Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> Molecular communication (MC) will enable the exchange of information among nanoscale devices. In this novel bio-inspired communication paradigm, molecules are employed to encode, transmit and receive information. In the most general case, these molecules are propagated in the medium by means of free diffusion. An information theoretical analysis of diffusion-based MC is required to better understand the potential of this novel communication mechanism. The study and the modeling of the noise sources is of utmost importance for this analysis. The objective of this paper is to provide a mathematical study of the noise at the reception of the molecular information in a diffusion-based MC system when the ligand-binding reception is employed. The reference diffusion-based MC system for this analysis is the physical end-to-end model introduced in a previous work by the same authors, where the reception process is realized through ligand-binding chemical receptors. The reception noise is modeled in this paper by following two different approaches, namely, through the ligand-receptor kinetics and through the stochastic chemical kinetics. The ligand-receptor kinetics allows to simulate the random perturbations in the chemical processes of the reception, while the stochastic chemical kinetics provides the tools to derive a closed-form solution to the modeling of the reception noise. The ligand-receptor kinetics model is expressed through a block scheme, while the stochastic chemical kinetics results in the characterization of the reception noise using stochastic differential equations. Numerical results are provided to demonstrate that the analytical formulation of the reception noise in terms of stochastic chemical kinetics is compliant with the reception noise behavior resulting from the ligand-receptor kinetics simulations. <s> BIB001 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> A diffusion-based molecular communication system has two major components: the diffusion in the medium, and the ligand-reception. Information bits, encoded in the time variations of the concentration of molecules, are conveyed to the receiver front through the molecular diffusion in the medium. The receiver, in turn, measures the concentration of the molecules in its vicinity in order to retrieve the information. This is done via ligand-reception process. In this paper, we develop models to study the constraints imposed by the concentration sensing at the receiver side and derive the maximum rate by which a ligand-receiver can receive information. Therefore, the overall capacity of the diffusion channel with the ligand receptors can be obtained by combining the results presented in this paper with our previous work on the achievable information rate of molecular communication over the diffusion channel. <s> BIB002 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> Abstract Designing an optimum receiver for diffusion-based molecular communication in nano-networks needs a well justified channel model. In this paper, we present a linear and time invariant signal propagation model and an additive noise model for the diffusion-based molecular communication channel. These models are based on Brownian motion molecular statistics. Using these models, we develop the first optimal receiver design for diffusion-based molecular communication scenarios with and without inter-symbol interference. We evaluate the performance of our proposed receiver by investigating the bit error rate for small and large transmission rates. <s> BIB003 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> We consider molecular communication networks consisting of transmitters and receivers distributed in a fluidic medium. In such networks, a transmitter sends one or more signaling molecules, which are diffused over the medium, to the receiver to realize the communication. In order to be able to engineer synthetic molecular communication networks, mathematical models for these networks are required. This paper proposes a new stochastic model for molecular communication networks called reaction-diffusion master equation with exogenous input (RDMEX). The key idea behind RDMEX is to model the transmitters as time series of signaling molecule counts, while diffusion in the medium and chemical reactions at the receivers are modeled as Markov processes using master equation. An advantage of RDMEX is that it can readily be used to model molecular communication networks with multiple transmitters and receivers. For the case where the reaction kinetics at the receivers is linear, we show how RDMEX can be used to determine the mean and covariance of the receiver output signals, and derive closed-form expressions for the mean receiver output signal of the RDMEX model. These closed-form expressions reveal that the output signal of a receiver can be affected by the presence of other receivers. Numerical examples are provided to demonstrate the properties of the model. <s> BIB004 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> This paper studies the mitigation of intersymbol interference in a diffusive molecular communication system using enzymes that freely diffuse in the propagation environment. The enzymes form reaction intermediates with information molecules and then degrade them so that they cannot interfere with future transmissions. A lower bound expression on the expected number of molecules measured at the receiver is derived. A simple binary receiver detection scheme is proposed where the number of observed molecules is sampled at the time when the maximum number of molecules is expected. Insight is also provided into the selection of an appropriate bit interval. The expected bit error probability is derived as a function of the current and all previously transmitted bits. Simulation results show the accuracy of the bit error probability expression and the improvement in communication performance by having active enzymes present. <s> BIB005 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> In the Molecular Communication (MC), molecules are utilized to encode, transmit, and receive information. Transmission of the information is achieved by means of diffusion of molecules and the information is recovered based on the molecule concentration variations at the receiver location. The MC is very prone to intersymbol interference (ISI) due to residual molecules emitted previously. Furthermore, the stochastic nature of the molecule movements adds noise to the MC. For the first time, we propose four methods for a receiver in the MC to recover the transmitted information distorted by both ISI and noise. We introduce sequence detection methods based on maximum a posteriori (MAP) and maximum likelihood (ML) criterions, a linear equalizer based on minimum mean-square error (MMSE) criterion, and a decision-feedback equalizer (DFE) which is a nonlinear equalizer. We present a channel estimator to estimate time varying MC channel at the receiver. The performances of the proposed methods based on bit error rates are evaluated. The sequence detection methods reveal the best performance at the expense of computational complexity. However, the MMSE equalizer has the lowest performance with the lowest computational complexity. The results show that using these methods significantly increases the information transmission rate in the MC. <s> BIB006 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> In this paper, we perform receiver design for a diffusive molecular communication environment. Our model includes flow in any direction, sources of information molecules in addition to the transmitter, and enzymes in the propagation environment to mitigate intersymbol interference. We characterize the mutual information between receiver observations to show how often independent observations can be made. We derive the maximum likelihood sequence detector to provide a lower bound on the bit error probability. We propose the family of weighted sum detectors for more practical implementation and derive their expected bit error probability. Under certain conditions, the performance of the optimal weighted sum detector is shown to be equivalent to a matched filter. Receiver simulation results show the tradeoff in detector complexity versus achievable bit error probability, and that a slow flow in any direction can improve the performance of a weighted sum detector. <s> BIB007 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> Implementing a realistic communication system using a diffusion-based molecular channel requires a well justified model for the reception process at the receiver nano-machine. In this paper, we model the reception process at a receiver nano-machine by means of ligand-receptor binding kinetics. For this purpose, we use a diffusion-based physical channel model and we show that the reception process can be interpreted as a low-pass filter. Then, we evaluate the effect of the reception process on the statistical characteristics of the noise added by the diffusion channel. In order to suppress the effect of the ligand-receptor binding process, we design a whitening filter which is placed before the demodulator and detection blocks at the receiver nano-machine. <s> BIB008 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> Within the domain of molecular communications, researchers mimic the techniques in nature to come up with alternative communication methods for collaborating nanomachines. This letter investigates the channel transfer function for molecular communications via diffusion. In nature, information-carrying molecules are generally absorbed by the target node via receptors. Using the concentration function, without considering the absorption process, as the channel transfer function implicitly assumes that the receiver node does not affect the system. In this letter, we propose a solid analytical formulation and analyze the signal metrics (attenuation and propagation delay) for molecular communication via diffusion channel with an absorbing receiver in a 3-D environment. The proposed model and the formulation match well with the simulations without any normalization. <s> BIB009 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> Diffusion-based