  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. In particular, we derive maximum likelihood (ML)
and least sum of square errors (LSSE) estimators. We also study the Cramer Rao
(CR) lower bound and training sequence design for the considered system.
Simulation results confirm the analysis and compare the performance of the
proposed estimation techniques with the CR lower bound.
