  This paper presents a stochastic analysis of the time-variant channel impulse
response (CIR) of a three dimensional diffusive mobile molecular communication
(MC) system where the transmitter, the absorbing receiver, and the molecules
can freely diffuse. In our analysis, we derive the mean, variance, probability
density function (PDF), and cumulative distribution function (CDF) of the CIR.
We also derive the PDF and CDF of the probability p that a released molecule is
absorbed at the receiver during a given time period. The obtained analytical
results are employed for the design of drug delivery and MC systems with
imperfect channel state information. For the first application, we exploit the
mean and variance of the CIR to optimize a controlled-release drug delivery
system employing a mobile drug carrier. We evaluate the performance of the
proposed release design based on the PDF and CDF of the CIR. We demonstrate
significant savings in the amount of released drugs compared to a
constant-release scheme and reveal the necessity of accounting for the
drug-carrier's mobility to ensure reliable drug delivery. For the second
application, we exploit the PDF of the distance between the mobile transceivers
and the CDF of p to optimize three design parameters of an MC system employing
on-off keying modulation and threshold detection. Specifically, we optimize the
detection threshold at the receiver, the release profile at the transmitter,
and the time duration of a bit frame. We show that the proposed optimal designs
can significantly improve the system performance in terms of the bit error rate
and the efficiency of molecule usage.
