Unified Analysis of Spatio-temporal Anomalous Diffusion for Nano-Bio Molecular Communication

In this paper, we analyze molecular communication (MC) channels governed by spatio-temporal anomalous diffusion (STAD), a phenomenon commonly observed in complex biological environments such as intracellular transport and microfluidic systems. We consider that information molecules (IMs) undergo anomalous diffusion while the mobile nanomachines, transmitter (TX) and passive observer follow Brownian mobility. A unified mathematical framework is developed to characterize this time varying stochastic channel via the channel impulse response (CIR) across diverse observer geometries: point and bar shaped in one-dimensional (1-D) settings, and cuboidal, spherical, and cylindrical in three-dimensional (3-D) environments. Classical diffusion is included as a special case of the STAD model. Performance is evaluated using average error probability (AEP), receiver operating characteristics (ROC), and area under the curve (AUC) metrics to study the impact of mobility and space-time anomalies. Analytical results are validated through Monte Carlo simulations, offering insights relevant to nano-bio communication and drug delivery systems.