In this paper, we delve into the capacity problem of additive vertically-drifted first arrival position noise channel, which models a communication system where the position of molecules is harnessed to convey information. Drawing inspiration from the principles governing vector Gaussian interference channels, we examine this capacity problem within the context of a covariance constraint on input distributions. We offer analytical upper and lower bounds on this capacity for a three-dimensional spatial setting. This is achieved through a meticulous analysis of the characteristic function coupled with an investigation into the stability properties. The results of this study contribute to the ongoing effort to understand the fundamental limits of molecular communication systems.

翻译：本文深入研究了加性垂直漂移首次到达位置噪声信道的容量问题，该信道模型利用了分子位置来传递信息的通信系统。受矢量高斯干扰信道原理的启发，我们在输入分布的协方差约束背景下考察了这一容量问题，并针对三维空间环境给出了该容量的解析上界和下界。通过精细分析特征函数并研究其稳定性性质，本文的研究成果为理解分子通信系统的基本极限做出了贡献。