communication refers to the transfer of information using molecules as message carriers whos ep rop- agation is governed by the laws of molecular diffusion. It has been identified that diffusion-based communication is one of the most promising solutions for end-to-end communication between nanoscale devices. In this paper, the design of a diffusion-based communication system considering stochastic signaling, arbitrary orders of channel memory, and noisy receptio ni s proposed. The diffusion in the cases of one, two, and three dimensions are all considered. Three signal processing techniques for the molecular concentration with low computational complexity are proposed. For the detector design, both a low-complexity one-shot optimal detector for mutual information maximization and a near Max- imum Likelihood (ML) sequence detector are proposed. To the best of our knowledge, our paper is thefirst that gives an analytical treatment of the signal processing, estimation, and detection prob- lems for diffusion-based communication in the presence of ISI and reception noise. Numerical results indicate that the proposed signal processing technique followed by the one-shot detector achieves near-optimal throughput without the need of ap riori information in both short-range and long-range diffusion-based communication scenarios, whic hs uggests an ML sequence de- tector is not necessary. Furthermore, the proposed receiver design guarantees diffusion-based communication to operate without failure even in the case of infinite channel memory. A channel capacity of 1 bit per channel utilization can be ultimately achieved by extending the duration of the signaling interval. <s> BIB010 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> Abstract In this paper, a strength-based optimum signal detection scheme for binary concentration-encoded molecular communication (CEMC) system has been presented. In CEMC, a single type of information molecule is assumed to carry the information from the transmitting nanomachine (TN), through the propagation medium, to the receiving nanomachine (RN) in the form of received concentration of information molecules at the location of the RN. We consider a pair of nanomachines communicating by means of on–off keying (OOK) transmission protocol in a three-dimensional ideal (i.e. free) diffusion-based unbounded propagation environment. First, based on stochastic chemical kinetics of the reaction events between ligand molecules and receptors, we develop a mathematical receiver model of strength-based detection scheme for OOK CEMC system. Using an analytical approach, we explain the receiver operating characteristic (ROC) curves of the receiver thus developed. Finally, we propose a variable threshold-based detection scheme and explain its communication range and rate dependent characteristics. We show that it provides an improvement in the communication ranges compared to fixed threshold-based detection scheme. (Part of this paper has been peer-reviewed and published in BWCCA-2012 conference in Victoria, BC, 12–14 November, 2012 [20] .) <s> BIB011 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> In this paper, a comprehensive analysis of strength-based optimum signal detection model has been presented for concentration-encoded molecular communication (CEMC) with spike (i.e., impulsive) transmission based on amplitude-shift keying (ASK) and on-off keying (OOK) modulations. Strength-based optimum signal detection problem in diffusion-based CEMC system has been investigated in detail in the presence of both diffusion noise and intersymbol interference (ISI). The receiver for optimum signal detection has been developed theoretically and explained with both analytical and simulation results of binary signal detection. Results show that the receiver thus developed can detect CEMC symbols effectively; however, the performance is influenced by three main factors, namely, communication range, transmission data rate, and receiver memory. For both ASK and OOK receivers, exact and approximate detection performances have been derived analytically depending on the probabilistic nature of molecular availability and the relationship between mean and variance of signal strengths. Correspondingly, bit error rate (BER) performance of the optimum receiver in a single CEMC link is further evaluated under various scenarios through extensive simulation experiments. <s> BIB012 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> In this work, we investigate the communication reliability for diffusion-based molecular communication, using the indicator of bit error rate (BER). A molecular classified model is established to divide molecules into three parts, which are the signal, inter-symbol interference (ISI) and noise. We expand each part separately using molecular absorbing probability, and connect them by a traditional-like formula. Based on the classified model, we do a theoretical analysis to prove the feasibility of improving the BER performance. Accordingly, an adaptive threshold variation (ATV) algorithm is designed in demodulation to implement the goal, which makes the receiver adapt the channel condition properly through learning process. Moreover, the complexity of ATV is calculated and its performance in various noisy channel is discussed. An expression of Signal to Interference plus Noise Ratio (SINR) is defined to verify the system performance. We test some important parameters of the channel model, as well as the ATV algorithm in the simulation section. The results have shown the performance gain of the proposal. <s> BIB013 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> To adapt their behaviour in changing environments, cells sense concentrations by binding external ligands to their receptors. However, incorrect ligands may bind nonspecifically to receptors, and when their concentration is large, this binding activity may interfere with the sensing of the ligand of interest. Here, I derive analytically the physical limit to the accuracy of concentration sensing amid a large number of interfering ligands. A scaling transition is found when the mean bound time of correct ligands is twice that of incorrect ligands. I discuss how the physical bound can be approached by a cascade of receptor states generalizing kinetic proof-reading schemes. <s> BIB014 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> In this paper, we present an analytical model for the diffusive molecular communication (MC) system with a reversible adsorption receiver in a fluid environment. The widely used concentration shift keying (CSK) is considered for modulation. The time-varying spatial distribution of the information molecules under the reversible adsorption and desorption reaction at the surface of a receiver is analytically characterized. Based on the spatial distribution, we derive the net number of newly-adsorbed information molecules expected in any time duration. We further derive the number of newly-adsorbed molecules expected at the steady state to demonstrate the equilibrium concentration. Given the number of newly-adsorbed information molecules, the bit error probability of the proposed MC system is analytically approximated. Importantly, we present a simulation framework for the proposed model that accounts for the diffusion and reversible reaction. Simulation results show the accuracy of our derived expressions, and demonstrate the positive effect of the adsorption rate and the negative effect of the desorption rate on the error probability of reversible adsorption receiver with last transmit bit-1. Moreover, our analytical results simplify to the special cases of a full adsorption receiver and a partial adsorption receiver, both of which do not include desorption. <s> BIB015 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> In this paper, we consider the bacterial point-to-point and multiple-access molecular communications with ligand-receptors. For the point-to-point communication, we investigate common signaling methods, namely the Level Scenario (LS), which uses one type of a molecule with different concentration levels, and the Type Scenario (TS), which employs multiple types of molecules with a single concentration level. We investigate the trade-offs between the two scenarios from the capacity point of view. We derive an upper bound on the capacity using a Binomial Channel (BIC) model and the symmetrized Kullback-Leibler (KL) divergence. A lower bound is also derived when the environment noise is negligible. For the TS, we also consider the effect of blocking of a receptor by a different molecule type. Then, we consider multiple-access communications, for which we investigate three scenarios based on molecule and receptor types, i.e., same types of molecules with Different Labeling and Same types of Receptors (DLSR), Different types of Molecules and Receptors (DMDR), and Same types of Molecules and Receptors (SMSR). We investigate the trade-offs among the three scenarios from the total capacity point of view. We derive some inner bounds on the capacity region of these scenarios when the environment noise is negligible. <s> BIB016 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> Molecular communication (MC) is a bio-inspired communication method based on the exchange of molecules for information transfer among nanoscale devices. MC has been extensively studied from various aspects in the literature; however, the physical design of MC transceiving units is largely neglected with the assumption that network nodes are entirely biological devices, e.g., engineered bacteria, which are intrinsically capable of receiving and transmitting molecular messages. However, the low information processing capacity of biological devices and the challenge to interface them with macroscale networks hinder the true application potential of nanonetworks. To overcome this limitation, recently, we proposed a nanobioelectronic MC receiver architecture exploiting the nanoscale field-effect transistor-based biosensor (bioFET) technology, which provides noninvasive and sensitive molecular detection while producing electrical signals as the output. In this paper, we introduce a comprehensive model for silicon nanowire FET-based MC receivers by integrating the underlying processes