Matched Filter-Based Molecule Source Localization in Advection-Diffusion-Driven Pipe Networks with Known Topology

Abstract

Synthetic molecular communication (MC) has emerged as a powerful framework for modeling, analyzing, and designing communication systems where information is encoded into properties of molecules. Among the envisioned applications of MC is the localization of molecule sources in pipe networks (PNs) like the human cardiovascular system (CVS), sewage networks (SNs), and industrial plants. While existing algorithms mostly focus on simplified scenarios, in this paper, we propose the first framework for source localization in complex PNs with known topology, by leveraging the mixture of inverse Gaussians for hemodynamic transport (MIGHT) model as a closed-form representation for advection-diffusion-driven MC in PNs. We propose a matched filter (MF)-based approach to identify molecule sources under realistic conditions such as unknown release times, random numbers of released molecules, sensor noise, and limited sensor sampling rate. We apply the algorithm to localize a source of viral markers in a real-world SN and show that the proposed scheme outperforms randomly guessing sources even at low signal-to-noise ratios (SNRs) at the sensor and achieves error-free localization under favorable conditions, i.e., high SNRs and sampling rates. Furthermore, by identifying clusters of frequently confused sources, reliable cluster-level localization is possible at substantially lower SNRs and sampling rates.

Figures (6)

• Figure 1: System model. a) Advection-diffusion-driven PN across different scales. b) (Multi-)graph representation of a PN. c) MF bank-based molecule source localization algorithm, exploiting the MIGHT model for MF design.
• Figure 2: MF $v_{\mathrm{Tx}_i}[k]$ used for source localization in the PN shown in Fig. \ref{['fig:sewage_network']}a) with $U=33$Tx at a sensor sampling frequency of $f_\mathrm{s}=2\,\mathrm{Hz}$.
• Figure 3: a) Topology of a SN in Zolkiewka Commune, Poland Nawrot2018. Pipe lengths $l_i$ are drawn to scale (see scale bar) and $r_i=5.5cm,\forall p_i$. Inlet, connecting, and outlet node positions are illustrated in orange, blue, and red, respectively. At each inlet node $n_{\mathrm{in},g}\in\mathcal{N}_\mathrm{in}$, a $\mathrm{Tx}_g$ is present with $Q_{\mathrm{in},g}=5e-3m\cubed\per s$. Flow directions are given by arrows, flow rates are color-coded in the edge colors. The Rx is located at the outlet node. b) Tx-Rx distances (orange) and Tx-Rx path mean arrival times (purple) for all Tx. c) Log-normal PDF for the number of released viral particles $M_g$ at the active $\mathrm{Tx}_g$. d) Four exemplary received signals from different active Tx with and without additive Rx noise.
• Figure 4: Likely confused Tx, illustrated using the empirically determined CM (left) and its binarized version (middle). Confusions predicted by the binarized CSM are shown on the right.
• Figure 5: Spatial distribution of Tx clusters. Below the SN, the normalized and time-shifted CIR of all clusters are shown.