  In this paper, we propose a novel concept for engineered molecular
communication (MC) systems inspired by animal olfaction. We focus on a
multi-user scenario where transmitters employ unique mixtures of different
types of signaling molecules to convey their messages to a central receiver,
which is equipped with an array comprising $R$ different types of receptors to
detect the emitted molecule mixtures. The hardware complexity of an MC system
employing \textit{orthogonal} molecule-receptor pairs would linearly scale with
the number of signaling molecule types $Q$ (i.e., $R=Q$). Natural olfaction
systems avoid such high complexity by employing arrays of
\textit{cross-reactive} receptors, where each type of molecule activates
multiple types of receptors and each type of receptor is predominantly
activated by multiple types of molecules albeit with different activation
strengths. For instance, the human olfactory system is believed to discriminate
several thousands of chemicals using only a few hundred receptor types, i.e.,
$Q\gg R$. Motivated by this observation, we first develop an end-to-end MC
channel model that accounts for the key properties of olfaction. Subsequently,
we formulate the molecule mixture recovery as a convex compressive sensing (CS)
problem which can be efficiently solved via available numerical solvers. Our
simulation results confirm the efficiency of the proposed CS problem for the
recovery of the molecular mixture signal and quantify the system performance
for various system parameters.
