A DFT-based UTD ray analysis of large finite phased arrays on a grounded substrate

A discrete Fourier transform (DFT)-based asymptotic high-frequency, uniform geometrical theory of diffraction (UTD) ray solution is developed to describe, in closed form, the collective field produced by large finite phased arrays of printed antenna elements on a grounded material substrate. Such a DFT-UTD ray analysis yields useful physical insights into the large array radiation and scattering mechanisms. This is in contrast to the conventional array element-by-element summation for the radiated field which lacks the above useful properties. In the present work, any realistic arbitrary array current distribution, i.e., in the presence of array mutual coupling, is represented by a DFT expansion so that each term in the expansion becomes a simple uniform array distribution with a linear phase, which then directly facilitates the development of the asymptotic UTD ray solution. Furthermore, another significant advantage of the DFT is that for most practical array excitations, only a relatively few DFT terms remain dominant in the expansion and are sufficient to provide reasonably accurate results. Some numerical examples are presented to illustrate the utility of this collective DFT-based asymptotic UTD ray solution for large array fields.