The parametric decay of lower hybrid (LH) pump waves is studied in a wide range of low frequency quasi-modes which drive the instabilities. The numerical results of the parametric dispersion relation show that an ion sound quasi-mode with frequency ωIR can excite a parametric instability with a growth rate γ ≥ ωIR or ωIR ≪ ωci at the plasma edge, even at low power levels of the pump wave. In this condition, solutions can be found where the two LH sidebands are resonant within a small frequency shift which is comparable to the growth rate, and also the upper sideband contributes to the instability. The estimated convective thresholds are in the range of the radiofrequency (RF) power used for heating experiments of tokamak plasmas. The parametric instability is related to the frequency broadening of the injected RF power observed during experiments with additional LH heating in FT and in other devices. In the range ωIR ≈ ℓωci the analysis shows that in the outer plasma region ion cyclotron quasi-modes can drive parametric instabilities with higher growth rates for ℓ ≃ 8-10 if a wave number broadening of the launched parallel wave is assumed. This kind of instability may explain the RF spectra observed in high density plasma regimes, which show a typical non-monotonic envelope of the sideband peaks.