Impulse Response of the Molecular Diffusion Channel with a Spherical Absorbing Receiver and a Spherical Reflective Boundary

In this letter, we derive the impulse response of the diffusion channel with a spherical absorbing receiver, a spherical reflective boundary, and a point transmitter in the molecular communication domain. The proposed model fits geometrically well with the intra-cellular diffusion environment and can be further extended to other cases by applying small deformations to the sphere. By exploring the channel characteristics and drawing comparisons with the unbounded case, we show the consequences of having the boundary on channel properties, such as peak time, peak amplitude, and the fraction of molecules that hit the receiver. In particular, we find that the existence of the reflective boundary can either increase (for high diffusion coefficient) or decrease (for low diffusion coefficient) the signal strength with respect to the unbounded case.