Astronomical images obtained on large ground based telescopes are blurred due to the effect of the atmospheric turbulence but this can be compensated by means of adaptive optics. A knowledge of the vertical profile of the turbulence might help to optimize the adaptive optics control system, especially when an attempt is made to correct over a wide field of view (MCAO). We present the development of a remote sensing technique called Single-Star SCIDAR (SSS) system for characterizing atmospheric parameters, such as the refractive-index structure function constant Cn2(h), using single star targets. The technique is based on the analysis of stellar scintillation produced by the passage of the light through the atmospheric turbulence. The instrument is intended to be used in generalized mode, i.e. with several measurement planes. The autocorrelation of scintillation images, taken at several measurement planes with a short exposure time using a 25cm diameter telescope, allows us to characterize atmospheric parameters for wide-ranging area in the sky. Computational simulations of a wave propagating through atmospheric turbulence are made using a Kolmogorov model. Retrieving the refractive-index fluctuation profile of the turbulence at different heights from single stars is challenging, contrary to the triangulation inherent to the binary star SCIDAR technique. The problem is an ill-posed one, made easier to solve by the use of multiple conjugated altitudes. A least square method solution with a Tikhonov regularization is used for the resolution. Methods to enforce non-negativity, reflecting the physical property of the quantity, are investigated.