Orthogonality in multibeam antennas is revisited. The difference between orthogonal beamforming and zero-forced highlighted. intriguing relation orthogonality, reciprocity losses recapitulated. Different approaches on the design of networks implementation strategies are shown with various examples from antenna-research-oriented literature. use discussed communication system perspective relevant...

We are interested in the relationships between three different concepts, first and foremost is that of the phase space, by which we generally mean the Euclidean space formed from the cross product of the spatial variable with the dual frequency variable. Next, we want to associate subsets of that space with functions, the subset describing the location of the function in natural ways. And final...

1 Dot product of R The inner product or dot product of R is a function 〈 , 〉 defined by 〈u,v〉 = a1b1 + a2b2 + · · ·+ anbn for u = [a1, a2, . . . , an] , v = [b1, b2, . . . , bn] ∈ R. The inner product 〈 , 〉 satisfies the following properties: (1) Linearity: 〈au + bv,w〉 = a〈u,w〉+ b〈v,w〉. (2) Symmetric Property: 〈u,v〉 = 〈v,u〉. (3) Positive Definite Property: For any u ∈ V , 〈u,u〉 ≥ 0; and 〈u,u〉 =...

The structure of a state property system was introduced to formalize in a complete way the operational content of the Geneva-Brussels approach to the foundations of quantum mechanics [7, 8, 9], and the category of state property systems was proven to be equivalence to the category of closure spaces [9, 10]. The first axioms of standard quantum axiomatics (state determination and atomisticity) h...