  We study the effect of multiple soft gluon radiation on the kinematical
distributions of the $t$-channel single top quark production at the LHC. By
applying the transverse momentum dependent factorization formalism, large
logarithms (of the ratio of large invariant mass $Q$ and small total transverse
momentum $q_\perp$ of the single-top plus one-jet final state system) are
resummed to all orders in the expansion of the strong interaction coupling at
the accuracy of next-to-leading logarithm, including the complete
next-to-leading order corrections. We show that the main difference from PYTHIA
prediction lies on the inclusion of the exact color coherence effect between
the initial and final states in our resummation calculation, which becomes more
important when the final state jet is required to be in the forward region. We
further propose a new experimental observable $\phi^*$ to test the effect of
multiple gluon radiation in the single-top events. The effect of bottom quark
mass is also discussed.
