Exact 3-D Channel Impulse Response Under Uniform Drift for Absorbing Spherical Receivers

TL;DR

This paper derives an exact analytical 3-D channel impulse response for a spherical receiver under uniform drift, providing a precise model that improves evaluation of wireless channel characteristics.

Contribution

It introduces the first exact series representation of the CIR for a fully absorbing spherical receiver with drift, using a novel Girsanov measure change approach.

Findings

Provides an explicit, noise-free evaluation method for channel metrics.

Enables rigorous analysis of 3-D molecular communication channels.

Offers a benchmark model for future research.

Abstract

An exact channel impulse response (CIR) for the three-dimensional point-to-sphere absorbing channel under drift has remained unavailable due to symmetry breaking. This letter closes this gap by deriving an exact analytical CIR for a fully absorbing spherical receiver under uniform drift with arbitrary direction. By formulating the problem in terms of joint first-hitting time-location statistics and applying a Girsanov-based measure change, drift effects are isolated into an explicit multiplicative factor, yielding an exact series representation. The resulting CIR provides a rigorous reference model and enables efficient, noise-free evaluation of key channel metrics without relying on Monte Carlo simulations.