Channel Estimation for Diffusive Molecular Communications

TLDR

In molecular communication, the channel impulse response describes the expected molecule count at the receiver over time after a transmitter release, and knowledge of this response is essential for designing detection and equalization schemes. The paper proposes a training‑based framework to estimate the channel impulse response in molecular communication by observing receiver molecule counts from known emission sequences, and designs optimal and suboptimal training sequences. The authors derive maximum likelihood, least‑squares, maximum a posteriori, and linear minimum mean‑square‑error estimators for CIR, along with classical and Bayesian Cramér‑Rao bounds, covering both cases with and without prior statistical channel knowledge. Simulations validate the proposed estimators and demonstrate their performance approaching the corresponding Cramér‑Rao bounds.

Abstract

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