A Closed-Form Molecule-Release Rule for Diffusion-Based Molecular Communications with Ligand Receptors

Abstract

The number of molecules released per bit is a fundamental design variable of diffusion-based molecular communication (MC), and ligand-receptor reception breaks the more-is-better intuition. Too few molecules leave the bound-receptor observations buried in binding noise, while too many amplify the accumulated intersymbol interference and saturate the finite receptor population, again making the observations indistinguishable. Reliability therefore peaks in an interior operating region whose location seems to require an exhaustive search over the channel dynamics. In this paper, we show that this search can be obviated for a biologically plausible receiver that compares consecutive bound-receptor counts without channel state information or a decision threshold. We derive a closed-form transmission rule, which sets the number of molecules released per bit such that the receptor dissociation constant equals the geometric mean of the two bit-conditioned received concentration levels, prove that it exactly minimizes the bit error probability of a memoryless binomial receptor model, and express it in the physical channel parameters through an Euler--Maclaurin evaluation of the interference. Time-domain Monte Carlo sweeps of the channel and receptor parameters, corroborated by particle-based simulations, show that the empirically optimal release count coincides with the prediction or lies above it by a small factor.