Analytical estimation for the impulse response of an n-dimensional diffusion channel with an absorbing receiver

Abstract

In this letter, we derive an analytic estimate of the impulse response for the n-dimensional unbounded diffusion channel with a spherical absorbing receiver. We use generalized method of images to exploit the hidden phase space symmetries while finding an estimate impulse response for the 2D unbounded channel, for which no exact result exists in the literature. Then, the analytic estimate is compared with effective geometry Monte-Carlo simulations and an error analysis is performed. In particular, a chi-squared analysis is carried out to illustrate the goodness of fit of the estimate. Finally, we propose a second method to derive a nearly exact impulse response with a trade-off of more computation, where the unbounded space is modelled by a bounded space with a far-away ad hoc boundary and the diffusion equation is solved in this finite region.