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Molecular communication (MC) is a new communication engineering paradigm where molecules are employed as information carriers. MC systems are expected to enable new revolutionary applications, such as sensing of target substances in biotechnology, smart drug delivery in medicine, and monitoring of oil pipelines or chemical reactors in industrial settings. As for any other kind of communication, simple yet sufficiently accurate channel models are needed for the design, analysis, and efficient operation of MC systems. In this paper, we provide a tutorial review on mathematical channel modeling for diffusive MC systems. The considered end-to-end MC channel models incorporate the effects of the release mechanism, the MC environment, and the reception mechanism on the observed information molecules. Thereby, the various existing models for the different components of an MC system are presented under a common framework and the underlying biological, chemical, and physical phenomena are discussed. Deterministic models characterizing the expected number of molecules observed at the receiver and statistical models characterizing the actual number of observed molecules are developed. In addition, we provide the channel models for time-varying MC systems with moving transmitters and receivers, which are relevant for advanced applications such as smart drug delivery with mobile nanomachines. For complex scenarios, where simple MC channel models cannot be obtained from first principles, we investigate the simulation- and experiment-driven channel models. Finally, we provide a detailed discussion of potential challenges, open research problems, and future directions in channel modeling for diffusive MC systems. [ABSTRACT FROM AUTHOR]

The possibility to guide and control magnetic nanoparticles in a non-invasive manner has spawned various applications in biotechnology, such as targeted drug delivery and sensing of biological substances. These applications are facilitated by the engineering of the size, selective chemical reactivity, and general chemical composition of the employed particles. Motivated by their widespread use and favorable properties, in this paper, we provide a theoretical study of the potential benefits of magnetic nanoparticles for the design of molecular communication systems. In particular, we consider a magnetic nanoparticle-based communication in a microfluidic channel where an external magnetic field is employed to attract the information-carrying particles to the receiver. We show that the particle transport affected by the Brownian motion, fluid flow, and an external magnetic field can be mathematically modeled as diffusion with drift. Thereby, we reveal that the key parameters determining the magnetic force are the particle size and the magnetic field gradient. Moreover, we derive an analytical expression for the channel impulse response, which is used to evaluate the potential gain in the expected number of observed nanoparticles due to the magnetic field. Furthermore, adopting the symbol error rate as performance metric, we show that using magnetic nanoparticles can enable a reliable communication in the presence of disruptive fluid flow. The numerical results obtained by the particle-based simulation validate the accuracy of the derived analytical expressions. [ABSTRACT FROM AUTHOR]

In this paper, we consider mobile molecular communication (MC) systems which are expected to find application in several fields including targeted drug delivery and health monitoring. We develop a mathematical framework for modeling the time-variant stochastic channels of diffusive mobile MC systems. In particular, we consider a diffusive mobile MC system consisting of a pair of transmitter and receiver nano-machines suspended in a fluid medium with a uniform bulk flow, where we assume that either the transmitter or the receiver or both are mobile, and we model the mobility by Brownian motion. The transmitter and receiver nano-machines exchange information via diffusive signaling molecules. Due to the random movements of the transmitter and receiver nano-machines, the statistics of the channel impulse response (CIR) change over time. We derive closed-form expressions for the mean, the autocorrelation function (ACF), the cumulative distribution function (CDF), and the probability density function (PDF) of the time-variant CIR. Exploiting the ACF, we define the coherence time of the time-variant MC channel as a metric for characterization of the variations of the CIR. The derived CDF is employed for calculation of the outage probability of the system. We also show that under certain conditions, the PDF of the CIR can be accurately approximated by a Log-normal distribution. Based on this approximation, we derive a simple model for outdated channel state information (CSI). Moreover, we derive an analytical expression for the evaluation of the expected error probability of a simple detector for the considered MC system. In order to investigate the impact of CIR decorrelation over time, we compare the performances of a detector with perfect CSI knowledge and a detector with outdated CSI knowledge. The accuracy of the proposed analytical expressions is verified via particle-based simulation of the Brownian motion. [ABSTRACT FROM AUTHOR]

