Field-Assisted Molecular Communication: Girsanov-Based Channel Modeling and Dynamic Waveform Optimization
This work provides a new analytical framework for a specific molecular communication scenario, enabling dynamic waveform optimization for improved detection.
The paper tackles analytical modeling of field-assisted molecular communication under dynamic electric fields, which is challenging due to coupled stochastic transport and complex boundaries. Using the Cameron-Martin-Girsanov theorem, they derive tractable channel impulse responses and propose a low-complexity waveform optimization algorithm (MRP) that achieves near-optimal detection performance.
Analytical modeling of field-assisted molecular communication under dynamic electric fields is fundamentally challenging due to the coupling between stochastic transport and complex boundary geometries, which renders conventional partial differential equation (PDE) approaches intractable. In this work, we introduce a stochastic framework based on the Cameron-Martin-Girsanov theorem to address this challenge. By leveraging a change-of-measure technique, we derive analytically tractable channel impulse response (CIR) expressions for both fully-absorbing and passive spherical receivers, where the latter serves as an exact mathematical baseline to validate our framework. Building upon these models, we establish a dynamic waveform design framework for system optimization. Under a maximum a posteriori decision-feedback equalizer (MAP-DFE) framework, we show that the first-slot received probability serves as the primary determinant of the bit error probability (BEP), while inter-symbol interference manifests as higher-order corrections. Exploiting the monotonic response of the fully-absorbing architecture and using the limitations of the passive model to justify this strategic focus, we reformulate BEP minimization into a distance-based optimization problem. We propose a unified, low-complexity Maximize Received Probability (MRP) algorithm, encompassing the Maximize Hitting Probability (MHP) and Maximize Sensing Probability (MSP) methods, to dynamically enhance desired signals and suppress inter-symbol interference. Numerical results validate the accuracy of the proposed modeling approach and demonstrate near-optimal detection performance.