Generally, an optical link between a UUV and a UAV comprises two parts: an underwater section and an aerial section, which is illustrated in Fig. 1. Taking into account the fact that laser beams dissipate within 100m in the sea water, we only consider 50m depth of sea water in the vertical direction. Moreover, recent field-measured data in the Yellow Sea and the Bohai Sea reveal that in autumn and winter the vertical variations of oceanic parameters are almost negligible in the upper layer waters, which is why we will model the oceanic turbulence as homogeneous in our case, independent of depth. Therefore, as indicated in Fig. 1, the oceanic turbulence is modeled by equally separated, statistically equivalent phase screens.
The power spectrum density(PSD) model of oceanic refractive index fluctuations adopted here is the one developed by Nikishov, which can be expressed as:
in which the following denotations have been defined:
among which κ is the spatial wave number, η is the Kolmogorov microscale, and ε is the rate of dissipation of turbulent kinetic energy per unit mass of fluid ranging from 10-1 to 10-10 m2/s3. For constant gradients of mean temperature and salinity, ω defines the ratio of temperature to salinity contributions to the spectrum, varying from -5(corresponding to temperature dominated turbulence) to 0(corresponding to salinity dominated turbulence). C0=0.72(the Obukhov-Corrsin constant), C1 is a free parameter to be determined by comparison with the experiment and its value is taken as 2.35. KT is eddy thermal diffusivity and KS is the diffusivity of salt. AT=1.683×10-2, AS=1.9×10-4, ATS=9.41×10-3, α=2.6×10-4 L/deg, and β=1.75×10-4 L/g. χT and χS represent the rate of dissipation of mean squared temperature and that of salinity, respectively. χTS denotes the correlation of χT and χS.
The phase screen generation process is to randomize the spatial PSD and then FFT it.
On the other hand, the altitude-dependent atmosphere density directly leads to a vertically varying atmospheric turbulence profile, for which the best acknowledged model is the H-V5-7, also shown in Fig. 1, where the horizontal scale marks the turbulence strength. To better reflect the unevenness of the H-V5-7 turbulence model and fully utilize the limited computational power, nonuniformly arranged phase screens are used to represent the effects of turbulent wavefront distortions. The partition is based on the path integral of the structure constant and the atmospheric turbulence PSD used here is the modified von Karman spectrum.
where Cn2(h) is the atmospheric refractive index structure constant at altitude h, κl= 5.92/l0, κm=5.92/L0, and where l0 and L0 are the inner scale and the outer scale.
The WOS numerical method provides a viable approach to studying complex optical propagation problems. In the scenario considered here, it is nearly impossible to derive analytically expressed results, comprising both underwater and slant-path atmospheric channels, so it is reasonable to use WOS instead. The basic principle of WOS is the split-step propagation between separate phase screens, which can be written as:
where r is the transverse position vector, Ui(ri) is the optical field at the ith screen, ψi(ri) is the wavefront distortion induced by the turbulence within the ith interval, L is the path length, and m is the number of phase screens. For the specific implementation of WOS, the readers can refer to related literature , which we will not reiterate here.
Link performance evaluation for air-sea free-space optical communications
摘要: 长期以来，空中平台与水下平台之间的有效通信一直是一个具有挑战性的课题，因为声波或电磁波只能有效地仅在海水或空气中传播，而无法同时在这两种介质中高效传输数据。相比电磁波，激光束能够穿透相当深度的海水，因而自由空间光通信被认为是一种很好的空潜通信替代手段。众所周知，吸收和散射引起的衰减是水下激光传播主要不利因素之一，然而这只能通过加大发射功率来补偿。尽管如此，即使发射功率大到能够保证一定的接收机灵敏度，大气和海洋湍流引起的光强起伏也会在很大程度上降低链路性能。本文重点研究水下载具与空中平台之间的自由空间光通信链路中的湍流效应，利用波动光学仿真，研究高斯光束和环形光束在空-潜两段链路中的传播，并根据数值结果对上行链路和下行链路之间的性能差异进行了比较说明。总体来说，由于湍流的主要部分离发射机更近，上行链路更容易受到湍流的影响。此外，研究中还发现环形光束往往能产生较小的闪烁指数和较高的信噪比。本项工作能够为未来的空潜光通信系统的研究和发展提供有益的参考。Abstract: Effective communication between underwater platforms and aerial platforms has been a challenging issue in a long-time, due to the fact that either acoustic waves or electromagnetic waves can efficiently transmit only in the sea water or air, rather than both. As laser beams are able to penetrate a decent depth of sea water, free-space optical communications(FSOC) is considered to be a good substitutive approach. As is well known, the attenuation caused by absorption and scattering has proved to be the most significant adverse factor for underwater laser propagation, which, however, can only be compensated by a larger power margin. Nonetheless, even if the launching power is large enough to allow for affordable receiver sensitivity, the intensity fluctuation induced by atmospheric and oceanic turbulence can degrade the link performance to a great extent. This study addresses the turbulence effects on FSOC links between an underwater vehicle and an aerial platform. By use of wave optics simulation(WOS), the propagation of both the Gaussian beams and the annular beams in an air-sea two-section link is examined. The difference in performance between the uplink and the downlink is compared and explained according to numerical results. Generally, uplink suffers more from turbulence because the majority of turbulence lies nearer to its transmitter. Moreover, it is found that an annular beam always delivers a smaller scintillation index and a greater signal-to-noise ratio. This study is supposed to benefit the research and development of future air-sea optical communication systems.
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