state of the transmitter. Meanwhile, the jitter error is employed to characterize the effect of seawater turbulence on the receiver body. For the effect of seawater turbulence, we adopt the Yue spectrum that considers the stratification instability of the ocean water body and give an analytical equation for the scintillation index of a Gaussian beam based on the Yue spectrum after aperture averaging. Additionally, we build a composite channel model including water body attenuation, pointing-jitter error loss, and seawater turbulence, and introduce a signal-to-noise ratio correction factor to simulate the positional attenuation of the Gaussian beam in the attenuation channel. At the same time, we give the bit error rate (BER) expressions of the system based on the on-off key (OOK) modulation with and without the jitter error to measure the system performance respectively.

To obtain the scintillation index of Gaussian beam transmission under the parameter of variable temperature salt vortex diffusion ratio in the water column, we numerically simulate the scintillation index of Gaussian beams in ocean turbulence with the transmission distance and different aperture sizes. The results show that the aperture averaging technique has the effect of suppressing the scintillation index caused by both stable and unstable seawater stratification, but the suppression effect is nonlinearly related to both aperture sizes (Fig. 6). The system decreases the turbulence suppression effect with the increasing aperture size. The effects of pointing error and jitter error in the composite channel on the UWOC system are further investigated. In the jitter error-free channel, a change of 0.04 m in the transmitter position sending can greatly affect the system performance, and the BER performance of the system decreases by 17.15 dB in strong turbulence, and 20.55 dB in weak turbulence (Figs. 7 and 8). In the composite channel that includes water body attenuation, pointing-jitter error loss, and seawater turbulence, we find that in the weak turbulence channel of the UWOC system, the effect of pointing error on the system performance is greater than that of jitter error on the system performance, while the effect of weak turbulence on the system performance is less (Fig. 11).

The results show that the aperture averaging technique has an inhibiting effect on the scintillation index caused by both stabilization and instability of seawater stratification, but the inhibiting effect is nonlinearly related to both aperture sizes. As the aperture size increases, the turbulence suppression effect gradually decreases. In the jitter error-free channel, a change of 0.04 m in the transmitter position sending can greatly affect the system performance, and the BER performance of the system decreases by 17.15 dB in strong turbulence and 20.55 dB in weak turbulence. In the composite channel containing water fading, pointing-jitter error loss, and seawater turbulence, we find that in the UWOC system of the weak turbulence channel, the pointing error has a greater effect on the system performance than the jitter error has on the system performance, while the weak turbulence has a smaller effect on the system performance. Additionally, the aperture averaging technique can significantly improve both turbulent channel attenuation and pointing-jitter error, while the suppression of seawater turbulence is the most obvious. Our study is of guiding significance for an in-depth understanding of the transmission characteristics of Gaussian beams in real ocean channels and provides an effective theoretical basis for the application of aperture averaging technique to suppress turbulence in complex ocean environments. Meanwhile, references are offered for related research on underwater laser localization.