Comments on "The vector space formulation of the rain crosspolarization problem and its compensation"

In the above paper (ibid., vol. COM-27, pp. 502-509, Feb. 1979) L.S. Lee proposes a method to compensate for the rain-induced cross polarization in a dual-polarization zation link. This method is based on a model of Chu, in which the effect of rain on two orthogonal linear polarizations, along unit vectors is represented by a given matrix. The idea is that the medium is characterized by two orthogonal axes which are, the eigenvectorsof the matrix. If these vectors are used as a new basis, the matrix takes the diagonal form. The compensation is obtained by rotating the emitted linear polarizations of an angle, which is necessary to align them with the eigenvectors. The Lee claims that a similar compensation is applicable to the case of circular polarizations. It is here shown that the two signals are linearly polarized along the principal axes given by the eigenvectors. This means that the antenna does not radiate circular polarizations in space, but linear ones as a result of the addition in each channel of two equal and opposite circularly polarized signals. The proposed compensation actually is an elegant method to perform the rotation of the linear polarizations by first transforming them to circular polarizations, then introducing a phase shift, and finally converting them back to linear polarizations.