對流擴散方程的積分核及其在分子通信上的應用

Abstract

Recent technology enables people to design tiny machines in nano-scale. These nanomachines bring us new applications in many fields, such as biomedical and military technology. Since the nano-scale devices have limited size and energy, molecular communication (MC) becomes a promising communication approach for nanonetworks. In this article, we propose a new molecular communication model that uses the particle position to carry information. To analyze the position modulation system, we consider the integral kernel of the steady-state convection diffusion equation: △u+⃗v•∇u=0. With the help of the Green's function of the Helmholtz equation, the integral kernel of the steady-state convection-diffusion equation can be written in explicit form. There is a close relation between the integral kernel of steady-state convection-diffusion equation and Brownian motion with drift. We discuss in this article why the integral kernel can be interpreted as the hitting position distribution of a Brownian motion particle. With the hitting distribution, we derive the optimal detection rule for the proposed MC system, and analyze the bit error rate performance for the zero drift case. For the non-zero drift case, we derive an approximated representation for the detection boundary.