  In this paper we study the scattering amplitudes of
$D^{0}D^{0}\pi^+$-$D^{*+}D^{0}$ coupled channels based on $K$-matrix within the
Chew-Mandelstam formalism. The $D^{0}D^{0}\pi^{+}$ invariant mass spectrum of
LHCb is fitted and the pole parameters of the $T_{cc}^+$ are extracted. The
analysis of pole behavior suggests that the $T_{cc}^+$ may originate from a
$D^{*+}D^{0}$ virtual state and is formed as a result of an interplay between
an attractive interaction between $D^0$ and $D^{*+}$ and coupling to
$D^{0}D^0\pi^+$ channel.
