Channel Estimation for Diffusive Molecular Communications

In molecular communication (MC) systems, the \textit{expected} number of molecules observed at the receiver over time after the instantaneous release of molecules by the transmitter is referred to as the channel impulse response (CIR). Knowledge of the CIR is needed for the design of detection and equalization schemes. In this paper, we present a training-based CIR estimation framework for MC systems which aims at estimating the CIR based on the \textit{observed} number of molecules at the receiver due to emission of a \textit{sequence} of known numbers of molecules by the transmitter. Thereby, we distinguish two scenarios depending on whether or not statistical channel knowledge is available. In particular, we derive maximum likelihood (ML) and least sum of square errors (LSSE) estimators which do not require any knowledge of the channel statistics. For the case, when statistical channel knowledge is available, the corresponding maximum a posteriori (MAP) and linear minimum mean square error (LMMSE) estimators are provided. As performance bound, we derive the classical Cramer Rao (CR) lower bound, valid for any unbiased estimator, which does not exploit statistical channel knowledge, and the Bayesian CR lower bound, valid for any unbiased estimator, which exploits statistical channel knowledge. Finally, we propose optimal and suboptimal training sequence designs for the considered MC system. Simulation results confirm the analysis and compare the performance of the proposed estimation techniques with the respective CR lower bounds.Comment: to be appeared in IEEE Transactions on Communications. arXiv admin note: text overlap with arXiv:1510.0861

Channel Estimation for Diffusive MIMO Molecular Communications

In diffusion-based communication, as for molecular systems, the achievable data rate is very low due to the slow nature of diffusion and the existence of severe inter-symbol interference (ISI). Multiple-input multiple-output (MIMO) technique can be used to improve the data rate. Knowledge of channel impulse response (CIR) is essential for equalization and detection in MIMO systems. This paper presents a training-based CIR estimation for diffusive MIMO (D-MIMO) channels. Maximum likelihood and least-squares estimators are derived, and the training sequences are designed to minimize the corresponding Cram\'er-Rao bound. Sub-optimal estimators are compared to Cram\'er-Rao bound to validate their performance.Comment: 5 pages, 5 figures, EuCNC 201

Local convexity inspired low-complexity non-coherent signal detector for nano-scale molecular communications

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

Diffusive MIMO Molecular Communications: Channel Estimation, Equalization and Detection

In diffusion-based communication, as for molecular systems, the achievable data rate is low due to the stochastic nature of diffusion which exhibits a severe inter-symbol-interference (ISI). Multiple-Input Multiple-Output (MIMO) multiplexing improves the data rate at the expense of an inter-link interference (ILI). This paper investigates training-based channel estimation schemes for diffusive MIMO (D-MIMO) systems and corresponding equalization methods. Maximum likelihood and least-squares estimators of mean channel are derived, and the training sequence is designed to minimize the mean square error (MSE). Numerical validations in terms of MSE are compared with Cramer-Rao bound derived herein. Equalization is based on decision feedback equalizer (DFE) structure as this is effective in mitigating diffusive ISI/ILI. Zero-forcing, minimum MSE and least-squares criteria have been paired to DFE, and their performances are evaluated in terms of bit error probability. Since D-MIMO systems are severely affected by the ILI because of short transmitters inter-distance, D-MIMO time interleaving is exploited as countermeasure to mitigate the ILI with remarkable performance improvements. The feasibility of a block-type communication including training and data equalization is explored for D-MIMO, and system-level performances are numerically derived.Comment: Accepted paper at IEEE transaction on Communicatio

Bounds on Distance Estimation via Diffusive Molecular Communication

This paper studies distance estimation for diffusive molecular communication. The Cramer-Rao lower bound on the variance of the distance estimation error is derived. The lower bound is derived for a physically unbounded environment with molecule degradation and steady uniform flow. The maximum likelihood distance estimator is derived and its accuracy is shown via simulation to perform very close to the Cramer-Rao lower bound. An existing protocol is shown to be equivalent to the maximum likelihood distance estimator if only one observation is made. Simulation results also show the accuracy of existing protocols with respect to the Cramer-Rao lower bound.Comment: 7 pages, 5 figures, 1 table. Will be presented at the 2014 IEEE Global Communications Conference (GLOBECOM) in Austin, TX, USA, on December 9, 201

Diffusive Mobile Molecular Communications Over Time-Variant Channels

This letter introduces a formalism for modeling time-variant channels for diffusive molecular communication systems. In particular, we consider a fluid environment where one transmitter nano-machine and one receiver nano-machine are subjected to Brownian motion in addition to the diffusive motion of the information molecules used for communication. Due to the stochastic movements of the transmitter and receiver nano-machines, the statistics of the channel impulse response change over time. We show that the time-variant behaviour of the channel can be accurately captured by appropriately modifying the diffusion coefficient of the information molecules. Furthermore, we derive an analytical expression for evaluation of the expected error probability of a simple detector for the considered system. The accuracy of the proposed analytical expression is verified via particle-based simulation of the Brownian motion.Comment: 4 pages, 3 figures, 1 table. Accepted for publication in IEEE Communications Letters (Author's comment: Manuscript submitted Jan. 19, 2017; revised Feb. 20, 2017; accepted Feb. 22, 2017