First-order Marcum $Q$ -function is observed in various problem formulations. However, it is not an easy-to-handle function. For this reason, in this article, we first present a semi-linear approximation of the Marcum $Q$ -function. Our proposed approximation is useful because it simplifies, e.g., various integral calculations including Marcum $Q$ -function as well as different operations such as parameter optimization. Then, as an example of interest, we apply our proposed approximation approach to the performance analysis of predictor antenna (PA) systems. Here, the PA system is referred to as a system with two sets of antennas on the roof of a vehicle. Then, the PA positioned in the front of the vehicle can be used to improve the channel state estimation for data transmission of the receive antenna that is aligned behind the PA. Considering spatial mismatch due to the mobility, we derive closed-form expressions for the instantaneous and average throughput as well as the throughput-optimized rate allocation. As we show, our proposed approximation scheme enables us to analyze PA systems with high accuracy. Moreover, our results show that rate adaptation can improve the performance of PA systems with different levels of spatial mismatch.

中文翻译：

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一阶Marcum的半线性近似 问功能及其在预测天线系统中的应用

一阶Marcum $ Q $ 在各种问题的表述中观察到功能。但是，它不是易于处理的功能。因此，在本文中，我们首先提出Marcum的半线性近似 $ Q $ -功能。我们建议的近似值很有用，因为它可以简化例如Marcum等各种积分计算 $ Q $ 功能以及不同的操作，例如参数优化。然后，作为一个有趣的例子，我们将我们提出的近似方法应用于预测器天线（PA）系统的性能分析。在此，PA系统被称为在车辆的车顶上具有两组天线的系统。然后，位于车辆前部的功率放大器可以用来改善信道状态估计，以用于对准功率放大器后面的接收天线的数据传输。考虑到由于移动性造成的空间不匹配，我们导出了瞬时和平均吞吐量以及吞吐量优化的速率分配的闭式表达式。如我们所示，我们提出的近似方案使我们能够高精度分析PA系统。而且，