Multi-Axis Concentration Modulation for Mobile Molecular Communication Systems

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.

💡 Research Summary

This paper addresses the critical challenge of reliable communication in mobile molecular communication (MMC) systems, where traditional on‑off keying (OOK) suffers from high error rates due to its dependence on accurate channel information (CI). The authors introduce a unified multi‑axis concentration modulation (MAxCM) framework that leverages K distinct molecular types as orthogonal axes in a K‑dimensional signal space. In this space, each axis’s concentration represents an amplitude‑like component, while the ratios among axes play a phase‑like role, analogous to quadrature amplitude modulation (QAM) in electromagnetic communications.

The authors first formalize both static and dynamic channel models. In the static case, the transmitter (TX) and receiver (RX) are fixed, and the diffusion‑based channel impulse response h(t,τ) is deterministic. In the dynamic case, both TX and RX undergo Brownian motion with diffusion coefficient D_TR, leading to stochastic time‑varying distances and consequently random channel responses. Molecule arrival at each receptor type is modeled as an independent Poisson process, and the total molecular budget per symbol is constrained to enable fair comparisons with OOK.

Maximum‑likelihood (ML) detectors are derived for MAxCM under two information regimes: (i) exact CI, where the full channel impulse response is known, and (ii) partial CI, where only statistical moments (e.g., mean distance, diffusion coefficient) are available. The ML rule reduces to a weighted sum of observed molecule counts, with weights determined by the known or estimated channel gains for each molecular type.

A special subclass, multi‑axis ratio shift keying (MAxRSK), is then proposed. Here, information is encoded solely in the concentration ratios of the K molecular types, while the total concentration (energy) remains constant across symbols. Because the authors assume the molecular types share identical diffusion coefficients, the ratio is invariant to the channel gain, rendering the ML detector independent of CI. The decision boundaries are shown to be hyperplanes passing through the origin, simplifying implementation.

The paper focuses on a concrete binary example, symmetric binary RSK (SBRSK), which uses two molecule types with ratios 1:1 for bit‑0 and 2:1 (or its inverse) for bit‑1. Under both passive and fully absorbing receiver models, analytical BER expressions are derived for static and dynamic scenarios. Numerical results demonstrate that SBRSK maintains a low BER even when only statistical CI is available, whereas OOK’s BER degrades dramatically under the same conditions. Moreover, when the total number of transmitted molecules and bit duration are equalized, SBRSK achieves a higher spectral efficiency and lower energy‑per‑bit cost than OOK.

To illustrate scalability, the authors extend the concept to higher‑order symmetric MAxRSK (SMAxRSK). By arranging constellation points on a sphere of constant radius (fixed total concentration) with symmetric angular separations, they preserve the channel‑independent property while increasing the modulation order. Design rules for constructing such constellations are provided, and simulation results confirm that the BER advantage over OOK persists for M‑ary schemes.

Extensive simulations explore the impact of mobility (varying D_TR), receiver type, molecular budget, and imperfect CSI. Key findings include: (1) SBRSK’s BER is virtually unaffected by mobility‑induced distance fluctuations; (2) OOK’s performance is highly sensitive to CSI errors; (3) the weighted‑combiner decoder for MAxRSK adapts gracefully to partial CSI, offering a trade‑off between complexity and robustness; (4) the optimal number of molecules per symbol for SBRSK depends on the receiver’s absorption efficiency, with absorbing receivers benefiting more from higher concentrations.

In summary, the paper makes the following contributions: (i) a general MAxCM framework that unifies OOK, CSK, and RSK as special cases; (ii) ML detection strategies for both exact and partial CI scenarios; (iii) a channel‑independent ratio‑based subclass (MAxRSK) with analytical BER and design constraints; (iv) concrete binary and higher‑order constellations (SBRSK, SMAxRSK) that outperform OOK in dynamic environments; and (v) comprehensive performance evaluation that highlights the practical advantages of multi‑axis concentration modulation for future bio‑nano networks such as the Internet of Bio‑Nano Things.