[论文解读] Multi Linear Regression applied to Communications systems Analysis

Federico Rodas Bajaña, Luis Hernan Montoya Lara+2 more|arXiv (Cornell University)|Feb 24, 2020

Antenna Design and Optimization被引用 1

一句话总结

本文提出了一种多元线性回归模型，以改进厄瓜多尔丛林地区VHF信号传播的预测，通过实地测量数据校正Longley-Rice模型的不准确性。通过调整距离、频率、发射功率和地形高度等因素，该模型将预测误差降低至5%以下，并通过稳健回归和异常值过滤显著提升了拟合度，在密集且极端的环境中，其精度显著优于商业仿真软件。

ABSTRACT

This paper develops a propagation model of electromagnetic signals emitted at frequencies of 20 and 40 MHz for the Ecuadorian jungle. It is expected that the results obtained at the end of this research will be applied to produce a complete coverage map for wireless communications technologies, which will optimize the radio spectrum in operations carried out by the Armed Forces in the Ecuadorian border jungle. The final expression found is an adjustment function that relates the Receiving Power (PRX) to factors that determine the geometry of the Fresnell Zone (Connectivity). The resulting model of the research improves the discrepancy between the simulated power (PRX) in commercial software and a sample of measured wireless transmissions in situ. The analysis was based on the results and methodology presented by Longley-Rice. It was determined the non-normality of the discrepancy between the losses (LLR) calculated by Longley-Rice Model (LMR) and the data obtained in the field, It was added correction coefficients on the expression of LMR. Subsequently, the mathematical expression was linearized to implement multivariate linear adjustment techniques. Alternative formulations to the Linear Regression model were sought and their goodness of fit was compared; all these techniques are introduced theoretically. To conclude, an analysis of the error of the found model is made. Mathematical modeling software such as MATLAB and SPSS were used for the formulation and numerical analysis, whose algorithms are also introduced. Finally, we propose future lines of research that allow a global understanding of the behavior of telecommunications technologies under hostile environments.

研究动机与目标

• 开发适用于厄瓜多尔丛林地区（20–40 MHz）VHF信号的传播模型，因为现有模型在极端环境条件下失效。
• 将接收功率（PRX）的预测误差与实地测量结果相比降低至5%以下。
• 通过多元回归识别并校正Longley-Rice模型中的系统性偏差，实现模型修正。
• 通过残差正态性检验和异常值过滤，验证模型的稳健性。
• 实现对偏远、敌对环境中军事行动的无线电频谱规划的高精度支持。

提出的方法

• 对256组实地测量数据（包括PRX、距离d、频率f、发射功率PTX和高度h）应用多元线性回归。
• 对变量进行对数变换以线性化关系并改善模型拟合度。
• 使用SPSS和MATLAB进行统计分析，包括最小二乘回归和稳健回归技术。
• 通过剔除低于-120 dB的数值来过滤数据，以消除噪声和异常值，提升同方差性。
• 应用Kolmogorov-Smirnov检验评估残差的正态性，并对比Longley-Rice模型与新模型的CDF。
• 通过剔除异常数据并优化变异系数，进一步优化模型，以满足<5%误差目标。

实验结果

研究问题

• RQ1 多元线性回归模型能否在厄瓜多尔丛林地区将VHF信号传播的预测误差降低至5%以下？
• RQ2 Longley-Rice模型的残差误差分布与所提出的校正后模型相比如何？
• RQ3 在热带雨林条件下，植被和地形高度等环境因素对信号衰减的影响程度如何？
• RQ4 过滤低功率（噪声）数据是否能改善回归模型的拟合优度和误差指标？
• RQ5 在极端传播条件下，校正后的模型能否优于商业软件仿真，实现更准确的接收功率预测？

主要发现

• 最终模型 log(PR X) = A log(d) - B log(f) + log(PLR) 解释了接收功率超过95%的方差，显著优于原始Longley-Rice模型的R平方值。
• 最终模型的变异系数降低至5%以下，达到了主要误差目标。
• Longley-Rice模型的残差显示非正态分布，表明存在系统性误差；而新模型的残差与正态CDF拟合更优，尽管仍不完全正态。
• 通过剔除PRX < -120 dB的异常值，显著降低了平方和误差（SSE），提升了模型精度和同方差性。
• 稳健回归技术优于标准线性回归，尤其在处理非正态残差和提升模型稳健性方面表现更优。
• 通过独立测试集验证了模型性能，确认其预测误差始终低于Longley-Rice模型。