Molecule Mixture Detection and Design for MC Systems with Non-linear, Cross-reactive Receiver Arrays

Abstract

Air-based molecular communication (MC) has the potential to be one of the first MC systems to be deployed in real-world applications, enabled by commercially available sensors. However, these sensors usually exhibit non-linear and cross-reactive behavior, contrary to the idealizing assumption of linear and perfectly molecule type-specific sensing often made in the MC literature. To address this mismatch, we propose several detectors and transmission schemes for a molecule mixture communication system where the receiver (RX) employs non-linear, cross-reactive sensors. All proposed schemes are based on the first- and second-order moments of the symbol likelihoods that are fed through the non-linear RX using the Unscented Transform. In particular, we propose an approximate maximum likelihood (AML) symbol-by-symbol detector for inter-symbol-interference (ISI)-free transmission scenarios and a complementary mixture alphabet design algorithm which accounts for the RX characteristics. When significant ISI is present at high data rates, the AML detector can be adapted to exploit statistical ISI knowledge. Additionally, we propose a sequence detector which combines information from multiple symbol intervals. For settings where sequence detection is not possible due to extremely limited computational power at the RX, we propose an adaptive transmission scheme which can be combined with symbol-by-symbol detection. Using computer simulations, we validate all proposed detectors and algorithms based on the responses of commercially available sensors as well as artificially generated sensor data incorporating the characteristics of metal-oxide semiconductor sensors. By employing a general system model that accounts for transmitter noise, ISI, and general non-linear, cross-reactive RX arrays, this work enables reliable communication for a large class of MC systems.

Figures (7)

• Figure 1: System overview. At the TX, a controller converts a sequence of symbols $s[k]$ to control signals for the ODD (ODD), which should release molecule mixtures $\mathbf{\bar{x}}[k]$, but releases mixtures $\mathbf{x}[k]$ due to hardware imperfections instead. At the RX, molecule mixtures $\mathbf{y}[k]$ are observed because $\mathbf{x}[k]$ is subject to attenuation, e.g., due to dispersion or adsorptions to materials, and interferers might introduce additional molecules. The output of the RX sensor array, $\mathbf{z}[k]$, is then used by the detector to derive a symbol estimate $\hat{s}[k]$.
• Figure 2: Impact of non-linear, cross-reactive sensor behavior. The UT-based detectors capture the likelihoods of $\mathbf{y}[k]$ (left) and of $\mathbf{z}[k]$ (center). On the other hand, the sensor responses predicted by the linearized sensor models (center, dashed lines) differ systematically from the actual sensor responses (center plot, dots). This is also reflected in the respective SER of the UT-based detector (right, purple) and the detector relying on a linearized sensor model (right, blue).
• Figure 3: Detector Comparison for ISI-free scenarios. The UT-based detector with the covariance-aware distance metric (solid) consistently achieves the lowest SER compared to centroid detector (dashed) and kNN detectors (dashed-dotted, dotted).
• Figure 4: Detector Comparison for ISI scenarios. The ISI-unaware detector (dashed) makes systematic decision errors, causing unacceptable SER for all SNR and alphabet sizes. The LC (dashed-dotted) detector improves the performance but still cause high SER for higher numbers of symbols, whereas the sequence detector (solid) yields fast SER decays with increasing SNR.
• Figure 5: Comparison of Mixture Design Algorithms for ISI-free scenarios. The SER of mixture alphabets in the SOD with the SNR-based distance metric (pink solid) is consistently lower than that of alphabet designs in the SID (purple) and baselines like CSK or random alphabets (blue).

Theorems & Definitions (30)

• Remark 1
• Remark 2
• Proposition 1: Moments of $\mathbf{x}$
• proof : Proof for \ref{['eq:detection:moments:x:general:mu']}
• proof : Proof for \ref{['eq:detection:moments:x:general:C']}
• Corollary 1.1: SIN, SDCN
• proof
• Proposition 2: Moments of $\bar{\mathbf{y}}$ for a given sequence
• proof : Proof for \ref{['eq:detection:moments:yprime:seq:general:mu']}
• proof : Proof for \ref{['eq:detection:moments:yprime:seq:general:C']}