Field-Assisted Molecular Communication: Girsanov-Based Channel Modeling and Dynamic Waveform Optimization

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 an effective stochastic modeling approach to address this challenge. By leveraging trajectory-reweighting techniques, we derive analytically tractable channel impulse response (CIR) expressions for both fully-absorbing and passive spherical receivers, where the latter serves as an exact theoretical baseline to validate our modeling accuracy. Building upon these models, we establish a dynamic waveform design framework for system optimization. Under a maximum \textit{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.