I. Introduction
Multibeam antenna arrays with passive beamforming networks (BFNs) have emerged as promising solutions for the evolving 5G wireless applications, due to their low-cost beam scanning capability [1], [2]. According to the principle of operation, the passive BFNs can be realized through three main categories: lens-based [3], reflector-based [4], and beamforming circuit-based arrays [5]. Although lens- and reflector-based arrays offer wide operating bandwidths due to their frequency-independent quasi-optical performance, their bulky volume limits their practicality to some extent [6]. On the other hand, beamforming circuit-based arrays, which rely on passive components with specific topologies, offer a more compact size. Among various beamforming circuits, the Blass matrix [7], Nolen matrix [8], and the Butler matrix [9] are widely recognized and developed in recent years. Compared with the lossy Blass matrix and asymmetry Nolen matrix, Butler matrices have garnered significant attention due to their lossless and symmetry topology, as well as excellent port isolation [10], [11], [12]. Typically, a Butler matrix is composed of hybrid couplers, crossovers, and phase shifters. In practical applications, additional bandpass filters are often employed to eliminate interference as well [13]. To achieve miniaturization and mitigate cascaded losses between filters and BFNs, the integration of frequency-selective characteristics into Butler matrices has become an area of active research [14].