Compressive Sensing-Based Recovery of Molecular Mixtures with Cross-Reactive Receptor Arrays

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.