Diffusion-based Molecular Communication Research Articles

Symbol-by-Symbol Maximum Likelihood Detection for Cooperative Molecular Communication

In this paper, symbol-by-symbol maximum likelihood (ML) detection is proposed for a cooperative diffusion-based molecular communication (MC) system. In this system, the transmitter (TX) sends a common information symbol to multiple receivers (RXs) and a fusion center (FC) chooses the TX symbol that is more likely, given the likelihood of its observations from all RXs. The transmission of a sequence of binary symbols and the resultant intersymbol interference are considered in the cooperative MC system. Three ML detection variants are proposed according to different RX behaviors and different knowledge at the FC. The system error probabilities for two ML detector variants are derived, one of which is in closed form. The optimal molecule allocation among RXs to minimize the system error probability of one variant is determined by solving a joint optimization problem. Also for this variant, the equal distribution of molecules among two symmetric RXs is analytically shown to achieve the local minimal error probability. Numerical and simulation results show that the ML detection variants provide lower bounds on the error performance of simpler, non-ML cooperative variants and demonstrate that these simpler cooperative variants have error performance comparable to ML detectors.

The Clock-Free Asynchronous Receiver Design for Molecular Timing Channels in Diffusion-Based Molecular Communications.

In diffusion-based molecular communications, time synchronization is a major reason for the increase of system structure complexity. In this paper, we consider the asynchronous receiver design for molecular communications with information symbols conveyed in the time of released molecules. The main contribution of this paper is that we develop a detector called clock-free asynchronous receiver design (CFARD), in which the receiver recovers the information symbols without measuring the arrival time of molecules. The theoretical analysis indicates that compared with the synchronous receiver designs, the proposed scheme considerably lowers the structure complexity for information demodulation, which is of great significance to the feasibility of nano-scale molecular communications systems with the limitation of energy and size. The numerical results show that in the comparison of bit error ratio (BER) performance, the proposed asynchronous receiver design outperforms the synchronous linear average filter (LAF) detector and approaches to the synchronous maximum likelihood (ML) detector and first arrival (FA) detector.

Compound Poisson Noise Sources in Diffusion-Based Molecular Communication

Diffusion-based molecular communication (DMC) is one of the most promising approaches for realizing nano-scale communications for healthcare applications. The DMC systems in in-vivo environments may encounter biological entities that release molecules identical to the molecules used for signaling as part of their functionality. Such entities in the environment act as external noise sources from the DMC system’s perspective. In this paper, the release of molecules by external bio-inspired noise sources is particularly modeled as a compound Poisson process. The impact of compound Poisson noise sources (CPNSs) on the performance of a point-to-point DMC system is investigated. To this end, the noise from the CPNS observed at the receiver is characterized. Considering a simple on-off keying modulation and formulating symbol-by-symbol maximum likelihood (ML) detector, the performance of the DMC system in the presence of the CPNS is analyzed. For the special case of CPNS in a high-rate regime, the noise received from the CPNS is approximated as a Poisson process whose rate is normally distributed. In this case, it is proved that a simple single-threshold detector is an optimal ML detector. Our results reveal that in general, adopting the conventional simple homogeneous Poisson noise model may lead to overly optimistic performance predictions, if a CPNS is present.

Channel Modeling of Molecular Communication via Diffusion With Multiple Absorbing Receivers

In a diffusion-based molecular communication system, molecules are employed to transmit information. When multiple absorbing receivers exist in an environment, the analysis results of channel characteristics for one absorbing receiver cannot be generalized because of the mutual interferences caused by multiple absorbing receivers. This letter investigates how the unintended receiver affects the intended receiver under the scenario of a point transmitter and two absorbing spherical receivers. Using the empirical inferences and simulation fitting algorithm of Levenberg–Marquardt, we propose the channel model by presenting cumulative absorbing probability and absorption probability density expressions on the intended receiver with respect to the variables of angle, distance, and time. The proposed channel model is validated through numerous particle-based simulations. The analysis results reveal that the peak time of the molecular concentration will not be influenced by the unintended receiver.

