I. Introduction
With the rapid development of wireless communication technologies, the demand for an enhanced spectrum efficiency increases. The switched beam antenna array has received much attention in the past decades because of its ability in reducing multipath fading and co-channel interference. Rotman lens [1], Nolen matrix [2], Blass matrix [3], and Butler matrix [4] are well-known beamforming networks. However, the Rotman lens is usually employed in radar systems due to its bulky size, while the Nolen matrix and the Blass matrix require more basic elements resulting in a complex structure and also bulky size. Therefore, the Butler matrix becomes one of the best candidates for the implementation of a beamforming network.