Determination of the Number of Valid Scan Pairs in a Multielement Waveguide Simulator

The multielement waveguide simulator is an experimental technique that enables computation of the active reflection coefficient for elements in a large array phased to a certain scan angle pair $(\theta ,\phi )$. This paper shows that the number of scan pairs is equal to the number of modes that are excitable in the waveguide simulator. The problem of solving for the number of valid scan pairs is seen to be a variant of the Gauss Circle Problem with those modes which cannot be excited removed. A 4×3 waveguide simulator is used as a case study to illustrate the design of a simulator and physics behind the inability to excite certain modes.