Synthesis of Angle Arrays by the NDF of the Radiation Integral

Linear arrays have been well studied for their widespread applications, but they suffer from severe limitations in the scanning capabilities due to the inherent main beam spreading. The combination of two linear arrays, radiating simultaneously, may provide the coverage of a wide angular domain by identical beams. More in general, first, we consider the radiation properties of a collection of continuous linear sources by following an inverse source approach which aims at investigating the spectral decomposition of the relevant radiation operator by discussing its singular value decomposition and the number of degrees of freedom of the source according to its geometry. Then, a connection with the known closed-form results of the single line case is established. Next, for an angle geometry, the discussion of the point spread function reveals the condition to be achieved for an angle source to radiate identical beams with a coverage larger than the one of a single linear source with the same total length. Finally, we consider the power synthesis of identical focusing beams by linear arrays, arranged in an angle geometry, also including the effect of the element factor, without excitation constraints, so to show how possibly to drive the design of electrically large arrays by such an analytical approach.