Ionospheric heating by high-power high-frequency (HF) waves has been widely recognized as a powerful tool to modify the ionosphere (P. Bernhardt et al., 2010). Such modifications have practical applications in the radio-communications and the regulation of high energy electrons to protect spacecraft in geospace. On the other hand, interactions between the injected electromagnetic (EM) waves and the ionosphere can effectively turn the ionosphere into a plasma laboratory without walls, to explore fundamental physical processes of plasma in the near-Earth space environment. Therefore, since the 1970s, the heating experiments by ground-based powerful HF facilities sprang up all over the world, such as the Arecibo, EISCAT, SUDA and HAARP (Gordon & Carlson, 1974;Rietveld et al., 2000). Numerous scientific observations have been obtained with these facilities, along with theoretical explanations which have been commonly accepted (Rietveld et al., 2016;Streltsov et al., 2018).The parametric decay instability (PDI) is one of the most fundamental and predominant physical processes generated in the ionospheric heating experiment, which can convert the ground-transmitted incident pump wave into another high-frequency-wave mode (EM or electrostatic wave) and a low-frequency-wave mode (Fejer, 1979;Gurevich, 2007;Robinson, 1989;Wang et al., 2016). As consequences of energy and momentum conservation, these waves must allow frequency and wavenumber matching relations, that is, f H ± f L = f pump , k H ± k L = k pump , where the subscripts H, L, and pump refer to the high-frequency-wave mode, the simultaneous low-frequency-wave mode, and the incident pump wave, respectively. f is the