In the present paper, the perturbation of the launched power spectrum of the Lower Hybrid wave at the separatrix by electron density fluctuations in the scrape-off layer is investigated. Considering a slab geometry with magnetic field lines parallel to the toroidal direction, the full wave equation is solved using Comsol Multiphysics r for a fully active multi-junction like LH antenna made of two modules. When electron density fluctuations are incorporated in the dielectric tensor over a thin perturbed layer in front of the grill, it is shown that the power spectrum may be strongly modified from the antenna mouth to the plasma separatrix as the wave propagates. The diffraction effect leads to the appearance of multiple satellite lobes with randomly varying positions, a feature consistent with the recently developed model that has been applied successfully to high density discharges on the Tokamak Tore Supra corresponding to the large spectral gap regime [Decker J. et al. Phys. Plasma 21 (2014) 092504]. The perturbation is found to be maximum for the Fourier components of the fluctuating spectrum in the vicinity of the launched LH wavelength.