Disclosed herein are electromagnetic resistivity logging systems and methods that employ an antenna configuration having at most two transmitter or receiver antenna orientations that rotate relative to the borehole. The measurements made by this reduced-complexity antenna configuration enable the determination of at least seven components of a coupling matrix, which may be determined using a linear system of equations that express the azimuthal dependence of the measurements. For increased reliability, measurement averaging may be performed in azimuthally spaced bins. The coupling matrix components can then be used as the basis for determining logs of various formation parameters, including vertical resistivity and anisotropy.