foreground APS, the CMB APS and the noise of the CMB observation. In this work, we ignore the error term of the sample variance, which should be smaller than other terms. In practice, the CMB temperature map includes the foreground residual, which can correlate with the foreground of the 21cm observation. However, the foreground contamination is sufficiently smaller than the CMB signal, and therefore we ignore this term. In addition, we consider the error propagation as described in the Appendix because we use the weighted CPS.

For the calculation, we use the 2015 CMB full mission Commander map stored in Planck Legacy Archive [^3]. The right panel of Fig. \[fig:image\] shows the CMB map associated with the EoR0 field.

Foreground removal {#S:FGRM}
==================

As shown in Eq. \[eq:error1\], the foregrounds contribute to 21cm-CMB cross power spectrum as a source of error. Since the foregrounds are a few orders of magnitude brighter than other contributions, the terms of the foreground and CMB PS dominate the total error. Thus, one has to remove the foreground from the MWA images. Although 1000 bright point sources have been subtracted from the MWA data, the diffuse emission and un-peeled sources remain in the data. In 