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In this paper, we obtain the NIRB and SBGWs from the early stars, which areconstrained by the observation of reionization and star formation rate. Westudy the transition from Pop III to Pop II stars via the star formation modelof different population, which takes into account the reionization and themetal enrichment evolution. We calculate the two main metal pollution channelsarising from the supernova-driven protogalactic outflows and "genetic channel".We obtain the SFRs of Pop III and Pop II and their NIRB and SBGWs radiation. Wepredict that the upper limit of metallicity in metal-enriched IGM (the galaxieswhose polluted via "genetic channel") reaches $Z_{\rm crit}=10^{-3.5}Z_{\odot}$at $z\sim13$ ($z\sim11$), which is consistent with our star formation model. Weconstrain on the SFR of Pop III stars from the observation of reionization. Thepeak intensity of NIRB is about $0.03-0.2~nW m^{-2}{sr}^{-1}$ at $\sim 1 \mu m$for $z>6$. The prediction of NIRB signal is consistent with the metallicityevolution. We also obtain the gravitational wave background from the blackholes formed by these early stars. The predicted gravitational wave backgroundhas a peak amplitude of $\Omega_{GW}\simeq8\times10^{-9}$ at $\nu=158$ Hz forPop II star remnants. However, the background generated by Pop III.2 stars ismuch less than Pop II stars, with a peak amplitude of$\Omega_{GW}\simeq1.2\times10^{-11}$ at $\nu=28~Hz$. The background of PopIII.1 shifts to lower frequencies, and the amplitude of $\Omega _{GW}$ for PopIII.1 stars shows a minimum value at $\nu\simeq 10$ Hz, due to the lack ofgravitational wave signals from the stars with$140~M_{\odot}<M_\ast<260~M_{\odot}$.

The near-infrared radiation background, gravitational wave background and star formation rate of Pop III and Pop II during cosmic reionization