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.

This paper studies the problem of receiver modeling in molecular communication systems. We consider the diffusive molecular communication channel between a transmitter nanomachine 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 nanomachine 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.

In this paper, we consider a multi-hop molecular communication network consisting of one nanotransmitter, one nanoreceiver, and multiple nanotransceivers acting as relays. We consider three different relaying schemes to improve the range of diffusion-based molecular communication. In the first scheme, different types of messenger molecules are utilized in each hop of the multi-hop network. In the second and third schemes, we assume that two types of molecules and one type of molecule are utilized in the network, respectively. We identify self-interference, backward intersymbol interference (backward-ISI), and forward-ISI as the performance-limiting effects for the second and third relaying schemes. Furthermore, we consider two relaying modes analogous to those used in wireless communication systems, namely full-duplex and half-duplex relaying. We propose the adaptation of the decision threshold as an effective mechanism to mitigate self-interference and backward-ISI at the relay for full-duplex and half-duplex transmission. We derive closed-form expressions for the expected end-to-end error probability of the network for the three considered relaying schemes. Furthermore, we derive closed-form expressions for the optimal number of molecules released by the nanotransmitter and the optimal detection threshold of the nanoreceiver for minimization of the expected error probability of each hop.

In this paper, we propose using mobile nanosensors (MNSs) for early stage anomaly detection. For concreteness, we focus on the detection of cancer cells located in a particular region of a blood vessel. These cancer cells produce and emit special molecules, so-called biomarkers, which are symptomatic for the presence of anomaly, into the cardiovascular system. Detection of cancer biomarkers with conventional blood tests is difficult in the early stages of a cancer due to the very low concentration of the biomarkers in the samples taken. However, close to the cancer cells, the concentration of the cancer biomarkers is high. Hence, detection is possible if a sensor with the ability to detect these biomarkers is placed in the vicinity of the cancer cells. Therefore, in this paper, we study the use of MNSs that are injected at a suitable injection site and can move through the blood vessels of the cardiovascular system, which potentially contain cancer cells. These MNSs can be activated by the biomarkers close to the cancer cells, where the biomarker concentration is sufficiently high. Eventually, the MNSs are collected by a fusion center (FC) where their activation levels are read and exploited to declare the presence of anomaly. We analytically derive the biomarker concentration in a network of interconnected blood vessels as well as the probability mass function of the MNSs’ activation levels and validate the obtained results via particle-based simulations. Then, we derive the optimal decision rule for the FC regarding the presence of anomaly assuming that the entire network is known at the FC. Finally, for the FC, we propose a simple sum detector that does not require knowledge of the network topology. Our simulations reveal that while the optimal detector achieves a higher performance than the sum detector, both proposed detectors significantly outperform a benchmark scheme that uses fixed nanosensors at the FC.

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.

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 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.