S.P. Skobelev

The concept of orthogonal beams in the antenna theory is associated with the design of multiple beam antennas for applications in communications, radar, and radio astronomy. The forming of orthogonal beams in the indicated antennas corresponds to achieving 100% efficiency of the antenna channels, and therefore it is of great interest. Numerous publications concerning the forming of orthogonal beams demonstrate significant progress in this area. However, the author of the present work never met any description of a general systematic approach which would allow one to determine optimum geometric parameters of planar array antennas using a specified number (arbitrary in general case) of orthogonal beams and their specified directions in space. Development of such an approach is the purpose of the present work. The problem is considered in the assumption that the array aperture is arranged in the plane z=0 of a rectangular Cartesian coordinate system 0xyz, while the directions of the beams arranged in a desired configuration are specified by the appropriate nodes of a regular lattice (beam lattice) in the space of direction cosines determined in the ordinary way by the angles measured from the z and x axes. The first step in the determination of the array aperture parameters is construction of a lattice in the plane z=0 reciprocal with respect to the beam lattice. The array aperture area is then determined as the area of a cell allotted to one node of this reciprocal lattice. The aperture shape may in principle be arbitrary. The second step is a selection of a sparse regular lattice in the beam lattice. The periods of the sparse lattice should be large enough to exclude overlapping of the specified beam configuration in the process of distributing it over the nodes of this new lattice. At the third step, using the sparse lattice, we construct, in the aperture plane, a lattice reciprocal with respect to the sparse one. The nodes of this new reciprocal lattice are just used for arrangement of the array elements. It is proven that the complex amplitude distributions over the elements of the arrays designed according to the approach described above, corresponding to forming of the specified beams are orthogonal to each other. It is also shown that the beams themselves will also be orthogonal if the array element patterns are orthogonal. The consequence of the indicated proofs is the orthogonality of the array factors corresponding to the specified beams on a cell allotted to one node of the sparse lattice in the direction cosine space. The issue of the number of the array elements which is necessary for forming of the specified number of orthogonal beams is discussed. A few demonstrative examples of the beam configurations for which the number of the array elements is equal to the number of the beams together with the corresponding array configurations are presented and discussed.