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The shape of the faint-end of the high-z galaxy luminosity function (LF)informs early star formation and reionization physics during the Cosmic Dawnand Epoch of Reionization. Until recently, based on the strong gravitationallensing cluster deep surveys, the Hubble Frontier Fields (HFF) has found apotential turnover in the ultraviolet (UV) LF at z$\sim$6. In this paper, weanalyze the contribution of extremely faint galaxies with the magnitude largerthan the turnover magnitude in LF to cosmic reionization. We apply themeasurement from HFF to our suppressed star formation efficiency model,including three free parameters: halo mass threshold $M_t$, curvature parameter$\beta$ and a UV conversion factor $l_{\rm UV}$. According to our fit of 68\%confidence level, the high-redshift star formation in haloes smaller than $M_t=1.82^{+2.86}_{-1.08}\times10^{10} \rm M_{\odot}$ is found to be dampened.The turnover magnitude $\rm \gtrsim -13.99-2.45$, correspondingly the halo mass$\lesssim(4.57+20.03)\times10^{9} \rm M_{\odot}$. We find that the absorptiontrough in the global 21-cm signal is sensitive to our SFE model parameters.Together with ($\beta$, $l_{\rm UV}$) = ($2.17^{+2.42}_{-1.72}$,$9.33^{+0.43}_{-0.42} \rm ~erg~yr ~s^{-1}M_{\odot}^{-1})$, the trough locatesat $\sim$ $134^{+10}_{-17}$ $\rm MHz$ with an amplitude of $\sim$$-237^{-6}_{+7}$ $\rm mK$, compared to (106\rm MHz, -212\rm mK) in the absenceof turnover. Besides, we find that the star formation of faint galaxies hasalso an impact on the 21-cm power spectra. The best fitting peak powerdecreases by $\sim4\%$ and shifts towards smaller scales from $0.88 h \rmMpc^{-1}$ to $0.91 h \rm Mpc^{-1}$. According to our calculation, such impactis distinguishable with the forthcoming Square Kilometre Array.

Impact of the turnover in the high-z galaxy luminosity function on the 21-cm signal during Cosmic Dawn and Epoch of Reionization