Using the matrix pencil method to analyze a 3D leaky wave antenna

A leaky-wave antenna (LWA) is a traveling wave antenna that uses a fast wave as the main radiating mechanism, which radiates continuously along the structure. Depending on the length of the antenna, the fast wave may get reflected from the termination, which causes another beam in the opposite direction. The effects of the reflected fast wave on the radiation pattern can be analyzed if the reflection coefficient at the termination is known. To calculate the reflection coefficient, we need to know the complex propagation constant and complex wave amplitudes. Furthermore, if the fast wave's complex propagation constant is already known, then the reflection coefficient at the termination can be used to obtain the radiation pattern. The complex propagation constants associated with the fast waves are extracted from a full-wave field solution by using the matrix pencil method (MPM). Then, the least-squares method is used to obtain the complex amplitude coefficients. The accuracy of this approach is verified by using the MPM extracted components to reconstruct the original pattern.