Multi-Axis Concentration Modulation for Mobile Molecular Communication Systems

TL;DR

A unified MC constellation framework that allows higher order modulation across multiple dimensions and designs efficient constellation for dynamic MC, and focuses on a special subclass, namely multiple-axis ratio shift keying (MAxRSK), that encodes information into the concentration ratios.

Abstract

Molecular communication (MC) is emerging paradigm that employs molecules as information carriers, inspired by biological signaling processes. Existing modulation schemes such as on-off keying (OOK), although simple to implement, suffer from high error probability in dynamic or hard-to-estimate channels due to their dependence on accurate channel information (CI). This work develops a unified MC constellation framework that allows higher order modulation across multiple dimensions and designs efficient constellation for dynamic MC. We propose a general multi-axis concentration modulation (MAxCM(K,M)) of modulation order M, utilizing K-dimensional constellation space with each axis corresponding to a particular molecular type, and information is jointly encoded in their concentrations. The corresponding ML decoders are derived for both static and dynamic MC under exact and partial CI. We show that the use of MAxCM can provide improvements in spectral efficiency (SE) and error rate. We then focus on a special subclass, namely multiple-axis ratio shift keying (MAxRSK), that encodes information into the concentration ratios. Its ML decoder is shown to be a weighted combiner, and design constraints are derived to enable channel-independent decoding. We study one such example, symmetric binary RSK (SBRSK), to show its robustness in dynamic channel conditions compared to OOK. Numerical investigations show significant performance gains over OOK and provide insights into optimal constellation design and receiver configurations.

Figures (10)

• Figure 1: Demonstration of the considered system model for the MMC scenario employing MAxCM modulation scheme. The point TX is shown as a small blue sphere. The figure depicts the red sphere for Type 1 RXP, the green sphere for Type 2 RXP, and the light blue sphere for Type $K$ RXP. $D_{\text{TX}}$ and $D_{\text{RX}}$ are the diffusion coefficients of TX and RX units respectively.
• Figure 3: An illustration of symbol constellation for BRSK along with decoding regions.
• Figure 4: An illustration of higher order ratio encoding as SMAxRSK(3,3) with (a) constellation symbols $\mathbf{a}_0$, $\mathbf{a}_1$, and $\mathbf{a}_2$ lying inside the plane $a_{1b}+a_{2b}+a_{3b}=c$ (shown with green boundary) and (b) decoding regions depicted as gray planes for each symbol.
• Figure 5: Decoding region for $m_{1}$ and $m_{2}$ ranging from 0 to 100 for fixed $c=400$ and $h_{\text{LOW}}=0.0281$. Pink and orange region represent decoding region of bit 0 and 1.
• Figure 6: The variation of the probability of error with $\lambda$ for the SBRSK and OOK, along with the one under Poisson approximation. Here, $c=400$ and $N_{a}=2c=800$. Simulated BER matches very closely with the exact bit error under binomial reception of molecules.

Theorems & Definitions (6)

• Theorem 1
• proof
• Remark 1.1
• Remark 1.2
• Corollary 1.1
• Corollary 1.2