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In the paper, an X-ray spectroscopy-based approach on laser pulse temporal profile characterization is described. The structure of dielectronic satellites to H-like Ly&alpha, lines strongly depends on a plasma electron density, so it can be applied for diagnostics. These spectral lines are mainly emitted during initial stage of laser plasma expansion. It means that plasma parameters obtained via them characterizes matter conditions in a region surrounding a spot of laser-matter interaction. In the case when a laser contrast is high enough, the radiation interacts with cold matter, which had not been preliminary perturbed by a laser prepulse, and the satellites structure shape corresponding to high densities should be observed. It allows us to consider the satellites as a diagnostic tool for the laser temporal profile quality. In the paper dependencies of the dielectronic satellites structure on electron densities obtained from detailed kinetic calculations in the wide range of plasma parameter for different elements are under discussion. Fundamental theoretical aspects of plasma diagnostic based on the feature of satellite structures shape in hot dense plasma, which led to development of the proposed method, are also explained.