The scintillation index (SI) is an important issue in studying the effect of the atmospheric turbulence in light wave propagation. As the computation time is important in case of mobile applications, a closed form for the SI of slant path is more attractive than its integral form. In a previous work (Fayed et al. in Opt Eng 55:056113, 2016), we derived the slant path SI in a closed form for spherical waves proposing a polynomial model for the refractive index structure parameter. In this paper, closed form expressions for uplink and downlink slant path SI are derived from the integral forms using the polynomial model of refractive index structure parameters for a plane wave propagating through atmospheric turbulence. The obtained results reveal the effects of propagation distance, transmitter/receiver height and elevation angle on the uplink and downlink SI. A comparison between uplink and downlink SI is carried out. The derived expressions for the plane wave are compared with that previously derived for the spherical wave. The obtained results demonstrate a way to improve the uplink SI of the plane wave by increasing the transmitter height to 150 m.

中文翻译：

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斜径大气湍流中的平面波闪烁指数：上行链路和下行链路的闭式表达式

闪烁指数（SI）是研究大气湍流对光波传播影响的重要问题。由于计算时间在移动应用程序中很重要，因此倾斜路径 SI 的封闭形式比其积分形式更具吸引力。在之前的工作中（Fayed 等人在 Opt Eng 55:056113, 2016 中），我们推导出了球面波的封闭形式的倾斜路径 SI，提出了折射率结构参数的多项式模型。在本文中，使用通过大气湍流传播的平面波的折射率结构参数的多项式模型，从积分形式推导出上行链路和下行链路倾斜路径SI的闭合形式表达式。获得的结果揭示了传播距离的影响，上行链路和下行链路 SI 上的发射机/接收机高度和仰角。进行上下行SI的比较。将平面波的导出表达式与先前为球面波导出的表达式进行比较。获得的结果证明了一种通过将发射机高度增加到 150 m 来改善平面波上行链路 SI 的方法。