Channel Characteristics for Molecular Communication via Diffusion With a Spherical Boundary

Molecular communication via diffusion is a short distance communication technology in the field of nanonetwork using molecules as the information carrier. This letter study the analytical formulation of the molecular concentration distribution function of diffusion-based molecular communication within a three-dimensional closed spherical boundary which can be a perfectly reflective or absorptive boundary. Furthermore, we also give the analytical expression of the peak concentration time. The simulation results validate the theoretical formulation perfectly.

The Asymmetric-Distance Metrics for Decoding of Convolutional Codes in Diffusion-Based Molecular Communications.

In this paper, we focus on the channel coding for diffusion-based molecular communications (MC) with information conveyed in the time of molecules released. The symbol error probability (SEP) is theoretically derived for multiple channel use. The conception called asymmetric-distance is introduced as the metric from the transmitted codeword to the received codeword. A new decoding scheme based on asymmetric-distance is proposed for convolutional codes, which significantly enhances the communication reliability. Biological circuits for the implementation of the proposed channel coding scheme in MC systems are designed by bio-nanomachines. The theoretical analysis indicates that the proposed decoding scheme provides an approximately maximum likelihood estimation. Compared with uncoded systems, Hamming codes, convolutional codes based on Hamming distance (CCHD) and some new coding schemes for molecular communications, numerical results show that the proposed convolutional codes based on asymmetric-distance (CCAD) offer better bit error ratio (BER) performance with the same throughput. The simulation results illustrate that the proposed channel coding scheme is efficient for a larger range of channel environment than other conventional channel coding schemes.

A Novel $A~Priori$ Simulation Algorithm for Absorbing Receivers in Diffusion-Based Molecular Communication Systems

A novel a priori Monte Carlo (APMC) algorithm is proposed to accurately simulate the molecules absorbed at spherical receiver(s) with low-computational complexity in diffusion-based molecular communication (MC) systems. It is demonstrated that the APMC algorithm achieves high-simulation efficiency since by using this algorithm, the fraction of molecules absorbed for a relatively large time step length precisely matches the analytical result. Therefore, the APMC algorithm overcomes the shortcoming of the existing refined Monte Carlo (RMC) algorithm, which enables accurate simulation for a relatively small time step length only. Moreover, for the RMC algorithm, an expression is proposed to quickly predict the simulation accuracy as a function of the time step length and system parameters, which facilitates the choice of simulation time step for a given system. Furthermore, a likelihood threshold is proposed for both the RMC and APMC algorithms to significantly save computational complexity while causing an extremely small loss in accuracy.

Using Spatial Partitioning to Reduce the Bit Error Rate of Diffusion-Based Molecular Communications

This work builds on our earlier work on designing demodulators for diffusion-based molecular communications using a Markovian approach. The demodulation filters take the form of an ordinary differential equation (ODE) which computes the log-posteriori probability of observing a transmission symbol given the continuous history of receptor activities. A limitation of our earlier work is that the receiver is assumed to be a small cubic volume called a voxel. In this work, we extend the maximum a-posteriori demodulation to the case where the receiver may consist of multiple voxels and derive the ODE for log-posteriori probability calculation. This extension allows us to study receiver behaviour of different volumes and shapes. In particular, it also allows us to consider spatially partitioned receivers where the chemicals in the receiver are not allowed to mix. The key result of this paper is that spatial partitioning can be used to reduce bit-error rate in diffusion-based molecular communications.

Parallel algorithms for simulating interacting carriers in nanocommunication

Diffusion-based molecular communication (DMC) with interacting carrier molecules allows exploring a variety of new communication paradigms. Simulating these interactions on a network scale is however hard from an analytic point of view, and continuous detection of which couples of particles may interact is a computationally expensive task. This work proposes different algorithms that allow detecting which particles are interacting. Hierarchical grid based approaches are explored and designed to maximally exploit the parallelism offered by multiple-graphics processing units (multi-GPU) systems. An implementation of the proposed algorithm is compared to some of our previous work in this domain and to a state-of-the-art collision detection library and nanosimulator. Performance tests indicate a speedup of up to a factor 100 compared to the collision detection algorithm implemented in the nanosimulator, and a factor 77 relative to the collision detection library.

