  Temperature and magnetic field dependences of the conductivity in heavily
doped, strongly disordered two-dimensional quantum well structures
GaAs/In$_x$Ga$_{1-x}$As/GaAs are investigated within wide conductivity and
temperature ranges. Role of the interference in the electron transport is
studied in the regimes when the phase breaking length $L_\phi$ crosses over the
localization length $\xi\sim l\exp{(\pi k_Fl/2)}$ with lowering temperature,
where $k_F$ and $l$ are the Fermi quasimomentum and mean free path,
respectively. It has been shown that all the experimental data can be
understood within framework of simple model of the conductivity over
delocalized states. This model differs from the conventional model of the weak
localization developed for $k_Fl\gg 1$ and $L_\phi\ll\xi$ by one point: the
value of the quantum interference contribution to the conductivity is
restricted not only by the phase breaking length $L_\phi$ but by the
localization length $\xi$ as well. We show that just the quantity
$(\tau_\phi^\ast)^{-1}=\tau_\phi^{-1}+\tau_\xi^{-1}$ rather than
$\tau_\phi^{-1}$, where $\tau_\phi\propto T^{-1}$ is the dephasing time and
$\tau_\xi\sim\tau\exp(\pi k_F l)$, is responsible for the temperature and
magnetic field dependences of the conductivity over the wide range of
temperature and disorder strength down to the conductivity of order $10^{-2}
e^2/h$.
