Correlation functions of CMB anisotropy and polarization

We give a full analysis of the auto- and cross-correlations between the Sto kes parameters of the cosmic microwave background. In particular, we derive the windowing function for an antenna with Gaussian response in polarizati on experiment, and construct correlation function estimators corrected for instrumental noise. They are applied to calculate the signal to noise ratio s for future anisotropy and polarization measurements. While the small-angu lar-scale anisotropy-polarization correlation would be likely detected by t he MAP satellite, the detection of electric and magnetic polarization would require higher experimental sensitivity. For large-angular-scale measureme nts such as the being planned SPOrt/ISS, the expected signal to noise ratio for polarization is greater than one only for reionized models with high r eionization redshifts, and the ratio is less for anisotropy-polarization co rrelation. Correlation and covariance matrices for likelihood analyses of g round-based and satellite data are also given.