  The cellular network of magnetic Induction (MI) communication holds promise
in long-distance underground environments. In the traditional MI communication,
there is no fast-fading channel since the MI channel is treated as a
quasi-static channel. However, for the vehicle (mobile) MI (VMI) communication,
the unpredictable antenna vibration brings the remarkable fast-fading. As such
fast-fading cannot be modeled by the central limit theorem, it differs
radically from other wireless fast-fading channels. Unfortunately, few studies
focus on this phenomenon. In this paper, using a novel space modeling based on
the electromagnetic field theorem, we propose a 3-dimension model of the VMI
antenna vibration. By proposing ``conjugate pseudo-piecewise functions'' and
boundary $p(x)$ distribution, we derive the cumulative distribution function
(CDF), probability density function (PDF) and the expectation of the VMI
fast-fading channel. We also theoretically analyze the effects of the VMI
fast-fading on the network throughput, including the VMI outage probability
which can be ignored in the traditional MI channel study. We draw several
intriguing conclusions different from those in wireless fast-fading studies.
For instance, the fast-fading brings more uniformly distributed channel
coefficients. Finally, we propose the power control algorithm using the
non-cooperative game and multiagent Q-learning methods to optimize the
throughput of the cellular VMI network. Simulations validate the derivation and
the proposed algorithm.