Inter-symbol interference reduction channel codes based on time gap in diffusion-based molecular communications

In diffusion-based molecular communication simple modulation techniques based on the concentration, type, or released time of molecules are commonly used. However, random delay of the diffused molecules in environment can cause some strong inter-symbol interference (ISI) among consecutive symbols. Due to the limited computational capabilities of nano-machines, sophisticated modulation and coding schemes cannot be used to resolve this issue . In this paper, we propose several new, yet simple, ISI-resistant coding schemes for diffusion-based communications over a one-dimensional noiseless channel. These schemes map the information bits into variable length codewords and place time-gaps between the consecutive codewords to mitigate ISI issue. Our analytical and simulation results indicate that the proposed schemes provide superior performances in terms of probability of error and throughput compared to the existing schemes.

Enhancing data rate of molecular communication system using Brownian motion.

Inter-symbol and co-channel interferences restrict the capacity of molecular communication (MC) systems. In this study, the effect of these interferences on the data rate of MC systems is investigated to design an efficient MC system. To this end, the authors propose an analytical model for a diffusion-based MC system comprised of two nanomachines when they exploit On/Off keying modulation. They model the Brownian motion of molecules in a one-dimensional environment as a wiener process and the life expectancy of diffused molecules as an exponential process. First, they consider the inter-symbol interference to derive the data rate of the MC system as a function of the receiver decision threshold and the symbol time duration. Hence, they propose an algorithm to obtain the optimal values of MC system parameters. Then, the effect of co-channel interference is considered by assuming parallel MC systems. They propose a minimum distance between adjacent MC systems that their co-channel interferences effect to be negligible. Moreover, they verify the accuracy of the analytical results by Monte-Carlo simulations. Results show a remarkable improvement in the data rate of MC systems. The derived results may find application in nanonetworks where nanomachines connect together to perform complex tasks.

Designing Molecular Circuits for Approximate Maximum a Posteriori Demodulation of Concentration Modulated Signals

Motivated by the fact that living cells use molecular circuits (i.e. a set of chemical reactions) for information processing, this paper investigates the problem of designing molecular circuits for demodulation. In our earlier work, we use a Markovian approach to derive a demodulator for diffusion-based molecular communication. The demodulation filters take the form of an ordinary differential equation which computes the log-posteriori probability of a transmission symbol being sent. This work considers the realisation of these demodulation filters using molecular circuits assuming the transmission symbols are rectangular pulses of the same duration but different amplitudes, i.e. concentration modulation. This paper makes a number of contributions. First, we use time-scale separation and renewal theory to analytically derive an approximation of the demodulation filter from our earlier work. Second, we present a method to turn this approximation into a molecular circuit. By using simulation, we show that the output of the derived molecular circuit is approximately equal to the log-posteriori probability calculated by the exact demodulation filter if the log-posteriori probability is positive. Third, we demonstrate that a biochemical circuit in yeast behaves similarly to the derived molecular demodulation filter and is therefore a candidate for implementing the derived filter.

On the Impact of Transposition Errors in Diffusion-Based Channels

In this work, we consider diffusion-based molecular communication with and without drift between two static nano-machines. We employ type-based information encoding, releasing a single molecule per information bit. At the receiver, we consider an asynchronous detection algorithm which exploits the arrival order of the molecules. In such systems, transposition errors fundamentally undermine reliability and capacity. Thus, in this work we study the impact of transpositions on the system performance. Towards this, we present an analytical expression for the exact bit error probability (BEP) caused by transpositions and derive computationally tractable approximations of the BEP for diffusion-based channels with and without drift. Based on these results, we analyze the BEP when background is not negligible and derive the optimal bit interval that minimizes the BEP. Simulation results confirm the theoretical results and show the error and goodput performance for different parameters such as block size or noise generation rate.

