  In this paper, we delve into the capacity problem of additive
vertically-drifted first arrival position noise channel, which models a
communication system where the position of molecules is harnessed to convey
information. Drawing inspiration from the principles governing vector Gaussian
interference channels, we examine this capacity problem within the context of a
covariance constraint on input distributions. We offer analytical upper and
lower bounds on this capacity for a three-dimensional spatial setting. This is
achieved through a meticulous analysis of the characteristic function coupled
with an investigation into the stability properties. The results of this study
contribute to the ongoing effort to understand the fundamental limits of
molecular communication systems.
