  In this paper, we present an analytical model for the diffusive molecular
communication (MC) system with a reversible adsorption receiver in a fluid
environment. The widely used concentration shift keying (CSK) is considered for
modulation. The time-varying spatial distribution of the information molecules
under the reversible adsorption and desorption reaction at the surface of a
receiver is analytically characterized. Based on the spatial distribution, we
derive the net number of newly-adsorbed information molecules expected in any
time duration. We further derive the number of newly-adsorbed molecules
expected at the steady state to demonstrate the equilibrium concentration.
Given the number of newly-adsorbed information molecules, the bit error
probability of the proposed MC system is analytically approximated.
Importantly, we present a simulation framework for the proposed model that
accounts for the diffusion and reversible reaction. Simulation results show the
accuracy of our derived expressions, and demonstrate the positive effect of the
adsorption rate and the negative effect of the desorption rate on the error
probability of reversible adsorption receiver with last transmit bit-1.
Moreover, our analytical results simplify to the special cases of a full
adsorption receiver and a partial adsorption receiver, both of which do not
include desorption.
