  We investigate features of the lateral distribution function (LDF) of the
radio signal emitted by cosmic ray air-showers with primary energies $>
0.1$~EeV and its connection to air-shower parameters such as energy and shower
maximum using CoREAS simulations made for the configuration of the Tunka-Rex
antenna array. Taking into account all significant contributions to the total
radio emission, such as by the geomagnetic effect, the charge excess, and the
atmospheric refraction we parameterize the radio LDF. This parameterization is
two-dimensional and has several free parameters. The large number of free
parameters is not suitable for experiments of sparse arrays operating at low
SNR (signal-to-noise ratios). Thus, exploiting symmetries, we decrease the
number of free parameters and reduce the LDF to a simple one-dimensional
function. The remaining parameters can be fit with a small number of points,
i.e. as few as the signal from three antennas above detection threshold.
Finally, we present a method for the reconstruction of air-shower parameters,
in particular, energy and $X_{\mathrm{max}}$ (shower maximum), which can be
reached with a theoretical accuracy of better than 15\% and 30~g/cm$^2$,
respectively.
