  We evaluate the effect of half-wave plate (HWP) imperfections inducing
intensity leakage to the measurement of Cosmic Microwave Background (CMB)
$B$-mode polarization signal with future satellite missions focusing on the
tensor-to-scalar ratio $r$. The HWP is modeled with the Mueller formalism, and
coefficients are decomposed for any incident angle into harmonics of the HWP
rotation frequency due to azimuthal angle dependence. Although we use a general
formalism, band-averaged matrix coefficients are calculated as an example for a
9-layer sapphire HWP using EM propagation simulations. We perform simulations
of multi-detector observations in a band centered at 140\,GHz using \LB
instrumental configuration. We show both theoretically and with the simulations
that most of the artefacts on Stokes parameter maps are produced by the dipole
leakage on $B$-modes induced by the fourth harmonics $M^{(4f)}_{QI}$ and
$M^{(4f)}_{UI}$. The resulting effect is strongly linked to the spin-2 focal
plane scanning cross linking parameters. We develop a maximum likelihood-based
method to correct the IP leakage by joint fitting of the Mueller matrix
coefficients as well as the Stokes parameter maps. % by modifying the standard
map-making procedure. We show that the residual leakage after correction leads
to an additional noise limited uncertainty on $r$ of the order of $10^{-7}$,
independently of the value of the Mueller matrix coefficients. We discuss the
impact of the monopole signal and the potential coupling with other systematic
effects such as gain variations and detector nonlinearities.