in MC and bioFET to provide a unified analysis framework. We derive closed-form expressions for the noise statistics, the signal-to-noise ratio (SNR) at the receiver output, and the symbol error probability (SEP). Performance evaluation in terms of SNR and SEP reveals the effects of individual system parameters on the detection performance of the proposed MC receiver. <s> BIB017 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> In a diffusion-based molecular communication network, transmitters and receivers communicate by using signalling molecules (or ligands) in a fluid medium. This paper assumes that the transmitter uses different chemical reactions to generate different emission patterns of signalling molecules to represent different transmission symbols, and the receiver consists of receptors. When the signalling molecules arrive at the receiver, they may react with the receptors to form ligand-receptor complexes. Our goal is to study the demodulation in this setup assuming that the transmitter and receiver are synchronised. We derive an optimal demodulator using the continuous history of the number of complexes at the receiver as the input to the demodulator. We do that by first deriving a communication model which includes the chemical reactions in the transmitter, diffusion in the transmission medium and the ligand-receptor process in the receiver. This model, which takes the form of a continuous-time Markov process, captures the noise in the receiver signal due to the stochastic nature of chemical reactions and diffusion. We then adopt a maximum a posteriori framework and use Bayesian filtering to derive the optimal demodulator. We use numerical examples to illustrate the properties of this optimal demodulator. <s> BIB018 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> Molecular communication is a promising approach to realize the communication between nanoscale devices. In a diffusion-based molecular communication network, transmitters and receivers communicate by using signalling molecules. The transmitter uses different time-varying functions of concentration of signalling molecules (called emission patterns) to represent different transmission symbols. The signalling molecules diffuse freely in the medium. The receiver is assumed to consist of a number of receptors, which can be in ON or OFF state. When the signalling molecules arrive at the receiver, they react with the receptors and switch them from OFF to ON state probabilistically. The receptors remain ON for a random amount of time before reverting to the OFF state. This paper assumes that the receiver uses the continuous history of receptor state to infer the transmitted symbol. Furthermore, it assumes that the transmitter uses two transmission symbols and approaches the decoding problem from the maximum a posteriori (MAP) framework. Specifically, the decoding is realized by calculating the logarithm of the ratio of the posteriori probabilities of the two transmission symbols, or log-MAP ratio. A contribution of this paper is to show that the computation of log-MAP ratio can be performed by an analog filter. The receiver can therefore use the output of this filter to decide which symbol has been sent. This analog filter provides insight on what information is important for decoding. In particular, the timing at which the receptors switch from OFF to ON state, the number of OFF receptors and the mean number of signalling molecules at the receiver are important. Numerical examples are used to illustrate the property of this decoding method. <s> BIB019 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> This paper studies detection algorithms for diffusion-based molecular communication systems, where molecules freely diffuse as information carrier from a transmitter to a receiver in a fluid medium. The main limitations are strong intersymbol interference due to the random propagation of the molecules, and the low-energy/low-complexity assumption regarding future implementations in so-called nanomachines. In this contribution, a new biologically inspired detection algorithm suitable for binary signaling, named adaptive threshold detection, is proposed, which deals with these limitations. The proposed detector is of low complexity, does not require explicit channel knowledge, and seems to be biologically reasonable. Numerical results demonstrate that the proposed detector can outperform the common low-complexity fixed threshold detector under certain conditions. As a benchmark, maximum-likelihood sequence estimation (MLSE) and reduced-state sequence estimation (RSSE) are also analyzed by means of numerical simulations. In addition, the effect of molecular denaturation on the detection performances is studied. It is shown that denaturation generally improves the detection performances, while RSSE is able to outperform MLSE in the case of no denaturation. <s> BIB020 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> Nanoscale molecular communication is a viable way of exchanging information between nanomachines. In this investigation, a low-complexity and noncoherent signal detection technique is proposed to mitigate the inter-symbol-interference (ISI) and additive noise. In contrast to existing coherent detection methods of high complexity, the proposed noncoherent signal detector is more practical when the channel conditions are hard to acquire accurately or hidden from the receiver. The proposed scheme employs the molecular concentration difference to detect the ISI corrupted signals and we demonstrate that it can suppress the ISI effectively. The difference in molecular concentration is a stable characteristic, irrespective of the diffusion channel conditions. In terms of complexity, by excluding matrix operations or likelihood calculations, the new detection scheme is particularly suitable for nanoscale molecular communication systems with a small energy budget or limited computation resource. <s> BIB021 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> Molecular communications via diffusion (MCvD) represents a relatively new area of wireless data transfer with especially attractive characteristics for nanoscale applications. Due to the nature of diffusive propagation, one of the key challenges is to mitigate inter-symbol interference (ISI) that results from the long tail of channel response. Traditional coherent detectors rely on accurate channel estimations and incur a high computational complexity. Both of these constraints make coherent detection unrealistic for MCvD systems. In this paper, we propose a low-complexity and noncoherent signal detector, which exploits essentially the local convexity of the diffusive channel response. A threshold estimation mechanism is proposed to detect signals blindly, which can also adapt to channel variations. Compared to other noncoherent detectors, the proposed algorithm is capable of operating at high data rates and suppressing ISI from a large number of previous symbols. Numerical results demonstrate that not only is the ISI effectively suppressed, but the complexity is also reduced by only requiring summation operations. As a result, the proposed noncoherent scheme will provide the necessary potential to low-complexity molecular communications, especially for nanoscale applications with a limited computation and energy budget. <s> BIB022 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> 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. <s> BIB023 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> In this paper, 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. <s> BIB024 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> In this paper, a novel Memory-Assisted Adaptive-Threshold detection (MAAT) scheme for diffusion-based molecular communications (MC) systems is proposed. The proposed scheme applies to MC systems in which single-type of molecules is assumed to carry the information from the transmitting nano-machine, through a fluid medium, to the receiving nano-machine. The information is represented by the received concentration of the information molecules. We consider a single transmitter (Tx) and receiver (Rx) problem, where the communication takes place in a three-dimensional free-flow diffusion-based unbounded propagation environment. We present a novel adaptive-threshold detection algorithm suitable for binary On-OFF Keying (BOOK signaling), where the Rx adapts the 1/0 bit detection threshold based on past received bits. The adjustment of the 1/0 detection threshold based on past received bits helps to alleviate the inter-symbol interference resulting from residual (tail) diffusion molecules arriving at the receiver due to past bit transmissions and noise molecules. Performance evaluation shows a promising improvement in the un-coded BER performance of our proposed scheme compared with the traditional Fixed-Threshold Detection (FTD) approach. In addition, our proposed approach delivers BER levels comparable with considerably more complex approaches found in the literature. <s> BIB025 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> Molecular communication requires low-complexity symbol detection algorithms to deal with the many sources of uncertainty that are inherent in these channels. This paper proposes two variants of a high-performance asynchronous peak detection algorithm for a receiver that makes independent observations. The first variant has low complexity and measures the largest observation within a sampling interval. The second variant adds decision feedback to mitigate inter-symbol interference. Although the algorithm does not require synchronization between the transmitter and receiver, results demonstrate that the bit error performance of symbol-by-symbol detection using the first variant is better than using a single sample whose sampling time is chosen a priori. The second variant is shown to have performance comparable to that of an energy detector. Both variants of the algorithm demonstrate better resilience to timing offsets than that of existing detectors. <s> BIB026 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> 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. <s> BIB027 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> This work studies optimal detection