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We present two novel methods for the estimation of the angular power spectrumof cosmic microwave background (CMB) anisotropies. We assume an absolute CMBexperiment with arbitrary asymmetric beams and arbitrary sky coverage. Themethods differ from earlier ones in that the power spectrum is estimateddirectly from time-ordered data, without first compressing the data into a skymap, and they take into account the effect of asymmetric beams. In particular,they correct the beam-induced leakage from temperature to polarization. Themethods are applicable to a case where part of the sky has been masked out toremove foreground contamination, leaving a pure CMB signal, but incomplete skycoverage. The first method (DQML) is derived as the optimal quadraticestimator, which simultaneously yields an unbiased spectrum estimate andminimizes its variance. We successfully apply it to multipoles up to$\ell$=200. The second method is derived as a weak-signal approximation fromthe first one. It yields an unbiased estimate for the full multipole range, butrelaxes the requirement of minimal variance. We validate the methods withsimulations for the 70 GHz channel of {\tt Planck} surveyor, and demonstratethat we are able to correct the beam effects in the $TT$, $EE$, $BB$, and $TE$spectra up to multipole $\ell$=1500. Together the two methods cover thecomplete multipole range with no gap in between.

Application of beam deconvolution technique to power spectrum estimation for CMB measurements