# Channel Impulse Response-based Source Localization in a Diffusion-based Molecular Communication System

## TL;DR

This paper introduces two novel methods for localizing a molecular source in diffusion-based molecular communication systems using passive sensors, achieving near-optimal accuracy and fast convergence through triangulation and iterative gradient descent techniques.

## Contribution

It proposes two new localization methods based on channel impulse response measurements, with one being a least-squares triangulation and the other an iterative gradient descent approach.

## Key findings

- Triangulation method performs close to the Cramer-Rao bound.
- Gradient descent method converges in less than 100 iterations.
- Both methods effectively localize the source within the convex hull of sensors.

## Abstract

This work localizes a molecular source in a diffusion based molecular communication (DbMC) system via a set of passive sensors and a fusion center. Molecular source localization finds its applications in future healthcare systems, including proactive diagnostics. In this paper, we propose two distinct methods which both utilize (the peak of) the channel impulse response measurements to uniquely localize the source, under assumption that the molecular source of interest lies within the open convex-hull of the sensor/anchor nodes. The first method is a one-shot, triangulation-based approach which estimates the unknown location of the molecular source using least-squares method. The corresponding Cramer-Rao bound (CRB) is also derived. The second method is an iterative approach, which utilizes gradient descent law to minimize a non-convex cost function. Simulation results reveal that the triangulation-based method performs very close to the CRB, for any given signal- to-noise ratio. Additionally, the gradient descent-based method converges to the true optima/source location uniformly (in less than hundred iterations).