for communication over diffusion-based molecular timing (DBMT) channels. The transmitter simultaneously releases multiple information particles, where the information is encoded in the time of release. The receiver decodes the transmitted information based on the random time of arrival of the information particles, which is modeled as an additive noise channel. For a DBMT channel without flow, this noise follows the L\'evy distribution. Under this channel model, the maximum-likelihood (ML) detector is derived and shown to have high computational complexity. It is also shown that under ML detection, releasing multiple particles improves performance, while for any additive channel with $\alpha$-stable noise where $\alpha<1$ (such as the DBMT channel), under linear processing at the receiver, releasing multiple particles degrades performance relative to releasing a single particle. Hence, a new low-complexity detector, which is based on the first arrival (FA) among all the transmitted particles, is proposed. It is shown that for a small number of released particles, the performance of the FA detector is very close to that of the ML detector. On the other hand, error exponent analysis shows that the performance of the two detectors differ when the number of released particles is large. <s> BIB028 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> Abstract This work studies time-slotted communication over molecular timing (MT) channels. The transmitter, assumed to be perfectly synchronized in time with the receiver, is required to send K bits to the receiver using K information particles. It releases a single information particle in each time-slot , where the information is encoded in the time of release . The receiver decodes the transmitted information based on the random time of arrivals of the information particles during a finite-time observation window. The maximum-likelihood (ML) detector is derived in terms of the permanent of a matrix involving the arrival times, and shown to have an exponential computational complexity, thus, rendering it impractical. Therefore, two additional (practical) detectors are presented: The first is a symbol-by-symbol detector. The second is a sequence detector which is based on the Viterbi algorithm (VA), yet, the VA is used differently than in its common application in electromagnetic communications where the channels are linear. Numerical simulations indicate that the proposed sequence detection algorithm significantly improves the performance compared to the symbol-by-symbol detector. For a short number of transmitted symbols, the numerical results indicate that the performance of the proposed sequence detector closely approaches the performance of the highly complicated ML detector. Finally, the proposed sequence detector is numerically compared with a one-shot transmission scheme that releases all K particles simultaneously to send a single symbol out of a constellation of size 2 K . It is shown that while for a small number of bits the one-shot scheme is better, when the number of bits is medium to large, the sequence detector achieves significantly better performance. <s> BIB029 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> We study non-coherent detection schemes for molecular communication (MC) systems with negligible inter-symbol interference that do not require knowledge of the channel state information (CSI). In particular, we first derive the optimal maximum likelihood (ML) multiple-symbol (MS) detector for MC systems. As a special case of the optimal MS detector, we show that the optimal ML symbol-by-symbol (SS) detector can be equivalently written in the form of a threshold-based detector, where the optimal decision threshold is constant and depends only on the statistics of the MC channel. The main challenge of the MS detector is the complexity associated with the calculation of the optimal detection metric. To overcome this issue, we propose an approximate MS detection metric that can be expressed in closed form. In addition, we develop a non-coherent decision-feedback detector, which introduces a lower detection delay compared with the optimal MS detector, and a suboptimal blind detector, which has a significantly lower complexity than the optimal MS detector. Finally, we derive analytical expressions for the bit error rate (BER) of the optimal SS detector, as well as upper and lower bounds for the BER of the optimal MS detector. Simulation results confirm the analysis and reveal the effectiveness of the proposed optimal and suboptimal detection schemes compared with the benchmark scheme that assumes perfect CSI knowledge, particularly, when the number of observations used for detection is sufficiently large. Simulation results are also presented that show the performance of the proposed detectors, when inter-symbol interference is non-negligible. <s> BIB030 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> This letter proposes a simple and novel method for mitigating inter-symbol interference (ISI) in molecular communication via diffusion (MCvD). In MCvD applications, the messenger molecules released from the transmitter need some time to reach the receiver. Therefore, the molecules absorbed at the beginning of a transmission interval can only belong to the previous transmissions. Therefore, if a receiver shifts its absorption interval, ISI can be potentially reduced. We find the optimal delay time that the receiver shifts its absorption interval both numerically and analytically to minimize the ISI in the channel. We demonstrate the improved performance of the proposed shift- $\tau $ method in molecular communication over conventional concentration shift keying modulation. The major benefits of the proposed method are its simplicity and applicability to many other schemes in the literature. <s> BIB031 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> The molecular communication via diffusion (MCvD) is one of the most promising techniques for nano-networks due to its advantages of bio-compatibility and energy efficiency. Due to the diffusion nature of the molecules, the peak time of the channel impulse response (CIR) is relatively large. To avoid severe inter-symbol-interference effect, the symbol interval is usually set larger than the peak time of the CIR. Therefore, the data rate becomes the main limitation of MCvD. In this letter, a derivative-based detection scheme is proposed based on the properties that the peak time of the CIR’s derivative is much shorter than that of CIR itself and the tail of CIR’s derivative vanishes much faster than that of the CIR. The simulation results demonstrate that the proposed scheme performs better than the state-of-the-art detection schemes in terms of bit error rate (BER) at high data rate where the symbol interval is shorter than the peak time of CIR. The impacts of the relative symbol interval, released molecule number, sampling rate, and receiver volume on the BER performance of the proposed scheme are investigated. <s> BIB032 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> 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. <s> BIB033 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> We study diversity in one-shot communication over molecular timing channels. We consider a channel model where the transmitter simultaneously releases a large number of information particles, while the information is encoded in the time of release. The receiver decodes the information based on the random time of arrival of the information particles. The random propagation is characterized by the general class of right-sided unimodal densities. We characterize the asymptotic exponential decrease rate of the probability of error as a function of the number of released particles, and denote this quantity as the system diversity gain. Four types of detectors are considered: the maximum-likelihood (ML) detector, a linear detector, a detector that is based on the first arrival (FA) among all the transmitted particles, and a detector based on the last arrival (LA). When the density characterizing the random propagation is supported over a large interval, we show that the simple FA detector achieves a diversity gain very close to that of the ML detector. On the other hand, when the density characterizing the random propagation is supported over a small interval, we show that the simple LA detector achieves a diversity gain very close to that of the ML detector. <s> BIB034 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> Molecular Communication (MC) is a bio-inspired communication technique that uses molecules as a method of information transfer among nanoscale devices. MC receiver is an essential component having profound impact on the communication system performance. However, the interaction of the receiver with information bearing molecules has been usually oversimplified in modeling the reception process and developing signal detection techniques. In this paper, we focus on the signal detection problem of MC receivers employing receptor molecules to infer the transmitted messages encoded into the concentration of molecules, i.e., ligands. Exploiting the observable characteristics of ligand-receptor binding reaction, we first introduce a Maximum Likelihood (ML) detection method based on instantaneous receptor occupation ratio, as aligned with the current MC literature. Then, we propose a novel ML detection technique, which exploits the amount of time the receptors stay unbound in an observation time window. A comprehensive analysis is carried out to compare the performance of the detectors in terms of bit error probability. In evaluating the detection performance, emphasis is given to the receptor saturation problem resulting from the accumulation of messenger molecules at the receiver as a consequence of intersymbol interference. The results reveal that detection based on receptor unbound time is quite reliable even in saturation, whereas the reliability of detection based on receptor occupation ratio substantially decreases as the receiver gets saturated. Finally, we also discuss the potential methods of implementing the detectors. <s> BIB035 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> © 2018 Kuscu, Akan. