A method for making downhole electromagnetic logging while drilling measurements includes rotating an electromagnetic logging while drilling tool in a subterranean wellbore. The logging tool includes a plurality of transmitter antennas and a plurality of receiver antennas symmetrically spaced along a logging while drilling tool body, the plurality of transmitter antennas including at least one axial transmitter antenna and at least one transverse transmitter antenna. The plurality of receiver antennas includes at least one axial receiver antenna and at least one transverse receiver antenna. The receiver antennas are used to acquire electromagnetic voltage measurements while rotating. The voltage measurements are processed to compute harmonic voltage coefficients, selected ratios of which are processed to compute gain compensated symmetrized and anti-symmetrized quantities and angles. These quantities may optionally be further processed to compute rotated gain compensated symmetrized and anti-symmetrized quantities.