Localizing the Unknown Receiver in a Diffusive SIMO Molecular Communication System

This letter introduces a method to estimate the position of an unknown fully absorbing (FA) spherical receiver in a diffusive molecular communication (MC) system. This latter consists of a point transmitter and multiple FA spherical receivers in a three-dimensional space. The method relies on a temporal asymptotic single-input multiple-output (SIMO) channel model for diffusive MC systems that takes into account the interaction among receivers. By relying on the asymptotic model, a grid-based likelihood function is a priori created from each known receiver's perspective. The likelihood function's computation requires information about the number of molecules released by the transmitter, its position, and the position of known receivers. From the cumulative number of molecules absorbed by the known FA receivers, different likelihood maps are obtained, where each map corresponds to the likelihood of the position of unknown receiver from a specific known receiver's perspective. By combining the receivers' likelihood maps, which is equivalent to cooperation by sharing their knowledge, the position of the unknown receiver is estimated. The quality of the estimation is evaluated in terms of root mean squared error (RMSE) between the estimated position of the unknown receiver and its true position for different number of released molecules.