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. We consider a microfluidic molecular communication (MC) system, where the concentration-encoded molecular messages are transported via fluid flow-induced convection and diffusion, and detected by a surface-based MC receiver with ligand receptors placed at the bottom of the microfluidic channel. The overall system is a convection-diffusion-reaction system that can only be solved by numerical methods, e.g., finite element analysis (FEA). However, analytical models are key for the information and communication technology (ICT), as they enable an optimisation framework to develop advanced communication techniques, such as optimum detection methods and reliable transmission schemes. In this direction, we develop an analytical model to approximate the expected time course of bound receptor concentration, i.e., the received signal used to decode the transmitted messages. The model obviates the need for computationally expensive numerical methods by capturing the nonlinearities caused by laminar flow resulting in parabolic velocity profile, and finite number of ligand receptors leading to receiver saturation. The model also captures the effects of reactive surface depletion layer resulting from the mass transport limitations and moving reaction boundary originated from the passage of finite-duration molecular concentration pulse over the receiver surface. Based on the proposed model, we derive closed form analytical expressions that approximate the received pulse width, pulse delay and pulse amplitude, which can be used to optimize the system from an ICT perspective. We evaluate the accuracy of the proposed model by comparing model-based analytical results to the numerical results obtained by solving the exact system model with COMSOL Multiphysics. <s> BIB036 </s> Transmitter and Receiver Architectures for Molecular Communications: A Survey on Physical Design with Modulation, Coding and Detection Techniques <s> 1) MC Detection with Passive and Absorbing Receivers: <s> Molecular Communications (MC) is a bio-inspired wireless communication technique that uses molecules as a means of information transfer among bio-nano devices. In this paper, we focus on the signal detection problem of MC receivers employing receptor molecules to infer the transmitted messages encoded into the concentration of molecules, i.e., ligands. We particularly consider a very common scenario in physiological conditions, where there is non-negligible concentration of interferer molecules in the channel, which have similar binding characteristics with the ligands, and thus, can bind to the receptors, causing substantial interference with the MC signal. We investigate three different maximum likelihood (ML) detection methods based on different observable parameters of the ligand-receptor binding mechanism, which are the instantaneous number of bound receptors and the amount of time the receptors stay unbound or bound within an observation time window. We carry out a comparative analysis to numerically evaluate the performance of the detection methods under different system settings. <s> BIB037
The nonlinearities and complexity of the MC system often lead researchers to use simplifying assumptions to develop detection methods and analyze their performances. To this end, the intricate relationship between molecular propagation and sampling processes is often neglected. Passive receiver (PA) concept is the most widely used simplifying assumption in MC literature, as it takes the physical sampling process out of the equation, such that researchers can focus only on the transport of molecular messages to the receiver location. Accordingly, the passive receiver is often assumed to be a spherical entity whose membrane is transparent to all kind of molecules, and it is a perfect observer of the number of molecules within its spherical reception space, as shown in Fig. 10 [259] . In the passive receiver approximation, the receiver has no impact on the propagation of molecules in the channel. Passive receivers can also be considered as if they include ligand receptors, which are homogeneously distributed within the reception space with very high concentration and infinitely high rate of binding with ligands, such that every single molecule in the reception space is effectively bound to a receptor at the time of sampling. Another modeling approach, i.e., absorbing receiver (AB) concept BIB009 , considers receiver as an hypothetical entity, often spherical, which absorbs and degrades every single molecule that hits its surface, as demonstrated in Fig. 10 . This approach improves the assumption of passive receiver one step further towards a more realistic scenario including a physical interaction between the receiver and the channel. In contrast to passive receiver, absorbing receiver can be considered to have receptors located over the surface. For a perfect absorbing receiver, this means very high concentration of receptors with infinitely high absorption rate, such that every molecule that hits the surface is bound and consumed instantly. Physical correspondence of both models is highly questionable. Nevertheless, they are widely utilized in the literature as they provide upper performance limits. However, ignoring the receptor-ligand reactions, which often leads to further intricacies, e.g., receptor saturation, stands as a major drawback of these approaches. a) Received Signal Models: When constructing the received signal models for diffusion-based MC, the transmitter (Tx) geometry is usually neglected assuming that the Tx is a point source that does not occupy any space. This assumption is deemed valid when the distance between the Tx and Rx are considerably larger than the physical sizes of the devices. Throughout this section, we will mostly focus on OOK modulation, where the Tx performs an impulsive release of a number of molecules to transmit bit-1, and does not send any molecule to transmit bit-0. This is the most widely used modulation scheme in MC detection studies, as it simplifies the problem while capturing the properties of the MC channel. However, we will also briefly review the detection schemes corresponding to other modulation methods, e.g., timing-based modulation and MoSK, throughout the section. Molecular propagation in the channel is usually assumed to be only through free diffusion, or through the combination of diffusion and uniform flow (or drift). In both cases, the channel geometry is often neglected and assumed to be unbounded, and molecules are assumed to propagate independently from each other. In some studies addressing passive receivers, researchers consider the existence of enzymes in the channel, which reduce the impact of the ISI by degrading the residual messenger molecules through first-order reaction BIB005 . For a three dimensional free diffusion channel with uniform flow in the presence of degrading enzymes, the number of molecules observed in the spherical reception space of a passive receiver follows non-stationary Poisson process BIB006 ,  , i.e., where the time-varying mean of this process λ RX (t) can be given by The mean depends on the number of transmitted molecules Q to represent bit 1, the symbols transmitted in the current symbol interval as well as in the previous symbol intervals, i.e., s [i] , and the length of a symbol interval T s . Most MC studies include an additive stationary noise in their models representing the interfering molecules available in the channel as a result of an independent process in the application environment. These molecules are assumed to be of the same kind with the messenger molecules and their number is represented by a Poisson process and captured by λ noise . Channel response is integrated into the model through the function P obs (t), which is the probability of a molecule transmitted at time t = 0 to be within the sampling space at time t. When Tx-Rx distance is considerably large, ligands are typically assumed to be uniformly distributed within the reception space. As a result, the channel response can be written as where RX is the volume of the spherical receiver with radius d RX , D is the diffusion coefficient, C E is the uniform concentration of the degrading enzymes in the channel, k is the rate of enzymatic reaction, and r eff is the effective Tx-Rx distance vector, which captures the effect of uniform flow  . Assuming that the Tx and Rx are located at r TX = (0, 0, 0), r RX = (x 0 , 0, 0), respectively, and the flow velocity is given by v x , v y , v z in 3D Cartesian coordinates, the magnitude of the effective distance vector can be written as follows For an absorbing receiver, the received signal is usually taken as the number of molecules absorbed by the Rx within a time interval BIB009 . For a diffusion channel without flow, the probability density for a molecule emitted at t = 0 to be absorbed by a perfectly absorbing receiver of radius r r and located at a distance r from the Tx at time t is given by and the cumulative distribution function (CDF) is given by where erfc is the complementary error function BIB009 . The CDF can be used to calculate the probability of a molecule transmitted at time t = 0 to be absorbed within the kth signaling interval, i.e., When considering multiple independent molecules emitted at the same time, the number of molecules absorbed at the kth interval becomes Bernoulli random variable with the success probability of P k . Assuming that the success probability is low enough, Gaussian approximation of the Bernoulli random process can be used to write where its signal-dependent mean and variance can be written as a function of current and previously transmitted bits s[i], i.e., Note that as in the case of passive receiver, the received signal model includes the contribution of a stationary noise through its variance σ 2 noise . Unfortunately, in the literature, there is no analytical model for absorbing receivers in diffusion-based MC channels with uniform flow and degrading enzymes. b) Detection Methods: Detection methods for MC in general can be divided into two main categories depending on the method of concentration measurement: sampling-based and energy-based detection. Passive receivers are usually assumed to perform sampling-based detection, which is based on sampling the