Lossy Beam Generation of Circular Arrays

This work examines the characteristic modes and measurement of various circularly distributed array topologies in which element radiators are used independently to deliver both sum and difference beams under lossy conditions. An associated moment generating function is derived, such that analytical patterns use even-odd symmetries for sum difference beam behavior. This approach generalizes the Fourier probabilistic methods by using the Laplace transform to analyze statistical averages catering to the degenerating effects of pattern behavior that is influenced by the environment.