Diffusive Molecular Communication System Research Articles

On Secrecy Performance in D-MoSK-Based 3-D Diffusive Molecular Communication System.

This paper studies the secrecy performance in a 3-D diffusive molecular communication system with the general depleted molecule shift keying (D-MoSK) modulation, where a point transmitter Alice transmits through diffusion multiple types of molecules modulation to a legitimate absorbing receiver Bob, suffering the eavesdropping from an absorbing eavesdropper Eve. We first develop a solid theoretical framework to determine the probabilistic distributions for the number of molecules absorbed by Bob and Eve, respectively. Based on the results, we then derive the average symbol error rate (SER) as well as the mutual information of Alice-Bob and Alice-Eve, and further apply the Shannon theory to determine the secrecy capacity of Alice-Bob transmission. We also develop the closed-form results for the optimal detection threshold at Bob to achieve the secrecy capacity, and thus devise a complete algorithm for secrecy capacity maximization. Finally, we provide numerical results to illustrate the secrecy performance in the concerned system.

Channel Characteristics for Diffusive Molecular Communications in a Spherical Shell

Diffusive molecular communication (DMC) is a bio-mimicking communications paradigm that exploits the Brownian motion of dedicated information carrying molecules for signal transmission. The characteristics of the communication channel in a DMC system heavily depends on the transmitter and receiver mechanisms, on the medium of propagation and its boundaries, and on the way they interact with the molecules. In this work, we investigate the DMC channel in a spherical shell, with inner and outer surfaces which may be partially or perfectly absorptive, or reflective, where either of the boundary surfaces can be considered as the DMC receiver. These geometry and boundary conditions can be used to model a variety of practically relevant scenarios, which are investigated in detail. We derive the general parametric solution of the partial differential equation for this case and provide, for the first time in the literature, expressions for the resulting channel response. We verify the results of our analysis numerically via particle based simulations.

Localizing the Unknown Receiver in a Diffusive SIMO Molecular Communication System

This letter introduces a method to estimate the position of an unknown fully absorbing (FA) spherical receiver in a diffusive molecular communication (MC) system. This latter consists of a point transmitter and multiple FA spherical receivers in a three-dimensional space. The method relies on a temporal asymptotic single-input multiple-output (SIMO) channel model for diffusive MC systems that takes into account the interaction among receivers. By relying on the asymptotic model, a grid-based likelihood function is a priori created from each known receiver’s perspective. The likelihood function’s computation requires information about the number of molecules released by the transmitter, its position, and the position of known receivers. From the cumulative number of molecules absorbed by the known FA receivers, different likelihood maps are obtained, where each map corresponds to the likelihood of the position of unknown receiver from a specific known receiver’s perspective. By combining the receivers’ likelihood maps, which is equivalent to cooperation by sharing their knowledge, the position of the unknown receiver is estimated. The quality of the estimation is evaluated in terms of root mean squared error (RMSE) between the estimated position of the unknown receiver and its true position for different number of released molecules.

Joint localization and channel estimation in flow-assisted molecular communication systems

In this paper, we present a joint localization and channel parameter estimation method in the presence of signal-dependent noise and inter-symbol interference for diffusive molecular communication systems. The joint parameter estimation of the nanomachine can provide reliable communication in a generic diffusive molecular communication system. In particular, an iterative maximum likelihood estimation (MLE) approach for jointly estimating locations, flow velocity, and diffusion coefficient is carried out. The Cramer–Rao lower bound on the variance of channel parameters and location is derived. The normalized estimation error is marginally higher for unknown parameters case than that of some known parameters. The individual result (location estimation or channel parameters estimation) outperforms the existing methods.