instantaneous number of molecules inside the reception space at a specific sampling time  . Absorbing receivers, on the other hand, are typically assumed to utilize energy-based detection, which uses the total number of molecules absorbed by the receiver during a prespecified time interval, that is usually the symbol interval BIB012 . In some studies, passive receivers are also considered to perform energy-based detection through taking multiple independent samples of number of molecules inside the reception space at different time instants during a single symbol interval, and passing them through a linear filter which outputs their weighted sum as the energy of the received molecular signal BIB007 ,  . As in conventional wireless communications, detection can be done on symbol-by-symbol or sequential basis. The symbol-by-symbol detection tends to be more practical in terms of complexity, whereas the sequence detectors require the receiver to have a memory to store the previously decoded symbols. Due to the MC channel memory causing a considerable amount of ISI for high data rate communication, the sequence detectors are more frequently studied in the literature. Next, we review the existing MC detection techniques developed for passive and absorbing receivers by categorizing them into different areas depending on their most salient characteristics. A comparison matrix for these methods can also be seen in Table IV . Symbol-by-Symbol (SbS) Detection: SbS MC detectors in the literature are usually proposed for very low-rate communication scenarios, where the ISI can be neglected, asymptotically included into the received signal model with a stationary mean and variance, or approximated by the weighted sum of ISI contributions of a few previously transmitted symbols. In BIB010 , a one-shot detector is proposed based on the asymptotic approximation of the ISI assuming that the sum of decreasing ISI contributions of the previously transmitted symbols can be represented by a Gaussian distribution through central limit theorem (CLT) based on Lindeberg's condition. A fixed-threshold detector is proposed maximizing the mutual information between transmitted and decoded symbols. Similarly, in BIB007 ,  , a matched filter in the form of a weighted sum detector is proposed using a different asymptotic ISI approximation as though it results from a continuously emitting source leading to a stationary Poisson distribution of interference molecules inside the reception space. In this scheme, a passive receiver performs energy-based detection taking multiple samples at equally spaced sampling times during a single symbol transmission, and the weights of the samples are adjusted according to the number of molecules expected at the corresponding sampling times. This matched filter is proven to be optimal in the sense that it maximizes SNR at the receiver. However, the optimal threshold of this detector does not lend itself to a closed-form expression, and thus, it should be numerically obtained through resource intensive search algorithms. Similarly, in BIB024 , considering also the external sources of interference, another linear matched filter is designed maximizing the expected signalto-interference-plus-noise-ratio (SINR) for SbS detection, and shown to outperform previous schemes especially when the ISI is severe. There are also adaptive-threshold-based SbS detection methods relying on receivers with memory of varying length taking into account only the ISI contribution of a finite number of previously transmitted symbols  BIB013 BIB025 BIB020 , BIB012 ,  . In these schemes, the adaptive threshold is updated for each symbol interval using the ISI estimation based on the previously decoded symbols. SbS detection is also considered in BIB030 , BIB026 , which will be discussed next in the context of noncoherent and asynchronous detection. Sequence Detection and ISI Mitigation: Optimal sequence detection methods based on Maximum a Posteriori (MAP) and Maximum Likelihood (ML) criteria are proposed in BIB006 for MC with passive receivers. Even though the complexity of the sequence detectors are reduced by applying Viterbi algorithm, it still grows exponentially with increasing channel memory length. To reduce the complexity further, a sub-optimal linear equalizer based on Minimum Mean-Square Error (MMSE) criterion is proposed. To improve the performance of the sub-optimal detection, a nonlinear equalizer, i.e., DecisionFeedback Equalizer (DFE), is also proposed in the same study. DFE is shown to outperform linear equalizers with significantly less complexity than optimal ML and MAP sequence detection methods. Similarly, a near-optimal ML sequence detector employing Viterbi algorithm is proposed in BIB010 . Another optimal ML sequence detector is proposed in BIB007 for MC with uniform flow and enzymes that degrade information molecules. In addition to the sequence detection methods and equalizers, there are other approaches proposed to overcome the effects of the ISI on detection. For example, in BIB031 , authors propose to shift the sampling time by increasing the reception delay to reduce the effect of ISI. In BIB032 , a derivative-based signal detection method is proposed to enable high data rate transmission. The method is based on detecting the incoming messages relying on the derivative of the channel impulse response (CIR). Noncoherent Detection: Most of the MC detection methods requires the knowledge of the instantaneous CSI in terms of CIR. However, CIR in MC, especially in physiologically relevant conditions, tends to change frequently, rendering the detection methods relying on the exact CIR knowledge useless. Estimating the instantaneous CIR is difficult and requires high computational power. To overcome this problem, researchers propose low-complexity noncoherent detection techniques. For example, in BIB020 , the authors develop a simple detection method for absorbing receivers, which does not require the channel knowledge. In this scheme, the receiver performs a threshold-based detection by comparing the number of absorbed molecules in the current interval to that of the previous symbol interval. The adaptive threshold is updated in every step of detection with the number of molecules absorbed. However, this method performs poorly when a sequence of consecutive bit-1s arrives. Similarly, in BIB021 , the difference of the accumulated concentration between two adjacent time intervals is exploited for noncoherent detection. In BIB022 , the local convexity of the diffusion-based channel response is exploited to detect MC signals in a noncoherent manner. A convexity metric is defined as the test statistics, and the corresponding threshold is derived. There are also methods requiring only the statistical CSI rather than the instantaneous CSI BIB030 . Additionally, constant-composition codes are proposed to enable ML detection without statistical or instantaneous CSI, and shown to outperform uncoded transmission with optimal coherent and noncoherent detection, when the ISI is neglected BIB033 . Asynchronous Detection: The synchronization between the communicating devices is another major challenge. However, in the previously discussed studies, synchronization is assumed to be perfect. To overcome this limitation, an asynchronous peak detection method is developed in BIB026 for the demodulation of MC signals. Two variants has been proposed. First method is based on measuring the largest observation within a sampling interval. This SbS detection method is of moderate complexity and non-adaptive, comparing the maximum observation to a fixed threshold. The second method is adaptive and equipped with decision feedback to remove the ISI contribution. In this scheme, the receiver takes multiple samples per bit and adjusts the threshold for each observation based on the expected ISI. Detection for Mobile MC: The majority of MC studies assumes that the positions of Tx and Rx are static during communication. The mobility problem of MC devices has just recently started to attract researchers' attention. For example, MC between a static transmitter and a mobile receiver is considered in  , where the authors propose to reconstruct the CIR in each symbol interval using the time-varying transmitter-receiver distance estimated based on the peak value of the sampled concentration. Two adaptive schemes, i.e., concentration-based adaptive threshold detection and peaktime-based adaptive detection, are developed based on the reconstructed CIR. In BIB027 , different mobility cases including mobile TX and RX, mobile TX and fixed RX, and mobile RX and fixed TX are considered to develop a stochastic channel model for diffusive mobile MC systems. The authors derive analytical expressions for the mean, PDF, and autocorrelation function (ACF) of the time-varying CIR, through an approximation of the CIR with a log-normal distribution. Based on this approximation, a simple model for outdated CSI is derived, and the detection performance of a single-sample threshold detector relying on the outdated CSI is evaluated. Discussion on Other Detection Techniques: MC detection problem is also addressed for molecule shift keying (MoSK) modulation. In BIB003 , an optimal ML sequence detector employing Viterbi algorithm is proposed assuming that a passive receiver can independently observe MC signals carried by different types of molecules. This assumption greatly simplifies the problem and enable the application of detection methods developed for CSK-modulated MC signals for MoSK signals as well. Diffusion-based molecular timing (DBMT) channels are also addressed from detection theoretical perspective. DBMT channels without flow are accompanied by a Levy distributed additive noise having a heavy algebraic tail in contrast to the exponential tail of inverse Gaussian distribution, which DBMT channel with flow follows BIB028 . In BIB029 , an optimal ML detector is derived for DBMT channels without flow; however, the complexity of the detector is shown to have exponential computational complexity. Therefore, they propose suboptimal yet practical SbS and sequence detectors based on the random time of arrivals of the simultaneously released information molecules, and show that the performance of the sequence detector is close to the one of computationally expensive optimal ML detector. In DBMT channels without flow, linear filtering at the receiver results in a dispersion larger or equal to the dispersion of the original, i.e., unfiltered, sample, rendering the performance of releasing multiple particles worse than releasing a single particle. Based on this finding, the authors in BIB028 develop a low-complexity detector, which is based on the first arrival (FA) time of simultaneously released particles by the TX. The method is based on the observation that the probability density of the FA gets concentrated around the transmission time when the number of released molecules M increases. Neglecting ISI, it is shown in the same paper that the proposed FA-based detector performs very close to the optimal ML detectors for small values of M . However, the ML detection still performs significantly better than the FA for high values of M . The detection based on the order statistics has been extended in the same authors' later work BIB034 , where they consider also the detection based on the last arrival (LA) time. Defining a system diversity gain as the asymptotic exponential decrease rate of error probability with the increased number of released particles, they showed that the diversity gain of LA detector approaches to that of computationally expensive ML detector. 