A method for obtaining gain compensated electromagnetic logging while drilling propagation measurements includes rotating an electromagnetic logging while drilling tool in a subterranean wellbore. The tool includes a plurality of transmitter antennas and a plurality of receiver antennas symmetrically spaced along a logging while drilling tool body with the transmitter antennas including at least one axial transmitter antenna and at least one transverse transmitter antenna and the receiver antennas including at least one axial receiver antenna and at least one transverse receiver antenna. Electromagnetic voltage measurements are acquired from the receiver antennas while rotating. The acquired voltage measurements are processed to compute harmonic voltage coefficients. Ratios of selected ones of the harmonic voltage coefficients are in turn processed to compute gain compensated quantities including symmetrized and anti-symmetrized quantities.