An Analytical Propagation Model for Diffusion-Based Molecular Communication Systems

A novel analytical propagation model for diffusive molecular communication systems in a three-dimensional fluid environment is derived. The model takes into account the geometry of a spherical receiver, the inclination angle, and the reaction rate of the receiver to accurately model the time-varying distribution and the number of absorbed information molecules at the receiver over a period of time. Accordingly, we derive an expression for the net number of accumulatively-absorbed information molecules at the surface of the receiver. We also study the bit error rate (BER) performance of diffusion-based molecular communications in the presence of the inter-symbol interference. Simulations based on the developed model show the impact of the transmitter-receiver distance, the reaction rate at the surface of the receiver and the diffusion constant of the environment on the fraction of absorbed molecules and the BER performance. A particle-based simulator is implemented to verify the accuracy of the proposed model. Moreover, our results are compared with that of a conventional model, where the geometry of the receiver and the inclination angle are ignored. It is shown that, especially at small transmitter-receiver separation distances, the proposed model predicts a significantly smaller number of absorbed molecules compared to the conventional models.

Molecule Harvesting Transmitter Model for Molecular Communication Systems

This paper develops mathematical models for molecule harvesting transmitters in diffusive molecular communication (MC) systems. In particular, we consider a communication link consisting of a spherical transmitter nano-machine and a spherical receiver nano-machine suspended in a fluid environment. The transmitter and the receiver exchange information via signaling molecules. The transmitter is equipped with molecule harvesting units on its surface. Signaling molecules which come into contact with the harvesting units may be re-captured by the transmitter. For this system, we derive closed-form expressions for the channel impulse response and harvesting impulse response. Furthermore, we extend the harvesting transmitter model to the case of continuous signaling molecule release. In particular, we derive closed-form expressions for the average received signal at the receiver and the average harvested signal at the transmitter for different temporal release rates namely, constant, linearly increasing, and linearly decreasing release rates. Finally, we validate the accuracy of the derived mathematical expressions via particle-based simulations.

Secrecy Capacity of Diffusive Molecular Communication Under Different Deployments

Currently, the physical layer security is considered as one of the most suitable security techniques in Diffusive Molecular Communication (DMC) because of ease to implement. A recent piece of literature has presented the Secrecy Capacity (SC) of DMC system under the rectangular deployment. To evaluate the information capacity (IC) and thereby SC using the Concentration Greens Function (CGF) in the molecular communication depends on the biological structures of tissues. In this paper, we have investigated the analytical expressions of IC under both the Biological Cylindrical Deployment (BCD) and Biological Spherical Deployment (BSD). Therefore, the analytical expressions of IC have been employed to derive the mathematical expressions of SC under the BCD and BSD environment. Further, the SC is analyzed as a function of distance/radius considering the power and/or bandwidth as the parameter. In addition, the effect of distance of authentic receiver on SC is also explored. It is observed that irrespective of the deployments, the distance of the authentic receiver illustrates predominant effect on the value of SC. The proposed analysis is useful in the implementation of DMC under different tissues structures. The numerically simulated results show close agreement with the theoretical background.

Equal-gain combining with interference mitigation for molecular type hopping assisted molecular shift keying systems

In multiple access molecular diffusive communications, many nano-machines exchange information and fuse data through a common Diffusive Molecular Communication (DMC) channel. Hence, there is Multiple-Access Interference (MAI), which should be sufficiently mitigated so as to achieve reliable communications. In this paper, we propose a novel low-complexity detection scheme, namely Equal-Gain Combining with Interference Mitigation (EGC-IM), for signal detection in the Molecular Type Hopping assisted Molecular Shift Keying (MTH-MoSK) DMC systems. By removing a number of entries from each row of the detection matrix formed during detection, the EGC-IM scheme shows its potential to significantly mitigate MAI and hence, outperform the conventional EGC scheme. Furthermore, the EGC-IM scheme has lower complexity than the conventional EGC scheme and therefore, it is beneficial for practical implementation.

A Novel Method to Improve Performance of Diffusive Molecular Communication Systems with On-Off Keying Modulation

The Bit Error Rate (BER) of the diffusive molecular communication (DMC) systems employing on-off keying (OOK) modulation. We also analyze the BER of the OOK-modulated DMC systems with inter- symbol interference cancellation (ISIC). Our main motivation is to introduce alternative tools for analyzing and efficiently computing the BER of the DMC systems without or with ISIC. Specifically, for the OOK-modulated DMC systems without ISIC, we first derive an exact BER expression based on the Poisson modeling of DMC systems. Then, the Gaussian- and Gamma-approximation approaches are introduced to approximate the discrete Poisson distribution, and based on the approximation approaches, the corresponding BER expressions are derived.