2) MC Detection with Reactive Receivers: Another type of receiver considered for MC is reactive receiver, which samples the molecular concentration of incoming messages through a set of reactions it performs via specialized receptor proteins or enzymes, as shown in Fig. 10 . The reactive receiver approach is more realistic in the sense that natural cells, e.g., bacteria and neurons, sense molecular communication signals through their receptors on the cell membrane, and many types of artificial biosensors, e.g., bioFETs, are functionalized with biological receptors for higher selectivity. Since synthetic biology, focusing on using and extending natural cell functionalities, and artificial biosensing are the two phenomena that are considered for practical implementation of MC receivers, studying MC detection with reactive receivers has more physical correspondence. Diffusion-based MC systems with reactive receivers, in most cases, can be considered as reaction-diffusion (RD) systems with finite reaction rates. Although RD systems, which are typically highly nonlinear, have been studied in the literature for a long time, they do not usually lend themselves to analytical solutions, especially when the spatio-temporal dynamics and correlations are not negligible. To be able to devise detection methods and evaluate their performance in the MC framework, researchers have come up with different modeling approaches, which will be reviewed next. For the sake of brevity, we focus our review on detection with receivers equipped with ligand receptors, which have only one binding site. Ligand-receptor binding reaction for a single receptor exposed to time-varying ligand concentration c L (t) can be schematically demonstrated as follows where k + and k − are the ligand-receptor binding and unbinding rates, respectively; U and B denote the unbound and bound states of the receptor, respectively. When there are N R receptors, assuming that all of them are exposed to the same concentration of ligands, reaction rate equation (RRE) for the number of bound receptors can be written as BIB001 dn As is clear, while the binding reaction is second-order depending on the concentrations of both ligands and available receptors, unbinding reaction is first-order and only depends on the number of bound receptors. Most of the time, the bandwidth of MC signals can be assumed to be low enough to drive the binding reaction to near equilibrium and allow applying quasi steady-state assumption for the overall system. In this case, time-varying concentration c L (t) can be treated constant, i.e., c L (t) = c L , and dn B (t)/dt = 0, which results in the following expression for the mean number of bound receptors where K D = k − /k + is the dissociation constant, which is a measure of affinity between the specific type of ligand and receptor. Even at equilibrium, the receptors randomly fluctuate between the bound and unbound state. The number of bound receptors n B , at equilibrium, is a Binomial random variable with success probability p B = c L /(c L +K D ), and its variance can be given accordingly by More insight can be gained by examining the continuous history of binding and unbinding events over receptors. The likelihood of observing a series of n binding-unbinding events at equilibrium can be given by where Z is the normalization factor, T U = BIB014 , BIB035 . Note that the likelihood is equally valid for the cases of single receptor and multiple receptors, as long as the collected n samples of unbound and bound time intervals are independent. These observable characteristics of the ligand-receptor binding reactions have been exploited to infer the incoming messages to different extents, as will be reviewed next. a) Received Signal Models: The nonlinearities arising from the interaction of time-varying MC signals with receptors have led to different approaches for modeling MC systems with reactive receivers compromising on different aspects to develop detection techniques and make the performance analyses tractable. A brief review of these modeling approaches are provided as follows. Reaction-Diffusion Models with Time-varying Input: One of the first attempts to model the ligand-receptor binding reactions from an MC theoretical perspective is provided in BIB001 , where the authors develop a noise model for the fluctuations in the number of bound receptors of a receiver exposed to time-varying ligand concentrations as MC signals. The model is based on the assumption of a spherical receiver, in which ligand receptors and information-carrying ligands are homogeneously distributed. For an analytically tractable analysis, the concentration of incoming ligands is assumed to be constant between two sampling times, i.e., during a sampling interval, and the ligand-receptor binding reaction is assumed to be at equilibrium at the beginning of each sampling interval. In light of these assumptions, the authors obtain the time-varying variance and mean of the number of bound receptors, which are valid only for the corresponding sampling interval. A more general approach without the equilibrium assumption to obtain the mean number of bound receptors with time-varying input signals, i.e., ligand concentration, is contributed by BIB023 and BIB015 , through solving the system of differential equations governing the overall diffusion-reaction MC system. The authors of the both studies consider a spherical receiver with ligand receptors on its surface and a point transmitter, which can be anywhere on a virtual sphere centered at the same point as the receiver but larger than that, to obtain a spherical symmetry to simplify the overall problem. As a result, the transmitter location cannot be exactly specified in the problem. In BIB015 , the authors consider that the spherical receiver is capable of binding ligands at any point on its surface, which is exactly equal to the assumption of infinite number of receptors. On the other hand, BIB023 considers finite number of receptors uniformly distributed on the receiver surface, and addresses this challenge through boundary homogenization. However, boundary homogenization for finite number of receptors does not take into account the negative feedback of the bound receptors on the second-order binding reaction (see (15) ), and thus, the developed analytical model is not able to capture the indirect effects of finite number of receptors, e.g., receptor saturation. This is clear from their analysis, such that the discrepancy between the analytical model and the particlebased simulation results is getting larger with increasing ligand concentration. Frequency Domain Model: Another modeling approach is provided in BIB008 , where the authors, assuming that the probability of a receptor to be in the bound state is very low, take the number of available, i.e., unbound, receptors equal to the total number of receptors at all time points. The completely first order characteristics of the resulting RRE enables them to carry out a frequency domain analysis, through which they show the ligand-receptor binding reaction manifests lowpass filter characteristics. However, this approximate model is relevant only when the probability of receptor-ligand binding is very low. Discrete Model based on Reaction-Diffusion Master Equation (RDME): To capture the stochasticity of the reaction-diffusion MC, another approach is introduced in BIB004 , where the authors develop a voxel-based model based on RDME, with the diffusion and reactions at the receiver modeled as Markov processes. The three-dimensional MC system is discretized and divided into equal-size cubic voxels, in each of which molecules are assumed to be uniformly distributed, and allowed to move only to the neighboring voxels. In the voxel accommodating the Tx, the molecules are generated according to a modulation scheme, and the Rx voxel hosts the receptor molecules, where the ligands diffusing into the Rx voxel can react based on law of mass action. The jump of a ligand from one voxel to another is governed by a diffusion rate parameter, which is a function of the voxel size and the ligand diffusion coefficient. The number of ligands and bound receptors are stored in a system state vector, which is progressed with a given state transition rate vector storing the reaction, diffusion, and molecule generation rates. In the continuum limit, the model is able to provide closedform analytical expressions for the mean and variance of the number of bound receptors for small-scale systems. However, for larger systems, with a high number of voxels, the efficiency of the model is highly questionable. Steady-state Model: In addition to the above approaches considering time-varying signals, some researchers prefer using the assumption of steady-state ligand-receptor binding reaction with stationary input signals at the time of sampling, based on fact that the bandwidth of incoming MC signals is typically low because the