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.
Abstract Molecular communication networks consist of transmitters and receivers distributed in a fluid medium. The communication in these networks is realised by the transmitters emitting signalling molecules, which are diffused in the medium to reach the receivers. This paper investigates the properties of noise, or the variance of the receiver output, in molecular communication networks. The noise in these networks come from multiple sources: stochastic emission of signalling molecules by the transmitters, diffusion in the fluid medium and stochastic reaction kinetics at the receivers. We model these stochastic fluctuations by using an extension of the master equation. We show that, under certain conditions, the receiver outputs of linear molecular communication networks are Poisson distributed. The derivation also shows that noise in these networks is a nonlinear function of the network parameters and is non-additive. Numerical examples are provided to illustrate the properties of this type of Poisson channels. Molecular communication networks can be used to realise communication between nanoscale devices. In a molecular communication network, transmitters and receivers communicate by using signalling molecules. At the receivers, the signalling molecules react, via a chain of chemical reactions, to produce output molecules. The counts of output molecules over time is the output signal of the receiver. The output signal is noisy due to the stochastic nature of diffusion and chemical reactions. This paper aims to characterise the properties of the output signal. We do this by modelling the transmission medium, transmitter and receiver. In order to simplify the analysis, we model the transmitter as a sequence which specifies the number of molecules emitted by the transmitter over time. This paper considers two receiver reaction mechanisms, reversible conversion and linear catalytic, which can be used to approximate, respectively, ligand-receptor binding and enzymatic reactions. These two mechanisms are chosen because, if we consider them on their own (i.e. without the transmitter and diffusion), the ordinary differential equations describing the mean behaviour of these two reaction mechanisms have the same form; however, if we consider the end-to-end behaviour from the transmitter signal to the mean variance of the number of output molecules, then these two receiver reaction mechanisms have very different behaviours. We show this by deriving analytical expressions for the mean, variance and frequency properties of the number of output molecules of these two receiver reaction mechanisms. In addition, for reversible conversion, we are able to derive the exact probability distribution of the number of output molecules. Our model allows us to study the impact of design parameters on the communication performance. For example, we assume that our receiver is enclosed by a membrane and we study the impact of the diffusibility of molecules across this membrane on the communication performance. 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. 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.