An $M$-ary Concentration Shift Keying with Common Detection Thresholds For Multitransmitter Molecular Communication

TL;DR

CSK-CT tackles the scalability and energy concerns of multi-transmitter CSK in molecular communication for IoBNT by introducing common detection thresholds and a distance-aware release-concentration schedule. It derives closed-form expressions for thresholding and symbol release, adding a scaling exponent to widen symbol separation and achieve linear-time complexity in the symbol alphabet size $M$ while remaining largely independent of the number of transmitters $K$. Compared with the benchmark CSK, CSK-CT delivers substantially lower symbol-error probabilities (e.g., from $10^{-4}$–$10^{-3}$ to $10^{-7}$–$10^{-4}$) and reduces computational complexity from $\mathcal{O}(n^2)$ to $\mathcal{O}(n)$, with potential ISI-mitigation benefits. These attributes make CSK-CT particularly suitable for IoBNT data-gathering tasks where receivers have limited processing capabilities.

Abstract

Concentration shift keying (CSK) is a widely studied modulation technique for molecular communication-based nanonetworks, which is a key enabler for the Internet of Bio-NanoThings (IoBNT). Existing CSK methods, while offering optimal error performance, suffer from increased operational complexity that scales poorly as the number of transmitters, $K$, grows. In this study, a novel $M$-ary CSK method is proposed: CSK with common detection thresholds (CSK-CT). CSK-CT uses \textit{common} thresholds, set sufficiently low to guarantee the reliable detection of symbols from all transmitters, regardless of distance. Closed-form expressions are derived to obtain the common thresholds and release concentrations. To further enhance error performance, the release concentration is optimized using a scaling exponent that also optimizes the common thresholds. The performance of CSK-CT is evaluated against the benchmark CSK across various $K$ and $M$ values. CSK-CT has an error probability between $10^{-7}$ and $10^{-4}$, which is a substantial improvement from that of the benchmark CSK (from $10^{-4}$ to $10^{-3}$). In terms of complexity, CSK-CT is $\mathcal{O}\big(n\big)$ and does not scale with $K$ but $M$ ($M\ll K$), whereas the benchmark is $\mathcal{O}\big(n^2\big)$. Furthermore, CSK-CT can mitigate inter-symbol interference (ISI), although this facet merits further investigation. Owing to its low error rates, improved scalability, reduced complexity, and potential ISI mitigation features, CSK-CT is particularly advantageous for IoBNT applications focused on data gathering. Its effectiveness is especially notable in scenarios where a computationally limited receiver is tasked with collecting vital health data from multiple transmitters.

Figures (14)

• Figure 1: Threshold levels and detection regions of information symbols in CSK.
• Figure 2: Network topology.
• Figure 3: Time-slotted channel model (top) and time-divided channel access (bottom) highlighting the signal and ISI molecules.
• Figure 4: CIRs of signal (green solid line) and ISI from previous $k$ transmissions from other transmitters (red dashed lines).
• Figure 5: $\varGamma$ versus $t_\text{sym}$ for $y_\text{min}=6µm$, $D=$ 79.4µm^2s, and $r=$ 5µm.

Theorems & Definitions (2)

• Remark 1
• Remark 2