Contents I. Introduction
Beamforming generally refers to a signal processing technique, which is used most commonly for directional transmission and reception of signal. During transmission, to change the directionality of array, the beamforming network controls the amplitude and phase at each port of transmitter in order to generate a constructive or destructive wavefront. The beamforming networks [1] are currently used in many applications as it has many advantages as boosting the channel capacity and rise in the spectrum range. There are three main topologies of the beamforming network which are parallel-feed, series-feed and matrix-feed. Among that matrix fed is efficient as it requires the smaller number of elements when compared to remaining two mentioned feeding networks [2]. Butler matrix [3]–[6] has been realized later, it contains Hybrid couplers, Phase shifters and crossovers, this design is complex as crossovers are present in the circuit, later Blass matrix [7] is designed with elements such as Phase shifters, Hybrid couplers and load terminations, insertion loss is low in this when compared to the Butler matrix because of its design, some of the signal splits into the termination loads resulting in low radiation efficiency. Nolen matrix [8] is then designed to overcome the limitations of the Butler and Blass matrices. It consists of Hybrid couplers and arbitrary phase shifters and is designed by slicing the half of the Blass matrix along the diagonal. It resolves the power loss issue and reduces the components by more than half.
