一阶Marcum $Q$函数的半线性逼近及其在预测天线系统中的应用
A Semi-Linear Approximation of the First-Order Marcum $Q$-function with Application to Predictor Antenna Systems
摘要：
一阶Marcum $Q$ -函数在各种问题公式中观察到。但是，它不是一个容易处理的功能。为此，本文首先给出了Marcum $Q$ -函数的半线性逼近。我们提出的近似是有用的，因为它简化了，例如，包括Marcum $Q$ -函数的各种积分计算以及诸如参数优化的不同操作。然后，作为一个感兴趣的例子，我们将我们提出的近似方法的预测天线（PA）系统的性能分析。这里，PA系统被称为在车辆车顶上具有两组天线的系统。然后，位于车辆前方的PA可以用于改善用于在PA后方对准的接收天线的数据传输的信道状态估计。考虑到由于移动性的空间失配，我们推导出封闭形式的瞬时和平均吞吐量以及吞吐量优化的速率分配的表达式。正如我们所示，我们提出的近似方案使我们能够分析PA系统的高精度。此外，我们的研究结果表明，速率自适应可以提高PA系统的性能与不同程度的空间失配。
英文摘要：
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 paper, 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.
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