Directional Receivers for Diffusion-Based Molecular Communications

The particle motion in diffusion-based molecular communication systems is typically modeled by using Brownian processes. In particular, this model is used to characterize the propagation of signal molecules after their release from the transmitter. This motion cannot include directionality in the propagating signal and translates into omnidirectional broadcast communications. In order to make such molecular communications system suitable for supporting communications protocols at the molecular scales, we propose to improve the receiver capabilities by introducing a form of directionality while receiving biological signals. Inspired by the directionality introduced in electromagnetic communications by means of directional antennas, we designed a nanomachine receiver having directionality properties. Our aim is to increase the average concentration of signal molecules, also referred to as carriers, in the area around the receiver surface. In this way, it is possible to increase the signal strength at the receiver. For this purpose, we propose to use a purely reflecting shell to be placed at a configurable distance from the receiver surface. The shape of the shell can be modeled as either a spherical cap or a cylinder with an empty basis. The presence of this surface causes a number of signal molecules to remain trapped in a region close to the receiver surface for a sufficiently long time. In this way, the probability of assimilating additional carriers by the compliant receptors present on the receiver surface increases. By means of an extensive simulation campaign, we identified the most suitable configuration able to provide a significant advantage with respect to those not adopting the proposed solution. The resulting approach can be regarded as an enabler of protocols for diffusive molecular communications taking advantage of directionality properties at the receiver site. It can result in an increased communication range or in improved capabilities of discriminating signals of coexisting molecular communication systems.

Diffusion-Based Molecular Communication Channel in Presence of a Probabilistic Absorber: Single Receptor Model and Congestion Analysis.

In this paper, a diffusion-based molecular communication channel is modeled in presence of a probabilistic absorber. The probabilistic absorber is an absorber which absorbs molecules upon collision with probability q . With random walk analysis, the discrete probability function of particle location in the presence of a probabilistic absorber can be found. Then, a continuous probability function is fitted to this Markov-based results with introducing several fitting parameters to the known probability function of particle location in an unbounded environment without an absorbing barrier. With this approach, a single receptor is modeled as an M/M/1/1 queue in which q represents the complementary blocking probability and the mean service time is the mean trafficking time. Therefore, we are able to model the stochastic nature of ligand-receptor binding, which comes from the incapability of a receptor to receive all molecules in its space; and also known as receptor occupancy. The proper consideration of the absorption effect leads to the accurate calculation of the concentration at the desired site, which is definitely less than the concentration obtained when neglecting it. These findings can have a crucial role in designing drug delivery systems in which determining the optimal rate of the drug transmitting nanomachines is critical to avoid toxicity while maintaining effectiveness.

Performance Analysis of Reversible Binding Receptor Based Decode-and-Forward Relay in Molecular Communication Systems

Molecular communication (MC) allows nano-machines to communicate and cooperate with each other in a fluid environment. The diffusion-based MC is easily constrained by the transmit distance due to the severe attenuation of molecule concentrations. In this letter, we present a decode-and-forward relay strategy for the reversible binding receptor in the diffusion-based MC system. The time-varying spatial distribution of the information molecules based on the reversible association and dissociation between ligand and receptor at the surface of receiver is characterized. An analytical expression for the evaluation of expected error probability is derived, and the key factors impacting the performance are exploited. Results show that the proposal can improve the performance significantly with a constant molecular budget, in which the performance gain can be maximized through optimizing the position of the relay nodes and the number of molecules assigned to the source nodes.

