Rectangular Concentration-Based Nanomachine Localization in Molecular Communication Networks With Unknown Emission Time

Localization of nanomachines is essential for optimal functionality, including optimizing transmission rates and detecting irregular cells. The sampling concentration received by the nanomachines can be used for this purpose. The localization based on received sampling concentration requires the emission time of molecules to improve the accuracy and establish synchronization among the nanomachine. In this paper, we derive the maximum likelihood estimation for localizing nanomachine in two scenarios, that is, known and unknown emission times. In contrast to the existing model, the proposed model considers a generic input (rectangular) concentration that can accommodate both non-zero emission duration and instantaneous emission, making it more practical for many applications. The model also considers multiple symbols and challenges like inter-symbol interference. Even with the rectangular input concentration, the proposed model achieves comparable individual localization performance to the impulse concentration. Additionally, the proposed model allows for joint estimation of location and emission time using correlated observations, making it a practical and generic solution for applications.