有界二维扩散通道脉冲响应的解析推导
Analytical Derivation of the Impulse Response for the Bounded 2-D Diffusion Channel
摘要：
本文着重于推导在有界环境中由一个代理人吸收的扩散粒子的分布。特别地，我们类似地考虑推导2-D和3-D环境中的分子通信信道的脉冲响应。在2-D中，通道涉及一个点发射器，该点发射器将分子释放到一个圆形吸收接收器，该圆形吸收接收器在由圆形反射边界包围的环境中吸收传入的分子。考虑到这一设置，圆形吸收接收器上的分子的联合分布相对于时间和角度的推导。使用此分布，检查信道特性。此外，我们还扩展此信道模型的3-D使用圆柱形接收机和调查的信道特性。我们还提出了如何获得一个解析解的无界2-D通道从我们的衍生解决方案，因为没有分析推导此通道是目前在文献中。
英文摘要：
This paper focuses on the derivation of the distribution of diffused particles absorbed by an agent in a bounded environment. In particular, we analogously consider to derive the impulse response of a molecular communication channel in 2-D and 3-D environment. In 2-D, the channel involves a point transmitter that releases molecules to a circular absorbing receiver that absorbs incoming molecules in an environment surrounded by a circular reflecting boundary. Considering this setup, the joint distribution of the molecules on the circular absorbing receiver with respect to time and angle is derived. Using this distribution, the channel characteristics are examined. Furthermore, we also extend this channel model to 3-D using a cylindrical receiver and investigate the channel properties. We also propose how to obtain an analytical solution for the unbounded 2-D channel from our derived solutions, as no analytical derivation for this channel is present in the literature.
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