Airborne Particle Communication Through Time-varying Diffusion-Advection Channels

TL;DR

The paper develops a rigorous analytical framework for airborne particle communication through time-varying diffusion–advection channels by solving the PDE with the method of moving frames, yielding a closed-form time-dependent channel impulse response $h(\tau,t)$. It derives the mean and autocorrelation of $h$ under Gaussian wind, and introduces the power delay profile and channel dispersion time $T_d$ to quantify channel memory, linking $T_d$ to the Péclet number $P_e$ and mean wind $\mu$. The work classifies channels as non-dispersive or dispersive based on $T_d$ and demonstrates, via MATLAB simulations under directed wind, that waveform design enables multi-symbol modulation with a single particle type and introduces a total pulse leakage metric to assess pulse separability. These results establish a principled, physics-grounded approach to designing and engineering macro-scale particle-based communication systems, bridging conventional digital communication concepts with diffusion–advection dynamics. The framework has potential applications in environmental monitoring, plant signaling, and industrial safety, and points to future work on multi-particle signaling and experimental validation.

Abstract

Particle based communication using diffusion and advection has emerged as an alternative signaling paradigm recently. While most existing studies assume constant flow conditions, real macro scale environments such as atmospheric winds exhibit time varying behavior. In this work, airborne particle communication under time varying advection is modeled as a linear time varying (LTV) channel, and a closed form, time dependent channel impulse response is derived using the method of moving frames. Based on this formulation, the channel is characterized through its power delay profile, leading to the definition of channel dispersion time as a physically meaningful measure of channel memory and a guideline for symbol duration selection. System level simulations under directed, time varying wind conditions show that waveform design is critical for performance, enabling multi symbol modulation using a single particle type when dispersion is sufficiently controlled. The results demonstrate that time varying diffusion advection channels can be systematically modeled and engineered using communication theoretic tools, providing a realistic foundation for particle based communication in complex flow environments.

Figures (8)

• Figure 1: $R_h(\tau_1 =\tau_2 =4;t_1,t_2)$ plots for different wind setups: \ref{['fig:Fig1_a']} WSS Exponential wind covariance and \ref{['fig:Fig1_b']} its slice at $t_1 = 0$, \ref{['fig:Fig1_c']} corresponding channel autocorrelation and \ref{['fig:Fig1_d']} its slice at $t_1 = 0$; \ref{['fig:Fig1_e']} WSS Gaussian wind covariance and \ref{['fig:Fig1_f']} its slice at $t_1 = 0$, \ref{['fig:Fig1_g']} corresponding channel autocorrelation and \ref{['fig:Fig1_h']} its slice at $t_1 = 0$; \ref{['fig:Fig1_i']} non-stationary Exponential wind covariance and \ref{['fig:Fig1_j']} its slice at $t_1 = 0$\ref{['fig:Fig1_k']} corresponding channel autocorrelation and \ref{['fig:Fig1_l']} its slice at $t_1 = 0$; \ref{['fig:Fig1_m']} non-stationary oscillatory wind covariance and \ref{['fig:Fig1_n']} its slice at $t_1 = 0$\ref{['fig:Fig1_o']} corresponding channel autocorrelation and \ref{['fig:Fig1_p']} its slice at $t_1 = 0$.
• Figure 2: Logarithm of $R_{h}(\tau_{1},\tau_{2};\, t_{1},t_{2})$ vs $\tau_2$ for different $\tau_1$ values where $t_1 = 120$\ref{['fig:Fig2_a']}$t_2 = 120$, \ref{['fig:Fig2_b']}$t_2 = 130$, and \ref{['fig:Fig2_c']}$t_2 = 200$.
• Figure 3: Power Delay Profile $R_h(\tau)$ of the channel for different wind assumptions at distances of \ref{['fig:Fig3_a']}$1 \, meters$, \ref{['fig:Fig3_c']}$5 \, meters$, \ref{['fig:Fig3_d']}$10 \, meters$ and \ref{['fig:Fig3_b']} the Fourier transforms of $R_h(\tau)$ for \ref{['fig:Fig3_a']}.
• Figure 4: Block diagram of the complete communication link, including transmitter processing, pulse-shaped emission through the time-varying diffusion-advection channel, sampling with AWGN, and the receiver detection stage.
• Figure 5: Constellation diagrams for \ref{['fig:Fig5_a']} 2-symbol modulation, \ref{['fig:Fig5_b']} 4-symbol modulation, \ref{['fig:Fig5_c']} 8-symbol symmetric modulation, \ref{['fig:Fig5_d']} 8-symbol wide modulation, \ref{['fig:Fig5_e']} 8-symbol tall modulation and \ref{['fig:Fig5_f']} 16-symbol modulation.