Fractionally Spaced Equalization and Decision Feedback Sequence Detection for Diffusive MC

In this letter, we consider diffusive molecular communication (MC) systems affected by signal-dependent diffusive noise, inter-symbol interference, and external noise. We design linear and nonlinear fractionally-spaced equalization schemes and a detection scheme which combines decision feedback and sequence detection (DFSD). In contrast to the symbol-rate equalization schemes in the MC literature, the proposed equalization and detection schemes exploit multiple samples of the received signal per symbol interval to achieve lower bit error rates (BERs) than existing schemes. The proposed DFSD scheme achieves a BER which is very close to that achieved by maximum likelihood sequence detection, but with lower computational complexity.

Generalized Molecular-Shift Keying (GMoSK): Principles and Performance Analysis

A generalized molecular-shift keying (GMoSK) modulation scheme is proposed for supporting diffusive molecular communication (DMC). Instead of activating one type of molecules in the traditional molecule shift keying (MoSK) modulation, GMoSK simultaneously activates several types of molecules, with the objective to increase data rate and the potential to further mitigate inter-symbol interference (ISI) beyond MoSK. For signal detection in the GMoSK-modulated DMC (GMoSK-DMC) systems, we first derive a symbol-based idealized maximum likelihood (IML) detector, from which we then deduce two practical detection schemes, namely, the zero-level decision feedback maximum likelihood (ZDF/ML) detector and the one-level decision feedback maximum likelihood (1DF/ML) detector. The error performance of the GMoSK-DMC systems with the IML- and ZDF/ML-detectors is mathematically analyzed. Furthermore, the error performance of the GMoSK-DMC systems with our proposed detection schemes is investigated and compared, which is also compared with that of the DMC systems employing the legacy MoSK modulation, the binary concentration shift keying (BCSK) modulation, the depleted MoSK (D-MoSK) modulation, and the Molecule-as-a-Frame (MaaF) modulation. Our studies and performance results demonstrate that GMoSK has the potential to achieve the performance beyond the above four modulation schemes, and employs the merit of high-flexibility for attaining relatively high data rate and also for ISI mitigation.

2-D Channel Characterization of a Molecular Motor Signal

In this article, a two-dimensional channel characterization of a molecular motor signal in a diffusive fluid environment is provided by deriving the first hitting time probability density function of the motor signal to an absorbing lattice point. A temporal modulation scheme to establish communication between two nodes using the motor signal is also proposed. Detection of the motor signal is achieved by using the maximum likelihood detector with erasures for a negligible or no-interference scenario. On the other hand, for motor signal reception with inter-symbol interference, the reception process is modeled as a hidden Markov model, and a Viterbi sequence detection algorithm is devised for decoding the sequence of input Markov states. Efficient criteria to determine the memory length of a diffusive molecular communication (MC) system are defined, which address the problem of choosing a detector for a given MC system. It is demonstrated using numerical results that the hitting probability and, consequently, the error performance of the motor signal worsens with an increase in the unbound probability (ϵ/2). Furthermore, it is also quantitatively established, as to, why in nature directed signals are preferred for communication over purely random diffusive signals at larger distances.

Energy efficiency analysis of multi-hop mobile diffusive molecular communication

Diffusive molecular communication (DMC), in which molecules are used to deliver information in diffusion channel, is one of the most prominent systems in nanonetworks. In particular, the research on end-to-end mobile DMC system is even more challenging. In this paper, we investigate the energy efficiency of multi-hop mobile DMC system. First, the energy model for this system is proposed based on the mobilities of transmitter nanomachine (TN), relays and receiver nanomachine (RN). Then the mathematical expressions of total energy consumption and throughput are derived. Furthermore, the energy efficiency which is defined as the throughput per unit energy consumption is analyzed. Finally, the numerical results show that the parameters including the diffusion coefficients and velocities of mobile TN, relays and RN, the initial distance of each hop, the number of molecules emitted in each time slot by TN and relays, and each time slot duration have different impacts on the energy efficiency. How to set these system parameters can be used to provide guidelines for designing energy efficient multi-hop mobile DMC system.

