The perturbation of the lower hybrid wave (LH) power spectrum by fluctuations of the plasma in the vicinity of the antenna is investigated by solving the full wave equation in a slab geometry using COMSOL Multiphysics®. The numerical model whose generality allows to study the effect of various types of fluctuations, including those with short characteristic wavelengths is validated against a coupling code in quiescent regimes. When electron density fluctuations along the toroidal direction are incorporated in the dielectric tensor over a thin perturbed layer in front of the grill, the power spectrum may be strongly modified from the antenna mouth to the plasma separatrix as the LH wave propagates. The diffraction effect by density fluctuations leads to the appearance of multiple satellite lobes with randomly varying positions and the averaged perturbation is found to be maximum for the Fourier components of the fluctuating spectrum in the vicinity of the launched LH wavelength. This highlights that fast toroidal inhomogeneities with short characteristics length scales in front of the grill may change significantly the initial LH power spectrum used in coupled ray-tracing and Fokker–Planck calculations.