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In this paper, we delve into the capacity problem of additivevertically-drifted first arrival position noise channel, which models acommunication system where the position of molecules is harnessed to conveyinformation. Drawing inspiration from the principles governing vector Gaussianinterference channels, we examine this capacity problem within the context of acovariance constraint on input distributions. We offer analytical upper andlower bounds on this capacity for a three-dimensional spatial setting. This isachieved through a meticulous analysis of the characteristic function coupledwith an investigation into the stability properties. The results of this studycontribute to the ongoing effort to understand the fundamental limits ofmolecular communication systems.

Capacity Bounds for Vertically-Drifted First Arrival Position Channels under a Covariance Constraint