Method of Synthesizing Orthogonal Beam-Forming Networks Using QR Decomposition

A synthesis method for orthogonal beam-forming networks (BFNs) with arbitrary N inputs and N outputs is presented. Compared to those formerly developed, the new method allows the design of a BFN in order to not only generate arbitrary N orthogonal beams and N inputs but also to make the 180° hybrids less. This skill is obtained by means of a new approach to decompose the matrices
$Q_{1}$
and
$Q_{2}$
which are mentioned by Sodin. The solution of such a design problem can be carried out by applying
$QR$
decomposition based on Givens transformations. Such a design method also takes into account the computer programming realization. Numerical results are obtained through the commercial simulator to prove the correctness of the method. The ease, accuracy, and efficiency of this synthesis method for the design of BFN make it very useful in modern applications of multi-beam antenna arrays.