Joint Localization and Clock Synchronization in Cuboid Bounded Diffusive Channel With Absorbing and Reflecting Boundaries

This paper proposes a joint localization and synchronization method in the presence of a 3-D (cuboidal-bounded) channel. Many biologically relevant structures, such as epithelium cell membranes, tissues, and blood vessel networks (particularly capillaries), can be effectively modeled as 3-D systems. Localization and synchronization among nanomachines play an important role in the optimal transmission rate, information exchange, and collaboration among nanomachines. Clock synchronization without localization or localization without clock synchronization affects the accuracy of the system. However, the existing methods consider that nanomachines are already synchronized for localization and vice-versa. Hence, the proposed method considers a combined model for location parameters, clock offset, and clock skew. Unlike the existing method, we consider this combined model in bounded environments, which are relevant for long-range molecular communication where released molecules need to be confined within a certain range to optimize power efficiency. However, deriving an analytical channel characterization for a constrained domain is challenging. We provide an analytical equation for the probability distribution function of the propagation delay of the molecules, taking into account the presence of both single and multiple absorbing walls.