diffusion channel shows low-pass filter characteristics and the reaction rates are generally higher than the diffusion rate of molecules. This assumption enables the separation of the overall system into two; a deterministic microscale diffusion channel and the stochastic ligand-receptor binding reaction at the interface between the receiver and the channel. Accordingly, at the sampling time, the ligand concentration around the receptors assumes different constant values corresponding to different symbols. The only fluctuations are resulting from the binding reaction, where the random number of bound receptors follows Binomial distribution, whose mean and variance are given in (16) and (17), respectively. The steady-state assumption is applied in BIB016 , BIB002 , where the authors derive reaction-diffusion channel capacity for different settings. Convection-Diffusion-Reaction System Model: Microfluidic MC systems with reactive receivers are studied by a few researchers. In BIB017 , authors develop a one-dimensional analytical model, assuming that the propagation occurs through convection and diffusion, and a reactive receiver, which is assumed to be a SiNW bioFET receiver with ligand receptors on its surface, is placed at the bottom of the channel. The interplay between convection, diffusion and reaction is taken into account by defining a transport-modified reaction rate, tailored for the hemicylindrical surface of the SiNW bioFET receiver. However, the authors assume steady-state conditions for the reaction, to be able to derive a closed-form expression for the noise statistics. The molecular-to-electrical transduction properties of the bioFET are reflected to the output current of the receiver through modeling the capacitive effects arising from the liquid-semiconductor interface and the 1/f noise resulting from the defects of the SiNW transducer channel. In BIB036 , the authors considered a two-dimensional convectionreaction-diffusion system, which does not lend itself to closedform analytical expressions for the received signal. Authors develop a heuristic model using a two-compartmental modeling approach, which divides the channel into compartments, in each of which either transport or reaction occurs, and derive an analytical expression for the time-course of the number of bound receptors over a planar receiver surface placed at the bottom of the channel. The model well captures the nonlinearities, such as Taylor-Aris dispersion in the channel, depletion region above the receiver surface, and saturation effects resulting from finite number of receptors, as validated through finite element simulations of the system in COMSOL. However, the model assumes the channel and the receiver is empty at the beginning of the transmission; therefore, does not allow an ISI analysis. b) Detection Methods: The literature on detection methods for MC with reactive receivers is relatively scarce, and the reason can be attributed partly to the lack of analytical models that can capture the nonlinear ligand-receptor binding reaction kinetics and resulting noise and ISI. Nevertheless, the existing methods can be divided into three categories depending on the type of assumptions made and considered receiver architectures. Detection based on Instantaneous Receptor States: The first detection approach is based on sampling the instantaneous number of bound receptors at a prespecified time, as shown in Fig. 11 , and comparing it to a threshold. In BIB015 , the authors study a threshold-based detection for OOK modulated ligand concentrations, using the difference between the number of bound molecules at the start and end of a bit interval. In BIB008 , converting the ligand-receptor binding reaction to a completely first-order reaction with the assumption that all of the receptors are always available for binding, the authors manage to transform the problem into the frequency domain. For the modulation, they consider MoSK with different receptors corresponding to different ligands; therefore, the problem basically reduces to a detection problem of the concentrationencoded signals for each ligand-receptor pair. To reduce the amount of noise, they propose to apply a whitening filter to the sensed signal in the form of number of bound receptors, and then utilize the same detection technique they proposed in BIB003 . An energy-based detection scheme is proposed in BIB011 , where the test statistics is the total number of binding events that occur within a symbol duration. They propose a variable threshold-detection scheme with varying memory length. The article also takes into account the ISI; however, the model assumes that all the receptors are always available for binding, and completely neglects the unbinding of ligands from the receptors, making the reaction irreversible. In BIB035 , the authors study the saturation problem in MC-Rxs with ligand receptors. As part of their analysis, they investigate the performance of an adaptive threshold ML detection using the instantaneous number of bound receptors. The effect of the receiver memory that stores the previously decoded bits, is also investigated, and their analysis reveal that the performance of MC detection based on number of bound receptors severely decreases when the receptors get saturated, which occurs when they are exposed to a high concentration of ligands as a result of strong ISI. This is because near saturation, it becomes harder for the receiver to discriminate between two levels of number of bound receptors corresponding to different bits. Detection based on Continuous History of Receptor States: The second detection approach is based on exploiting the continuous history of binding and unbinding events occurring at receptors, or the independent samples of time intervals that the receptors stay bound and unbound, as demonstrated in Fig. 11 . As we see in the likelihood function in (18) , the unbound time intervals are informative of the total ligand concentration, whereas the bound time intervals are informative of the type of bound molecules. This is exploited in BIB035 , where the authors tackle the saturation problem in reactive receivers. For a receiver with ligand receptors and with a memory storing a finite number of previously decoded bits, they propose to exploit the amount of time the individual receptors stay unbound. Taking the ligand concentration stationary around the sampling time, and assuming steadystate conditions for the ligand-receptor binding reaction, they developed an ML detection scheme for OOK concentrationencoded signals, which outperforms the detection based on number of bound receptors in the saturation case. A simple intracellular reaction network to perform the transduction of unbound time intervals into the concentration of certain type of molecules inside the cell is also designed. In a similar manner, in BIB018 , BIB019 , using a voxel-based MC system model introduced in BIB004 , and by neglecting the ISI, the authors developed an optimal MAP demodulator scheme based on the continuous history of receptor binding events. Different from BIB035 , the authors assume time-varying input signal. The resulting demodulator is an analog filter, which requires the biochemical implementation of mathematical operations, such as logarithm, multiplication, and integration. The demodulator also needs to count the number of binding events. In BIB018 , they provide an extension of the demodulator for the ISI case by incorporating a decision feedback, and show the performance improvement with increasing receiver memory. One of the challenges of reactive receivers is their selectivity towards the messenger molecules, which is not perfect in practice. It is highly probable, especially in physiologically relevant environments, that there are similar ligands in the channel, which can also bind the same receptors, even though their unbinding rate is higher than that of the correct, i.e., messenger, ligands. This causes a molecular interference, which impedes the detection performance of the receiver especially when the concentration of interferer molecules is not known to the receiver. In BIB037 , the authors evaluate the performance of the one-shot ML detection schemes based on number of bound receptors and unbound time intervals in the presence of interference from a similar ligand available in the environment, number of which in the reception space follows Poisson distribution, with a known mean. They proposed a new ML detection scheme based on estimating the ratio of messenger ligands to the inferring ligands using the bound time intervals sampled from each receptor. It is shown that the proposed method substantially outperforms the others, especially when the concentration of interferer molecules is very high. Note that the above detection techniques are built on MC models that neglect the receiver geometry by treating it as a transparent receiver, inside which ligands and receptors are homogeneously distributed, and they require the receiver to store an internal model, i.e., CIR, of the reaction-diffusion channel. Detection for Biosensor-based MC Receivers: The third set of detection methods deal with the biosensor-based receivers, where the binding events are transduced into electrical signals. In bioFET-based receivers the concentration of bound charge-carrying ligands are converted into electrical signals that are contaminated with additional noise. It is not possible to observe individual receptors states; therefore, the detection based on continuous history of binding events is not applicable for these receivers. Accounting for the 1/f noise and binding fluctuations at steady-state conditions, in BIB017 , authors develop an optimal ML detection scheme for CSK in the absence of ISI. Approximating the binding and 1/f noise with a Gaussian distribution, they reduce the overall problem to a fixed-threshold detection problem and provide closedform analytical expressions for the optimal thresholds and corresponding symbol error rates. The performance evaluation reveals that the 1/f noise, which is resulting from the defects of the semiconductor FET channel, surpasses binding noise resulting from the fluctuations of the receptor states, especially at low frequencies, and severely degrades the detection performance.