Recently the fine experimental data on the behavior of the ela stic scattering cross-section in the region of diffraction peak and first diffraction minimum was obtained by TOTEM experiment for 7 and 8 TeV pp collisions at LHC [1, 2]. The first restrictions on pp scattering amplitude imposed by this data were discussed in [3, 4]. In this work we present the systematic analysis of the problem in the framework of the dipole model [5] and quasi-eikonal Regge approach [6] taking into account the unitarity condition for the amplitude. We show that to resto re the real and imaginary parts of the pp scattering amplitude in the region of the first diffraction minimum we need also the information on the elastic scattering cross-section in vicinity of the second minimum. So we model the behavior of the elastic scattering cross-section in wide range of momentum transfer at various initial energies, using the impact parameter profile function as a starting point. We discuss which further restrictions on the elastic pp-sc