Extension of the Kennaugh null theory

In radar polarimetry, Kennaugh (1952) first introduced the concept of the characteristic polarization states. This paper introduced the concepts of the co-null and the co-null Abelian group for extending the Kennaugh null theory to the case of two independent polarization states. For two arbitrary targets, it is proved that there exists one pair of polarization states such that the received powers of both targets equal zero. This polarization states´ pair is called the co-null of the two targets, which can easily be obtained by solving an eigenvalue problem. Based on group theory, another concept- the co-null Abelian group is introduced for the symmetric scattering matrix case, and many important results are presented: e.g., the relations between the co-null and the co-pol/X-pol nulls, the structure of the co-null Abelian group, and the relations between the co-null Abelian group and two classes of targets: symmetric targets and H-targets. Finally, the co-null for the asymmetric scattering matrix case is studied. The concepts of the mono-co-null Abelian group and the bi-co-null Abelian group are introduced, and the relations between both groups are presented.