Sum capacity analysis of mobile broadcast diffusive molecular communication

In this paper, we study the mobile broadcast diffusive molecular communication (DMC) system which is composed of one mobile transmitter nanomachine (TN) and multiple mobile receiver nanomachines (RNs). Considering that the reception event at each RN is different due to the time-varying impulse response of the mobile diffusion channel, in order to ensure that RNs can share the common information from TN with lower bit error probability (BEP), we add two fusion centers (FCs) in this system which are used to gather the information from RNs to make global decisions by using an N-out-of-K fusion rule. We propose three reporting schemes for the transmission between RNs and FCs including perfect reporting, different type of molecules and same type of molecules. Then the mathematical expressions of the optimal decision thresholds at RNs and FCs by using maximum-a-posterior detection method are obtained. On this basis, the BEP and sum capacity under the three reporting schemes are analyzed. Furthermore, the impacts of different parameters and reporting schemes on the performance of this system are evaluated and discussed by the numerical results. The setting of these parameters and reporting schemes can be used to provide the guideline for designing the mobile broadcast DMC system with lower BEP and higher sum capacity.

Expected Received Signal in Diffusive Molecular Communication With Finite Binding Receptors

This letter focuses on the diffusive molecular communication system with a reversible reactive receiver. By assuming the receiver is uniformly covered by finite receptors, a new boundary condition is proposed to model the reception reaction. In addition, an iterative approximation method is developed to model the expected received signal in this system. The simulation results verify the effectiveness of the approximation method.

Semi-Blind Channel Estimation for Diffusive Molecular Communication

In this letter, we consider the problem of channel estimation for diffusive molecular communication (MC) systems. The presence of memory in diffusive MC channels, along with channel noise caused by various sources, necessitate the development of accurate channel estimators to acquire the channel impulse response (CIR). Previous works proposed pilot-based estimators based on the maximum likelihood (ML) and least squares (LS) criteria. In contrast, we propose three novel semi-blind estimators, one based on the expectation maximization (EM) framework and two based on the decision-directed (DD) estimation strategy. We also obtain the corresponding semi-blind Cramer-Rao bound (CRB). Our simulation results show that all the proposed semi-blind estimators offer substantially lower mean-squared error than the existing pilot-based estimators. The EM estimator provides the highest accuracy and converges to the semi-blind CRB, while the DD estimators offer convenient low-complexity alternatives. Importantly, the proposed estimators allow for a significant reduction in the number of transmitted pilots, without compromising the estimation accuracy.

Synaptic Channel Modeling for DMC: Neurotransmitter Uptake and Spillover in the Tripartite Synapse

In Diffusive Molecular Communication (DMC), information is transmitted by diffusing molecules. Synaptic signaling, as a natural implementation of this paradigm, encompasses functional components that, once understood, can facilitate the development of synthetic DMC systems. To unleash this potential, however, a thorough understanding of the synaptic communication channel based on biophysical principles is needed. Since synaptic transmission critically depends also on non-neural cells, such understanding requires the consideration of the so-called tripartite synapse. In this paper, we develop a comprehensive channel model of the tripartite synapse encompassing a three-dimensional, finite-size spatial model of the synaptic cleft, molecule uptake at the presynaptic neuron and at glial cells, reversible binding to individual receptors at the postsynaptic neuron, and spillover to the extrasynaptic space. Based on this model, we derive analytical time domain expressions for the channel impulse response (CIR) of the synaptic DMC system and for the number of molecules taken up at the presynaptic neuron and at glial cells, respectively. These expressions provide insight into the impact of macroscopic physical channel parameters on the decay rate of the CIR and the reuptake rate, and reveal fundamental limits for synaptic signal transmission induced by chemical reaction kinetics and the channel geometry. Adapted to realistic parameters, our model produces plausible results when compared to experimental and simulation studies and we provide results from particle-based computer simulations to further validate the analytical model. The proposed comprehensive channel model admits a wide range of synaptic configurations making it suitable for the investigation of many practically relevant questions, such as the impact of glial cell uptake and spillover on signal transmission in the tripartite synapse.