Instantaneous or statistical channel state information (CSI) is needed for most detection schemes developed for molecular communication (MC) systems. Since the MC channel changes over time, e.g., due to variations in the velocity of flow, the temperature, or the distance between transmitter and receiver, CSI acquisition has to be conducted repeatedly to keep track of CSI variations. Frequent CSI acquisition may entail a large overhead whereas infrequent CSI acquisition may result in a low CSI estimation accuracy. To overcome these challenges, we design codes which enable maximum likelihood sequence detection at the receiver without instantaneous or statistical CSI. In particular, assuming concentration shift keying modulation, we show that a class of codes, known as constant-composition (CC) codes, enables optimal CSI-free sequence detection at the expense of a decrease in data rate. We analyze the code rate, the error rate, and the average number of released molecules for the adopted CC codes. In addition, we study the properties of binary CC codes and balanced CC codes in further detail. Simulation results verify our analytical derivations and reveal that CC codes with CSI-free detection outperform uncoded transmission with optimal coherent and noncoherent detection. [ABSTRACT FROM PUBLISHER]

In this letter, we design matched filters for diffusive molecular communication systems taking into account the following impairments: signal-dependent diffusion noise, inter-symbol interference (ISI), and external interfering molecules. The receiver counts the number of observed molecules several times within one symbol interval and employs linear filtering to detect the transmitted data. We derive the optimal matched filter by maximizing the expected signal-to-interference-plus-noise ratio of the decision variable. Moreover, we show that for the special case of an ISI-free channel, the matched filter reduces to a simple sum detector and a correlator for the channel impulse response for the diffusion noise-limited and (external) interference-limited regimes, respectively. Our simulation results reveal that the proposed matched filter considerably outperforms the benchmark schemes available in literature, especially when ISI is severe. [ABSTRACT FROM PUBLISHER]

This letter introduces a formalism for modeling time-variant channels for diffusive molecular communication systems. In particular, we consider a fluid environment where one transmitter nano-machine and one receiver nano-machine are subjected to Brownian motion in addition to the diffusive motion of the information molecules used for communication. Due to the stochastic movements of the transmitter and receiver nano-machines, the statistics of the channel impulse response change over time. We show that the time-variant behavior of the channel can be accurately captured by appropriately modifying the diffusion coefficient of the information molecules. Furthermore, we derive an analytical expression for evaluation of the expected error probability of a simple detector for the considered system. The accuracy of the proposed analytical expression is verified via particle-based simulation of the Brownian motion. [ABSTRACT FROM PUBLISHER]

In molecular communication (MC) systems, the expected number of molecules observed at the receiver over time after the instantaneous release of molecules by the transmitter is referred to as the channel impulse response (CIR). Knowledge of the CIR is needed for the design of detection and equalization schemes. In this paper, we present a training-based CIR estimation framework for MC systems, which aims at estimating the CIR based on the observed number of molecules at the receiver due to emission of a sequence of known numbers of molecules by the transmitter. Thereby, we distinguish two scenarios depending on whether or not statistical channel knowledge is available. In particular, we derive maximum likelihood and least sum of square errors estimators, which do not require any knowledge of the channel statistics. For the case, when statistical channel knowledge is available, the corresponding maximum a posteriori and linear minimum mean square error estimators are provided. As performance bound, we derive the classical Cramer Rao (CR) lower bound, valid for any unbiased estimator, which does not exploit statistical channel knowledge, and the Bayesian CR lower bound, valid for any unbiased estimator, which exploits statistical channel knowledge. Finally, we propose the optimal and suboptimal training sequence designs for the considered MC system. Simulation results confirm the analysis and compare the performance of the proposed estimation techniques with the respective CR lower bounds. [ABSTRACT FROM PUBLISHER]

This paper studies the problem of receiver modeling in molecular communication systems. We consider the diffusive molecular communication channel between a transmitter nano-machine and a receiver nano-machine in a fluid environment. The information molecules released by the transmitter nano-machine into the environment can degrade in the channel via a first-order degradation reaction and those that reach the receiver nano-machine can participate in a reversible bimolecular reaction with receiver receptor proteins. Thereby, we distinguish between two scenarios. In the first scenario, we assume that the entire surface of the receiver is covered by receptor molecules. We derive a closed-form analytical expression for the expected received signal at the receiver, i.e., the expected number of activated receptors on the surface of the receiver. Then, in the second scenario, we consider the case where the number of receptor molecules is finite and the uniformly distributed receptor molecules cover the receiver surface only partially. We show that the expected received signal for this scenario can be accurately approximated by the expected received signal for the first scenario after appropriately modifying the forward reaction rate constant. The accuracy of the derived analytical results is verified by Brownian motion particle-based simulations of the considered environment, where we also show the impact of the effect of receptor occupancy on the derived analytical results. [ABSTRACT FROM PUBLISHER]