“…Various types of passive RF beamforming techniques, such as Butler matrix [ 5 ], Rotman lens [ 6 , 7 ], Blass matrix [ 8 ], and Nolen matrix [ 9 , 10 ], have been reported. Of all these, the advantages of the Butler matrix make it an ideal candidate in terms of size, manufacturing costs, bandwidth, reliability, and reciprocity; therefore, it is widely used in several applications, such as Internet of Things (IoT), Wi-Fi, base stations, satellite communications, and automotive radars [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ].…”