Equalisation and performance of diffusive molecular communication systems with binary molecular‐shift keying modulation

This study investigates the equalisation techniques for the diffusive molecular communication (DMC) systems with binary molecular-shift keying (BMoSK) modulation, referred to as the BMoSK-DMC systems, in order to mitigate the effect of inter-symbol interference (ISI). The authors first show that in terms of receiving equalisation, a BMoSK-DMC system is in fact equivalent to a conventional binary phase-shift keying modulated radio communication system encountering ISI. Hence, a wealth of equalisation techniques developed with the conventional radio communication systems may be introduced for equalisation of BMoSK-DMC signals. However, considering the limited capability of molecular transceivers on computation and storage, in this study, the authors investigate only the linear equalisers (LEQ) in the principles of matched-filtering, zero-forcing (ZF) and minimum mean-square error (MMSE). They characterise the effects of the different aspects related to DMC signalling and propagation on the achievable performance of the BMoSK-DMC systems with these LEQ. Their studies and performance results demonstrate that both the ZF- and MMSE-LEQ are capable of efficiently suppressing the ISI and attaining promising performance, while still have low-complexity to facilitate implementation.

Performance of diffusive molecular communication systems with binary molecular shift keying modulation

The authors analyse and investigate the bit error rate (BER) performance of the diffusive molecular communication (DMC) systems employing binary molecular shift keying (BMoSK) modulation. The DMC systems both without and with inter-symbol interference compression (ISIC) are considered. Specifically, by modelling the number of molecules of one type presenting in a three-dimensional (3D) detection space as a Poisson or Gaussian distributed random variable, they derive the BER expressions of the BMoSK-modulated DMC systems without/with ISIC. However, the strong inter-symbol interference (ISI) present in DMC systems makes the computation of the above-mentioned BER formulas highly involved or even impossible. Therefore, they introduce some simplified approaches, namely the Monte–Carlo and the simplified Poisson (or simplified Gaussian) approaches, to reduce the computation complexity in the cases of long ISI. Furthermore, based on the statistics of decision variables, they analyse the effect of decision threshold on the BER performance. Finally, the BER performance of the BMoSK-modulated DMC systems without/with ISIC is investigated by considering the impact from different aspects, while the different analytical approaches are compared in terms of the accuracy of the BER evaluated based on these approaches.

Diffusive Mobile MC With Absorbing Receivers: Stochastic Analysis and Applications

This paper presents a stochastic analysis of the time-variant channel impulse response (CIR) of a three dimensional diffusive mobile molecular communication (MC) system where the transmitter, the absorbing receiver, and the molecules can freely diffuse. In our analysis, we derive the mean, variance, probability density function (PDF), and cumulative distribution function (CDF) of the CIR. We also derive the PDF and CDF of the probability ${p}$ that a released molecule is absorbed at the receiver during a given time period. The obtained analytical results are employed for the design of drug delivery and MC systems with imperfect channel state information. For the first application, we exploit the mean and variance of the CIR to optimize a controlled-release drug delivery system employing a mobile drug carrier. We evaluate the performance of the proposed release design based on the PDF and CDF of the CIR. We demonstrate significant savings in the amount of released drugs compared to a constant-release scheme and reveal the necessity of accounting for the drug-carrier’s mobility to ensure reliable drug delivery. For the second application, we exploit the PDF of the distance between the mobile transceivers and the CDF of ${p}$ to optimize three design parameters of an MC system employing on-off keying modulation and threshold detection. Specifically, we optimize the detection threshold at the receiver, the release profile at the transmitter, and the time duration of a bit frame. We show that the proposed optimal designs can significantly improve the system performance in terms of the bit error rate and the efficiency of molecule usage.