Optimum pattern synthesis of non-uniform spherical arrays using the Euler rotation

Method of least squares is employed for synthesis of non-uniform spherical arrays using Euler rotation of coordinate axes for reduction of side-lobe levels, controllability of 3-db beam-width of main-lobe etc. It is useful for synthesis of conformal arrays, where pattern multiplication is not applicable and array synthesis is involved. This method for synthesis of spherical arrays is general that determines radius of sphere, longitude and latitude angles of elements and their current excitations (amplitudes and phases). The authors investigate several examples to demonstrate its capability. Studies on conformal arrays deal with non-uniform excitation currents, leading to complicated input networks. Therefore the authors suggest non-uniform spacing, which shows that array synthesis by variable element spacing will realise any specifications, same as non-uniform excitations. An error function is constructed for pattern synthesis, which is a function of element spacing and excitations. The authors use combination of global and local minimisation algorithms. In examples of spherical array synthesis, 2.5 and 5.5 dB reduction of side-lobe levels have been achieved in the E- and H-plane patterns, respectively, relative to the available design data. In addition, reduction of beam-width of main-beams in E- and H-planes has been obtained by 39% and 34%, respectively.