  The Quadratic Maximum Likelihood estimator can be used to reconstruct the
Cosmic Microwave Background (CMB) power spectra with minimal error bars. Still,
it requires an accurate estimate of the datasets noise covariance matrix in
order to be corrected for spurious bias. We describe an extension of this
method to cross-correlation, thus removing noise bias and mitigating the impact
of systematic effects, providing they are uncorrelated. This estimator is
tested on two simulation surveys at large and intermediate angular scales,
respectively corresponding to satellite and ground-based CMB experiments. The
analysis focuses on polarization maps, over a wide range of noise levels from
0.1 to 50 muK.arcmin. We show how this estimator minimizes the increase of
variance due to polarization leakage between E and B modes. We compare this
method with the pure pseudo-spectrum formalism which is computationally faster
but less optimal, especially on large angular scales.
