case.

In addition to the foreground removal, the cross correlation with other observable can mitigate the contamination from the foregrounds. For instance, the distribution of Lyman-$\alpha$ emitter correlates with the 21cm line signal [e.g. @2009ApJ...690..252L; @2017ApJ...836..176H] but not with the foregrounds. Thus, the foregrounds contribute to the observation as a source of error and can be statistically reduced. Although the foreground removal is required to mitigate the error [@2017arXiv170904168Y], many works show that the MWA and the SKA1\_LOW have potential to detect the 21cm-LAE cross power spectrum [@Kubota].

Furthermore, the cross correlation between the 21cm line signal and the CMB is also a useful observable. During the EoR, the peculiar motion of ionized bubbles generates the Doppler anisotropy to the scattered CMB photons. Because the 21cm line signal distribution reflects the topology of ionized bubbles, the Doppler anisotropy and the 21cm line signal have correlation at large scales ($l=100$). According to the analytic formulae, the expected 21cm-CMB signal consists of homogeneous part which is negative and in-homogeneous part which is positive. [Furthermore, the CMB includes other kSZ fluctuations such as the Ostriker-Vishniac effect [@1986ApJ...306L..51O] and patchy components (e.g. [@2016ApJ...824..118A].) The angular power spectrum of the fluctuations has peaks at $l>300$, 