Systems and methods for correcting beam weighting factors for a radio system include obtaining measurements of cross-polarization transfer functions between respective pairs of dual-polarized antenna elements in the antenna system and computing coupling values for the respective pairs and reflection coefficient values by numerically solving a system of equations in which a subset of the coupling values are set to zero and the measurements of the cross-polarization transfer functions of the respective pairs are a function of the coupling values for the respective pairs of the dual-polarized antenna elements and the reflection coefficient values. Correction factors are computed for the antenna elements based on the computed coupling values and reflection coefficients. Based on the respective correction factors, beam weighting factors are calculated for at least some of the antenna elements for a desired beam direction.