Receiver Techniques for Diffusion-Based Molecular Nano Communications Using an Adaptive Neuro-Fuzzy-Based Multivariate Polynomial Approximation

Molecular communication (MC) nanonetworks, the interconnection of biological nanomachines (Bio-NMs), are envisaged to significantly expand the applications of nano-technology in the areas of the biomedical, material science, and electrical engineering. In this paper, we consider the scenario of a diffusion-based molecular communication (DMC) system that is a promising bio-inspired approach to implementing nanonetwork systems. Considering the limited computation capability, ultra-low energy assumption, and expensive information exchange cost among Bio-NMs, this paper proposes a pulse-based demodulation scheme in three biologically inspired techniques for the detection of the molecular pulses: 1) a multivariate polynomial approximation (MPA) scheme; 2) an adaptive fuzzy threshold-based detection (AFTD) scheme; and 3) an adaptive neuro-fuzzy-based MPA (ANF-MPA) scheme. These methods are suitable for binary ON- OFF keying (BOOK signaling), where the Rx Bio-NM adapts the 1/0-bit detection threshold based on the previously received bits that help to alleviate the inter-symbol interference (ISI) problem resulting from residual (tail) diffusion molecules arriving at the receiver due to past bit transmissions and reception noise. To evaluate the performance of DMC systems, the essential communication metrics in each detection scheme are identified, and the numerical results are obtained and validated by MATLAB simulation. Moreover, the complexity of the proposed schemes is calculated, and the performance evaluation in various noisy channel sources shows a promising improvement in the un-coded bit error rate (BER) performance compared with the threshold detection schemes in the literature. These results provide insights that may guide the implementation of future DMC nanonetworks.

Optimal detector design for molecular communication systems using an improved swarm intelligence algorithm

The authors optimise the detection process of diffusion-based molecular communication systems utilising the weighted sum detector with appropriate weight values. Interestingly, no optimisation technique has ever been proposed for the calculation of the weights. To this end, they build on the standard particle swarm optimisation (PSO) technique and propose a robust iterative optimisation algorithm, called acceleration-aided PSO (A-APSO). While modified swarm-based optimisation algorithms focus on slight variations of the standard mathematical formulas, in A-APSO, the acceleration variable of the particles in the swarm is also involved in the search space of the optimisation problem. Particularly, they implement the A-APSO algorithm to evaluate the detector's weights that minimise the closed-form expression of the error probability. Their findings reveal that, when employing the A-APSO weights, the error performance is superior to that achieved by utilising the weight values already existing in the literature or those evaluated with the standard PSO algorithm.

Array Gain Analysis in Molecular MIMO Communications

In this paper, spatial transmission techniques in the area of multiple-input multiple-output (MIMO) diffusion-based molecular communications (DBMC) are investigated. For transmitter-side spatial coding, Alamouti-type coding and repetition MIMO coding are analyzed. At the receiver-side, selection diversity and equal-gain combining are studied as combining strategies. Throughout the numerical analysis, a symmetrical $2\!\times \! 2$ MIMO-DBMC system is assumed. Furthermore, a trained artificial neural network is utilized to acquire the channel impulse responses. The numerical analysis demonstrates that there is no spatial diversity gain in the DBMC system under investigation, but that it is possible to achieve an array gain instead. In addition, it is shown that for MIMO-DBMC systems repetition MIMO coding is superior to Alamouti-type coding.

Anti-ISI Demodulation Scheme and Its Experiment-Based Evaluation for Diffusion-Based Molecular Communication.

In diffusion-based molecular communication, the most common modulation technique is based on the concentration of information molecules. However, the random delay of molecules due to the channel with memory causes severe inter-symbol interference (ISI) among consecutive signals. In this paper, we propose a detection technique for demodulating signals, the increase detection algorithm (IDA), to improve the reliability of concentration-encoded diffusion-based molecular communication. The proposed IDA detects an increase (i.e., a relative concentration value) in molecule concentration to extract the information instead of detecting an absolute concentration value. To validate the availability of IDA, we establish a real physical tabletop test bed. And we evaluate the proposed demodulation technique using bit error rate (BER) and demonstrate by the tabletop molecular communication platform that the proposed IDA successfully minimizes and even isolates ISI, so that a lower BER is achieved than the common demodulation technique.