With the large-scale deployment of underwater vehicles and ocean sensing networks, underwater high-speed wireless optical communication systems have become an important data acquisition means. The analysis of beam scintillation and transmission characteristics caused by oceanic turbulence and the exploration of effective oceanic turbulence suppression techniques have become a key technology for building underwater wireless laser communication systems with high stability, high speed rate, and long-range transmission. However, the inconsistency of salt transfer and thermal diffusion mechanisms in the real oceanic environment leads to unstable water stratification, and meanwhile, the refractive index power spectrum based on the infinite outer scale results in possible singularity problems at the poles. As a result, the scintillation effects of Gaussian beams in the oceanic turbulence channel and the theoretical model of spatial coherence radius deviate significantly from the real oceanic environment. Therefore, a Gaussian beam-based Reed-Solomon (RS) coded joint single-input multiple-output (SIMO) communication system using the equalized equal gain combining (EEGC) algorithm is developed to further mitigate the light intensity flicker caused by oceanic turbulence and improve the transmission performance of the system under a weak oceanic channel with a finite outer scale and oceanic water stratification instability.

We derive closed analytical formulas for the scintillation index and spatial coherence radius for a Gaussian beam based on Yue spectrum, and quantify the turbulence intensity and the detector spacing threshold in a Gaussian beam-based oceanic diversity receiver system under a weak oceanic turbulence channel with a finite outer scale and oceanic water stratification instability. A Gaussian beam-based composite communication system is proposed. This system combines the RS codes technique with the SIMO technique through the EEGC algorithm in light of the aforementioned study. In addition, a closed analytic formula for the upper bound average bit error rate (ABER) of our proposed system using the hyperbolic tangent distribution method is derived.

To verify the designed scheme, we employ the derived closed analytical formulas of scintillation index and spatial coherence radius to determine the turbulence intensity and the detector spacing thresholds for four different channels in our proposed composite communication system (Table 1). Based on this, the performance of the Gaussian beam-based RS coded joint SIMO communication system is investigated in detail by numerical simulations under different detector distribution methods and the instability of oceanic water stratification (Fig. 4). When avalanche photodiodes (APDs) in the receiving plane are placed in symmetrical distribution and asymmetric distribution, the emitting optical power at an upper bound ABER of 10-8 is summarized in Table 4 and Table 5, respectively. Results show that the performance of our proposed RS coded joint SIMO communication system can be significantly underestimated or overestimated by treating oceanic water stratification as a stable state in optical oceanic turbulence caused by salinity fluctuations or temperature fluctuations (Fig. 4). By further comparing the EEGC SIMO communication system (Fig. 3) with the RS coded joint EEGC SIMO communication system (Fig. 4), the proposed RS coded joint EEGC SIMO communication system can significantly improve the transmission performance of the system under different turbulent channels. Additionally, the improvement in system performance is noticed to be more significant as the oceanic turbulence intensity increases in the weak oceanic composite channel. Therefore, comparing emitting optical power at an upper bound ABER of 10-8 in an RS-SIMO system with symmetrically and asymmetrically distributed APDs, it can be seen that the performance of the RS coded joint SIMO system with symmetric distributed APDs is about 1.5 dB better than that of the asymmetrically distributed APDs RS coded joint SIMO system when the EGC algorithm is adopted. When the APD position at the receiver is symmetrically distributed, the performance of the EEGC algorithm improves by about 1 dB over the EGC algorithm (Table 4). When the APD at the receiver is asymmetrically distributed, the performance of the RS coded joint SIMO system with the EEGC algorithm improves by about 2.4 dB (Table 5). The RS coded joint SIMO communication system using the proposed EEGC algorithm can effectively compensate the system performance loss caused by the non-linearity of the Gaussian beams and reduce the influence of the detector distribution method on the system performance.

An EEGC algorithm for light intensity equalization is proposed for the Gaussian distribution characteristics of the light intensity in the receiving plane in the SIMO communication system, and an RS coded joint EEGC SIMO composite communication system based on Gaussian beams is established. The closed analytic formula for the upper bound ABER of the proposed system using the hyperbolic tangent distribution method is further derived. The simulation results show that the instability of the oceanic water stratification exerts a significant influence on the system performance. The designed communication system significantly mitigates the effect of oceanic turbulence on the system's performance, especially the suppression effect, which becomes more significant as the oceanic turbulence intensity increases. Additionally, the proposed system eliminates the influence of the detector distribution on the Gaussian beam-based SIMO system performance. We not only provide guidance for the characteristics of high-order complex beams in real marine channels but also a useful theoretical basis for the underwater applications of composite communication systems using multiple turbulence suppression techniques for complex beam transmission.