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

Abstract

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.

Figures (7)

• Figure 1: System illustration of MCvD with a time-varying assisted electric field. A point Tx located at $\mathbf{x}_0$ releases charged particles, while a spherical Rx centered at the origin captures the signal either passively or via full absorption. The trajectories are influenced by a composite drift field $\boldsymbol{\Phi}(t)$, combining periodic background flow with an externally designed electric field aligned along the $x_1$-axis.
• Figure 2: Illustration of the optimized assisted electric-field waveforms $E_1(t)$ for the two receiver architectures. (a)Fully-absorbing Rx: The waveform is designed to maximize the hitting density at $t_{\mathrm{peak}}$ through the MHP method, with a strategic suppression phase $V_2$ to divert residual particles. (b)Passive Rx: The waveform optimizes the sensing probability at the sampling time $t_s$ using the MSP method. Both designs are generated by the unified MRP engine under a total energy constraint $\xi$.
• Figure 3: Arbitrary time-varying drift realizations $\boldsymbol{\Phi}(t)$.
• Figure 4: Verification of the analytical CIR for the fully-absorbing spherical receiver and the passive spherical receiver. The left panel compares the analytical hitting probability density (dashed lines, computed via \ref{['eq:hit_time_varying_final']}) with particle-based Monte Carlo simulations. The right panel compares the analytical sensing probability (dashed lines, computed via \ref{['eq:spherical_rx']}) with particle-based Monte Carlo simulations.
• Figure 5: Performance metrics versus energy constraint $\xi$ under different electric-field design methods. (Top Row) The signal-to-ISI difference $p_{\mathrm{R}}[1] - p_{\mathrm{R}}[2]$ for FA (left) and PA (right) receivers. (Bottom Row) The corresponding BEP for FA (left) and PA (right) receivers. The fully-absorbing architecture (left) guarantees robust optimization and monotonic improvement, whereas the passive receiver (right) faces performance saturation at higher energy levels due to its intrinsic physical limitation.

Theorems & Definitions (4)

• Remark 1: Modeling Consistency
• Remark 2: On the Robustness and Monotonicity of the Target Function
• Remark 3: Surrogate Objective for System Optimization
• Remark 4: Universality of the MRP Engine