Models for the self- and cross-correlation of orthogonal polarized quasi-transverse incoherent scatter returns are presented. The models are used to estimate the F region plasma densities with dual-polarization transverse-beam incoherent scatter data collected at the Jicamarca Radio Observatory using a technique introduced by Kudeki et al. <2003>. The cross-correlation model takes into account magneto-ionic propagation effects associated with quasi-transverse O- and X-modes in an inhomogeneous ionosphere. The phase of the cross-correlation provides the information to convert the measured power data into ionospheric density estimates via a least squares fitting procedure.