Initial Distance Estimation for Diffusive Mobile Molecular Communication Systems

Mobile molecular communication (MC) attracts much attention in recent years where mobile nanomachines exchange information using molecules. In this paper, we consider a diffusion-based mobile MC system consisting a pair of diffusive nanomachines. Due to the Brownian motion of nanomachines, the distance between them is a stochastic process. In this paper, its probability density function (PDF) is derived by characterizing nanomachines' motion as Wiener process. Besides, the initial distance between nanomachines is a significant parameter of diffusive mobile MC systems. With the knowledge of initial distance, the expected channel impulse response (CIR) can be obtained and the detection threshold can be set in advance. A novel two-step scheme is proposed to estimate the initial distance by maximum likelihood (ML) estimation. Firstly, the releasing distance is estimated based on observations of the number of received molecules. Secondly, the estimation of the releasing distance is used as an observation to estimate the initial distance by ML estimation. The performance of proposed scheme is evaluated via particle-based simulation of the Brownian motion.