This paper introduces a novel unified framework for calculating the first arrival position (FAP) density in diffusion-based molecular communication (MC) systems with fully-absorbing receivers, applicable to any spatial dimension or receiver shape. We validate the effectiveness of our proposed method by presenting two concrete examples from the MC literature: the 2D line receiver and 3D spherical receiver. Our approach successfully reproduces existing results on FAP density and further enhances the original formula for the 2D line receiver by accommodating arbitrary drift directions. The proposed framework offers a comprehensive and versatile solution for determining FAP density in diffusive MC channels with fully-absorbing receivers, paving the way for more robust and efficient system designs.

翻译：本文提出了一种新颖的统一框架，用于计算具有全吸收接收器的扩散型分子通信系统中的首到达位置 (FAP) 密度，适用于任何空间维度或接收器形状。我们通过提供两个来自分子通信文献的具体例子来验证我们提出的方法的有效性: 2D 线接收器和 3D 球形接收器。我们的方法成功重现了 FAP 密度的现有结果，并进一步改进了对于 2D 线接收器的原始公式，以适应任意漂移方向。所提出的框架为在具有全吸收接收器的扩散型 MC 通道中确定 FAP 密度提供了全面而多样化的解决方案，为更加健壮和高效的系统设计铺平了道路。